ab initio modelling of acid catalyzed hydrocarbon...

Faculteit Ingenieurswetenschappen

Vakgroep Chemische Proceskunde en Technische Chemie Laboratorium voor Petrochemische Techniek

Directeur: Prof. dr. ir. Guy B. Marin

Ab initio modelling of acid catalyzed hydrocarbon conversion processes

door

Eva KINT

Promotoren: Prof. dr. ir. Guy B. Marin Prof. dr. Marie-Françoise Reyniers Begeleider: Ir. Bart De Moor Scriptie ingediend tot het behalen van de academisc he graad van burgerlijk scheikundig ingenieur Academiejaar 2005-2006

Ab initio modelling of acid catalyzed hydrocarbon conversion

door Eva KINT

Scriptie ingediend tot het behalen van de academische graad van Burgerlijk Scheikundig Ingenieur

Academiejaar 2005-2006

Promotoren: Prof. dr. ir. Guy B. Marin Prof. dr. Marie-Françoise Reyniers Begeleider: Ir. Bart De Moor Universiteit Gent Faculteit Ingenieurswetenschappen Vakgroep Chemische Proceskunde en Technische Chemie Laboratorium voor Petrochemische Techniek Directeur: Prof. dr. ir. Guy B. Marin

Abstract In Chapter 1, a short introduction is given, where the justification and the objective of my master thesis are elucidated. In Chapter 2, three computational methods, which are nowadays frequently used for the study of acid catalyzed hydrocarbon conversion processes, are described: cluster calculations, periodic Denstity Functional Theory (DFT) calculations and hybrid “quantum mechanics – interatomic potential functions” (QM-Pot) calculations. In Chapter 3, cluster calculations were performed to gain insight in the structure of the physisorption and chemisorption complexes of the different butenes. The double bond isomerization reaction of 1-butene to 2-butene is also studied by means of cluster calculations. In Chapter 4, physisorption is studied for different alkenes in H-ZSM-5, H-FAU and H-MOR and for different alkanes in H-ZSM-5. In Chapter 5, it is examined how different factors affect the zeolite acidity. Therefore, the influence of the zeolite framework, the influence of the Si/Al ratio and the influence of the distance of the Al substitution to the acid site on the acid strength of the Brønsted acid site are examined calculating the deprotonation energy. Finally, in Chapter 6, the conclusions are summarised. Keywords Cluster calculations, QM-Pot, physisorption, zeolite acidity

Opleidingscommissie Scheikunde

Verklaring in verband met de toegankelijkheid van de scriptie

Ondergetekende,

afgestudeerd aan de UGent in het academiejaar 2005 – 2006 en auteur van de

scriptie met als titel:

AB INITIO MODELLING OF ACID CATALYZED HYDROCARBON CONVERSION PROCESSES

verklaart hierbij:

1. dat hij/zij geopteerd heeft voor de hierna aangestipte mogelijkheid in verband

met de consultatie van zijn/haar scriptie:

� de scriptie mag steeds ter beschikking gesteld worden van elke aanvrager

� de scriptie mag enkel ter beschikking gesteld worden met uitdrukkelijke,

schriftelijke goedkeuring van de auteur

� de scriptie mag ter beschikking gesteld worden van een aanvrager na een

wachttijd van … jaar

� de scriptie mag nooit ter beschikking gesteld worden van een aanvrager

2. dat elke gebruiker te allen tijde gehouden is aan een correcte en volledige

bronverwijzing

Gent, 16 juni 2006

FACULTEIT INGENIEURSWETENSCHAPPEN

Chemische Proceskunde en Technische Chemie Laboratorium voor Petrochemische Techniek

Directeur: Prof. Dr. Ir. Guy B. Marin

Krijgslaan 281 S5, B -9000 Gent (Belgium) tel. +32 (0)9 264 45 16 • fax +32 (0)9 264 49 99 • G SM +32 (0)475 83 91 11 •

e-mail: [email protected] http://allserv.ugent.be/tw12/

Dankwoord

Vandaag, 16 juni 2006, wordt het al eens stilletjes aan tijd om iedereen te bedanken die hetzij

rechtstreeks, hetzij onrechtstreeks heeft bijgedragen tot wat mijn thesis vandaag geworden is.

Het schrijven van dit eindwerk zou immers nooit zo vlot en aangenaam verlopen zijn zonder

de hulp en het vertrouwen van vele mensen.

In de eerste plaats wil ik graag mijn promotoren Prof. Marin en Prof. Reyniers bedanken voor

de mogelijkheid die ze me gegeven hebben om dit eindwerk te verwezenlijken en voor de

opvolging ervan gedurende het jaar.

Hierbij wil ik ook Bart bedanken voor de aangename samenwerking en voor zijn schitterende

begeleiding. Omdat hij altijd voor me klaar stond en steeds bereid was me te hulp te schieten

als dat nodig was. Dit het hele jaar door maar zeker nog extra de laatste maand tijdens het

lezen, verbeteren en herlezen van mijn schrijfsels. Bedankt Bart, want zonder jou was dit

werk nooit geworden wat het vandaag is!! Verder wens ik hem nog veel succes met het

verdere verloop van zijn doctoraat, zijn verdere professionele carrière en zijn privé-leven.

Graag wil ik ook iedereen van het labo in Zwijnaarde bedanken voor de leuke babbels tijdens

de ontspannende koffiepauzes en al de ‘technische’ bijstand.

Wie ik zeker ook niet mag vergeten zijn mijn vrienden medestudenten. Een dikke merci aan

hen voor het aangename gezelschap, hun steun en toeverlaat, dit zowel tijdens momenten van

inspanning als van ontspanning!!!

En tot slot wil ik ook zeker mijn ouders en mijn broer bedanken. Dank jullie wel voor de

ontzettende steun, de interesse, en nog veel meer… Mijn mama wil ik hierbij in het bijzonder

nog eens in de bloemetjes zetten voor de fantastische catering en mijn papa voor al de

zondagavondritjes naar Gent gedurende de voorbije 5 jaar.

Ab initio modelling of acid catalyzed hydrocarbon conversion processes

Eva kint

Supervisor: Ir. Bart De Moor Promotors: Prof. dr. Marie-Françoise Reyniers, Prof. dr. ir. Guy B. Marin

Abstract�In this work, the influence of the catalyst characteristics, e.g. acid strength and zeolite topology as well as the influence of the hydrocarbon structure and carbon number on acid catalyzed reactions is studied. As a starting point, cluster calculations are performed to study 1. physisorption and chemisorption for the different butenes and 2. the double bond isomerisation reaction. Then, for a better description of the zeolite environment, physisorption is studied for C2-C8 alkenes in H-FAU and for C2-C5 alkenes in H-ZSM-5 and H-MOR by a combined quantum mechanics - interatomic potential functions approach (QM-Pot). More specifically, the influence of the zeolite framework, alkene carbon number and hydrocarbon structure has been investigated. The sequence in order of decreasing physisorption strength is found to be as follows: H-ZSM-5 > H-MOR > H-FAU. The predicted physisorption energies for 1-alkenes are found to decrease with increasing carbon number. Further, the structure of the hydrocarbon determines the ability of the alkene to fit in the zeolite pore thereby minimizing the steric hindrance and maximizing the stabilizing interactions with the zeolite wall. The physisorption of C2-C5 alkanes is also studied in H-ZSM-5. Finally, the influence of the zeolite framework and the influence of the Si/Al ratio on the acid strength of the Brønsted acid site are examined calculating the deprotonation energy.

Keywords� zeolite, acidity, physisorption, QM-Pot

I. INTRODUCTION

cid catalyzed hydrocarbon conversion processes such as catalytic cracking of hydrocarbons, isomerisation of

olefins, alkylation of aromatic compounds, etc. play an important role in the (petro)chemical industry. Due to the continually increasing competition in these industrial sectors, the ever raising quality requirements and the need for more environment-friendly processes, there is a permanent incentive to understand and to improve processes.

Physisorption and chemisorption of alkenes are the first elementary steps occurring in many acid catalyzed reactions (e.g. alkylation of aromatics, double bond isomerisation reaction). Physisorption structures are characterized by the formation of a π-complex between the acid site of the zeolite and the double bond of the alkene. Protonation of the π-complex yields a chemisorption complex, the nature of which is very sensitive to the local geometry of the active site and to the structure of the hydrocarbon (primary, secondary or tertiary). In this study a special interest goes to the study of the influence of the catalyst characteristics, e.g. acid strength and zeolite topology as well as in the influence hydrocarbon structure and carbon number on the physisorption energy.

II. COMPUTATIONAL METHOD

The cluster calculations are performed with the Gaussian03 using a 6-31 g* basis set and a B3LYP functional. Within this approach the zeolite active site is described by a small fragment of the zeolite framework, a 3T-cluster saturated with hydrogen atoms.

For a better description of the interactions between the hydrocarbon and zeolite, a the hybrid quantum mechanics-interatomic potential function (QM-Pot) method is applied, which uses periodic boundary conditions and treats the entire zeolite structure. The Brønsted acid site, typically represented by a 3T cluster with hydrogen link atoms on the broken O-Si bond, and the hydrocarbon (the “cluster”) are treated by Density Functional Theory (B3LYP functional and T(O)DZP basis set) using TURBOMOLE (QM-part). The remainder of the zeolite structure (the “host”) is modelled by a shell-model ion-pair potential using GULP (Pot-part). Lennard-Jones parameters are included in the force field to describe the important dispersion (van der Waals) interactions between the hydrocarbon and the zeolite wall. The QM-Pot energy is obtained by the following subtraction scheme:

Pot,clusterPot,hostQM,clustertotal,PotQM EEEE −+=−

Calculations have been performed on H-ZSM-5, H-FAU and H-MOR zeolites. For H-ZSM-5, two different tetrahedral positions for the Al substitution are considered. All three simulation cells contain 289 atoms.

III. RESULTS

A. Cluster calculations

The physisorption energies ∆Ephys are similar for the different butenes (1-, 2- and isobutene) and vary from -28.1 kJ/mol for 1-butene to -34.4 kJ/mol for 2-butene. The protonation of these physisorbed complexes leads to the formation of alkoxy complexes. The activation energies for the protonation Ea differ a lot for the different butenes and increase from 89.3 kJ/mol for protonation of isobutene to t-butoxy to 141.7 kJ/mol for protonation of isobutene to isobutoxy. These differences are due to the fact that the transition states resemble carbenium ions and the most stable carbenium ion (tertiary) is characterized by the lowest activation barrier. The chemisorption energy ∆Echem varies between -56.6 kJ/mol for isobutoxy and -79.8 kJ/mol for 2-butoxy.

The double bond isomerisation of 1-butene to 2-butene is studied by two reaction mechanisms: on the one hand by a concerted mechanism, where the double bond isomerisation

A

proceeds in one step from the physisorbed state and on the other hand by a two-step mechanism via adsorption/ desorption forming a chemisorbed intermediate. It is found that the double bond isomerisation reaction favorably occurs through the concerted mechanism, since the activation energy is almost 30 kJ/mol less than the one required for the highest activated reaction step of the two-step mechanism.

Calculated energies using the cluster approach however are considerably higher than the experimentally determined values. This is easily explained by the fact that the 3T-cluster clearly does not give a correct description of the real zeolite environment and, as a consequence neither steric constraints nor the stabilizing van der Waals interactions are taken into account. It can therefore be expected that more advanced QM-Pot calculations, which allow accounting for these influences, will lead to results which correspond better with the experimental data.

B. Physisorption in H-ZSM-5, H-FAU and H-MOR

The QM-Pot calculations for the three zeolites are performed in simulation cells characterized by a Si/Al ratio of 95. Physisorption (i.e. the π-complexes) of ethylene, propylene, 1-butene, 2-butene, i-butene, 1-pentene, 2-Me-1-butene, 2-Me-2-butene, 1-hexene, 1-heptene and 1- to 4-octene in H-FAU and of ethylene, propylene, 1-butene, 2-butene, i-butene, 1-pentene, 2-Me-1-butene, 2-Me-2-butene in H-ZSM-5 and H-MOR is investigated. The physisorption energy, ∆Ephys, is defined as:

alkene,QMzeolite,PotQM,PotQMphys EEEE −−=∆ −π−

Comparing physisorption of the different alkenes in H-ZSM-5, H-FAU and H-MOR indicates that the physisorption energy depends on the carbon number of the alkene. In H-ZSM-5 at the Al 7-O17(H)-Si4 acidic site, which is located in the sinusoidal channel, ∆Ephys changes from -56.5 kJ/mol for ethylene to -99.8 kJ/mol for 1-pentene. ∆Ephys for the Al12-O24(H)-Si12 site, located at the intersection of a straight and a sinusoidal channel, varies from -54.7 kJ/mol for ethylene to -84.3 kJ/mol for 1-pentene. In H-FAU ∆Ephys decreases from -36.7 kJ/mol for ethylene to -79.9 kJ/mol for 1-octene and from -44.3 kJ/mol for ethylene to -79.8 kJ/mol for 1-pentene in H-MOR. This corresponds with a decrease of the physisorption energy of 14.2 kJ/mol, 8.6 kJ/mol, 12.3 kJ/mol and 6.9 kJ/mol per extra –CH2– group for the linear alkenes in H-ZSM-5(Al7), H-ZSM-5(Al12), H-MOR and H-FAU respectively. These values agree rather good with experimental data. In literature, incremental values have been reported in the range of -6.4 to -7.0 kJ/mol for H-FAU, -11.0 to -12.0 kJ/mol for H-ZSM-5 and -10.1 to -10.5 kJ/mol for H-MOR for the physisorption of alkanes. Further investigation of the QM-Pot results shows that the decrease of the physisorption energy with increasing carbon number can be attributed to stabilizing van der Waals and long range interactions in the “host” structure. As expected, stronger physisorption occurs in the medium pore zeolite H-ZSM-5 compared to the large pore zeolites H-FAU and H-MOR, as the smaller channels cause higher stabilization energies by dispersion interactions.

Differences in physisorption energy of the various C4 (1-butene, 2-butene and i-butene) and C5 (1-pentene, 2-Me-1-butene and 2-Me-2-butene) alkenes in H-ZSM-5, H-FAU and H-MOR and of the various C8 alkenes (1- to 4-octene) in H-FAU are related to their ability to fit in the zeolite framework thereby maximizing the stabilizing interactions. The order of

stability differs in the different zeolites: in H-MOR, for example, physisorbed i-butene and 1-pentene are most stable of all C4 and C5 alkenes whereas in H-ZSM-5(Al12) physisorbed 1-butene and 2-Me-1-butene are found to be most stable.

In addition to the physisorption of alkenes, physisorption of C2-C5 alkanes in H-ZSM-5(Al12) has been studied. ∆Ephys varies from -34.6 kJ/mol for ethane to -74.7 kJ/mol for n-pentane corresponding with a decrease of the physisorption energy of 13.0 kJ/mol. In contrast with the alkenes, no π-complex is formed with the alkanes and consequently, the van der Waals interactions are relatively more important for alkane stabilization. Mention that the positioning of alkanes is totally different from those of alkenes: the alkane molecule is located in the centre of the straight channel, whereas alkenes are positioned close to the zeolite wall due to the formation of a π-complex with the acidic proton.

C. Acid strength of Brønsted sites

In this study, the energy of deprotonation, ∆EDP, is used as a measure for the intrinsic acid strength of the specific Brønsted sites. It is defined as the energy difference between the deprotonated zeolite and the protonated zeolite.

First, ∆EDP of an isolated Brønsted site is calculated in different zeolites and specifically the influence of the zeolite framework (ZSM-5, MOR and FAU) and the crystallographic position (Al7 and Al12 in ZSM-5) on the acidity of zeolites is investigated. All zeolite unit cells are characterized by a Si/Al ratio of 95. According to the calculated deprotonation energies, H-FAU has the most acidic Brønsted site with a deprotonation energy of 1205.9 kJ/mol while H-ZSM-5(Al7) is the weakest acid site, with a deprotonation energy of 1236.6 kJ/mol. The following sequence in order of decreasing intrinsic acidity has been found, namely H-FAU > H-MOR ≈ H-ZSM-5(Al12) > H-ZSM-5(Al7).

Secondly, both the influence of the Si/Al ratio as well as the influence of the distance of the Al substitutions to the acid site on the deprotonation energy are studied. All the calculations have been performed in the ZSM-5 zeolite lattice and deprotonation of the Al7-O17(H)-Si4 site is considered. From the obtained results, some obvious trends could be observed. 1. an Al has the largest effect on the deprotonation energy if it is bonded to the Si atom, part of the Si-O(H)-Al bridge (next nearest neighbour, NNN). The effect of other NNN substitutions is much smaller, 2. the distance to the Brønsted acid site of the Al substitution does generally not lead to a variation of the deprotonation energy and 3. the influence of the Si/Al ratio to the deprotonation energy weakens as the amount of Al atoms in the unit cell increases.

IV. FUTURE WORK

QM-Pot calculations have been performed to study the physisorption of alkenes and alkanes. Protonation is another elementary step in many acid catalyzed reactions and will be subject of further research. Further, double bond isomerisation and alkylation are also important reactions in the reaction network for e.g. the production of linear alkylbenzenes.

List of symbols

Symbol Description Units

E energy kJ/mol

Ea activation energy kJ/mol

Z-OH protonated zeolite -

Z-O- deprotonated zeolite -

∆ difference -

Subscript

chem chemisorption -

phys physisorption -

prot protonation -

QM quantum mechanics -

Pot interatomic potential functions -

QM-Pot quantum mechanics- interatomic potential functions -

C cluster -

S entire zeolite system, i.e. zeolite unit cell -

DP deprotonation -

π physisorbed complex -

σ chemisorbed complex -

Table of contents

Nederlandse samenvatting……………………………………………………………………...1

Chapter 1: Introduction ........................................................................................................16

1.1 Zeolites in general.................................................................................................16

1.2 Scope and justification..........................................................................................16

1.3 Objective ..............................................................................................................18

Chapter 2: Computational method ........................................................................................22

2.1 Cluster calculations...............................................................................................22

2.2 Quantum chemical periodic calculations ...............................................................24

2.3 Hybrid QM-Pot calculations on embedded clusters...............................................26

2.3.1 QM-Pot computational details.......................................................................28

2.3.2 Hydrocarbons in zeolites: extension of the zeolite force field ........................30

2.3.3 Implementation .............................................................................................34

2.4 Conclusions ..........................................................................................................34

Chapter 3: Cluster Calculations ............................................................................................40

3.1 Physisorption and chemisorption of alkenes..........................................................41

3.2 Double bond isomerization ...................................................................................47

3.2.1 Concerted mechanism ...................................................................................47

3.2.2 Mechanism via adsorption/desorption ...........................................................49

3.3 Conclusions ..........................................................................................................50

Chapter 4: Physisorption of C2-C8 alkenes in H-FAU, H-MOR and H-ZSM-5 zeolites.........53

4.1 Introduction ..........................................................................................................54

4.2 Method .................................................................................................................56

4.2.1 Computational details....................................................................................56

4.2.2 Details on the zeolite structures studied.........................................................57

4.3 Results and discussion ..........................................................................................59

4.3.1 Details of the Brønsted acid sites...................................................................59

4.3.2 Physisorption in H-ZSM-5, H-FAU and H-MOR ..........................................62

4.4 Conclusions ..........................................................................................................73

Chapter 5: Zeolite acidity .....................................................................................................81

5.1 Deprotonation and periodicity in QM-Pot .............................................................83

5.2 Single aluminium substitution...............................................................................84

5.3 Extra aluminium substitutions...............................................................................86

5.3.1 Influence of 2T and 2T’ Al substitution........................................................89

5.3.2 Influence of distance to acid site....................................................................90

5.3.3 Influence of the Si/Al ratio ............................................................................92

5.4 Conclusions ..........................................................................................................93

Chapter 6: Conclusions ........................................................................................................95

6.1 Cluster calculations...............................................................................................95

6.2 Physisorption in H-ZSM-5, H-FAU and H-MOR..................................................96

6.3 Zeolite acidity.......................................................................................................97

6.4 Future work ..........................................................................................................98

Appendix……………………………………………………………………………………... 99

Nederlandse samenvatting 1

Nederlandse samenvatting

In dit hoofdstuk wordt een kort overzicht te geven van de verschillende hoofdstukken van

mijn thesis. Voor elk hoofdstuk zullen de belangrijkste resultaten beknopt besproken worden

en zullen de conclusies vermeld worden.

1 Inleiding

Zeolieten worden heden frequent als katalysator gebruikt in de (petro)chemische industrie. In

het bijzonder zure katalysatoren die verkregen worden na substitutie van een siliciumatoom

door een aluminiumatoom en toevoeging van een proton om de negatieve lading te

compenseren, hebben interessante eigenschappen. Toch zijn een groot deel van de reacties die

plaatsvinden in deze zure katalysatoren nog steeds niet volledig doorgrond en wordt nog

steeds veel onderzoek gedaan naar de katalytische eigenschappen van de verschillende

zeolieten. Kwantumchemische berekeningen kunnen hier bijdragen tot een kwantitatieve

beschrijving van de reactie en zullen het mogelijk maken de invloed van de

katalysatoreigenschappen op de selectiviteit en reactiviteit van de reactie na te gaan. Speciale

interesse in dit onderzoeksgebied gaat uit naar de adsorptie van alkenen in zeolieten omdat dit

de eerste elementaire stap is in de meeste zuur gekatalyseerde omzettingsprocessen van

koolwaterstoffen. Een eerste doel van mij thesis is dan ook om zowel de invloed van de

zeolietstructuur als de invloed van de structuur van de koolwaterstof op de fysisorptie-energie

na te gaan. Hiervoor werden simulaties uitgevoerd voor een uitgebreide reeks alkenen in

verschillende zeolietstructuren (MFI, FAU en MOR) die industrieel relevant zijn en die

vergelijking met experimentele data toelaten. In het tweede deel komt het bestuderen van de

zuursterkte van het zure centrum van het zeoliet aan bod. Enerzijds is het de bedoeling om een

goed idee te krijgen van de invloed van de zeolietstructuur en de positie van het zure centrum

in het zeoliet op de aciditeitseigenschappen; anderzijds wordt de invloed van de Si/Al

verhouding en invloed van de posities van de verschillende aluminium substituties ten

opzichte van het zure centrum nagegaan.


2 Computationele methode

Drie methodes worden heden frequent gebruikt bij de studie van reacties gekatalyseerd door

zeolieten, namelijk clusterberekeningen, periodieke Denstity Functional Theory (DFT)

berekeningen en hybride “quantum mechanics – interatomic potential functions” (QM-Pot)

berekeningen. Enkel deze laatste, ook “quantum mechanics/molecular mechanics”

berekeningen genoemd worden in hetgeen volgt besproken. Voor meer informatie omtrent de

eerste twee methoden wordt verwezen naar Hoofdstuk 2 van deze thesis. In deze thesis werd

het overgrote deel van de simulaties uitgevoerd aan de hand van deze laatste methode, de

QM-Pot methode. Hierbij wordt het volledige systeem (S), i.e. de zeoliet eenheidscel in twee

delen opgesplitst die elk apart behandeld worden. Het eerste deel omvat het actieve deel van

het zeoliet, waar reactie plaatsvindt: de koolwaterstofmolecule en het in het zeoliet ingebedde

cluster (C), meestal een 3T-cluster, dat het zure centrum omvat en getermineerd wordt met

waterstof linkatomen. Dit eerste deel wordt behandeld met de Density Functional Theory

(DFT) door gebruik te maken van het programma TURBOMOLE. Het tweede deel omvat al

de overige atomen van de zeolieteenheidscel en wordt beschreven met een ‘shell model ion-

pair potential’ krachtveld door gebruik te maken van het programma GULP. In deze laatste

methode worden de zuurstofatomen van het zeoliet beschreven door middel van een “core” en

een “shell”, wat toelaat de polariseerbaarheid van het zeoliet in rekening te brengen. In Figuur

1 wordt een grafische voorstelling gegeven van de ingebedde cluster, de terminerende

waterstof linkatomen en de rest van de zeolieteenheidscel.

Deze QM-Pot berekeningen bieden enkele voordelen ten opzichte van clusterberekeningen of

periodieke DFT berekeningen. Terwijl bij clusterberekeningen slechts een kleine fractie van

het zeolietrooster, typisch een 3T- tot 5T-cluster, wordt beschouwd, wordt bij QM-Pot

berekeningen de volledige zeolietstructuur in rekening gebracht. Dit maakt het mogelijk om

de effecten van sterische hindering en elektrostatische interacties, die ontstaan onder invloed

van het zeolietrooster, in rekening te brengen. Vergeleken met volledig periodieke DFT

berekeningen, die ook rekening houden met de hierboven vermelde effecten, is de

computationele kost, vereist voor QM-Pot berekeningen, significant minder groot, waardoor

ook zeolieten met een groot aantal atomen in hun eenheidscel bestudeerd kunnen worden. Bij

de QM-Pot methode wordt een goed compromis geboden tussen de correctheid van de

berekeningen en de tijd nodig om deze uit te voeren, wat dit type berekeningen aantrekkelijk

maakt voor de studie van zeolieten. Bovendien biedt de QM-Pot methode voor het berekenen


van de fysisorptie-energieën het bijkomende voordeel dat de zwakke dispersiekrachten, de

van der Waals interacties, goed beschreven worden in het krachtveld door de interatomaire

Lennard-Jones potentiaal.

Figuur 1: Het QM-Pot schema dat het QM-gedeelte, i.e. de ingebedde cluster getermineerd met waterstofatomen, en het Pot-gedeelte (MM) , i.e. de rest van de zeolieteenheidscel, weergeeft

3 Clusterberekeningen

In Hoofdstuk 3 van deze thesis worden clusterberekeningen uitgevoerd omdat deze heel

gunstig zijn om snel een inzicht te krijgen in de structuur van stabiele intermediairen en

transitietoestanden alsook in de mogelijke reactiepaden die kunnen optreden tijdens zuur

gekatalyseerde omzettingsprocessen van koolwaterstoffen. Deze clusterberekeningen werden

uitgevoerd met het programma Gaussian03 en er werd gebruik gemaakt van een 6-31 g*

basisset en een B3LYP functionaal. Om de actieve plaats van het zeolietrooster te beschrijven

werd gekozen voor een 3T-cluster. In de eerste plaats werd voor de verschillende butenen,

uitgaande van de geoptimaliseerde structuur van de transitietoestanden voor de protonering

van deze butenen, gezocht naar de geoptimaliseerde fysisorptie- en chemisorptiestructuren.

Daarna werd het mechanisme van de dubbelebindingsisomerisatie van 1-buteen naar 2-buteen

onder de loep genomen.


3.1 Fysisorptie en chemisorptie van butenen

De gefysisorbeerde structuren van alkenen zijn gekarakteriseerd door de vorming van een π-

complex tussen de zure plaats van het zeoliet en de dubbele binding van het alkeen.

Protonering van deze π-complexen geeft aanleiding tot de vorming van een gechemisorbeerd

complex (σ-complex), dat in ons geval bij 0 K een alkoxide is. Er wordt aangenomen dat de

protonering van zowel 1-buteen als 2-buteen leidt tot de vorming van een 2-butoxy complex.

Door de protonering van isobuteen kan zowel een isobutoxy complex als een tertiair butoxy

complex gevormd worden en beide gevallen werden bestudeerd. De verkregen resultaten voor

de verschillende energieën zijn weergegeven in Tabel 1. De verschillende berekende

energieën worden verduidelijkt in Figuur 2.

Tabel 1: fysisorptie-, activatie- en protoneringsenergieën voor 1-buteen, 2-buteen en isobuteen op een 3T cluster

alkeen type alkoxy Energie [kJ/mol]

complex ∆Ephys Ea Eacomp ∆Eprot ∆Echem

1-buteen secondair -28.1 93.4 65.3 -51.7 -79.8

2-buteen secondair -34.4 107.3 72.9 -39.8 -74.1

isobuteen tertiar -29.2 89.3 60.1 -31.6 -60.8

isobuteen primair -28.9 141.7 112.9 -27.8 -56.6

Figuur 2: relatief energiediagram voor de protonering van een alkeen


De fysisorptie-energieën van de verschillende butenen liggen allemaal dicht bij elkaar en zijn

gesitueerd tussen -28.1 kJ/mol en -34.4 kJ/mol. De activeringsenergieën daarentegen variëren

heel sterk voor de verschillende butenen. Zo heeft de vorming van een isobutoxy complex

uitgaande van isobuteen de hoogste activeringsenergie (141.7 kJ/mol), terwijl de vorming van

t-butoxy complex, eveneens uitgaande van isobuteen, de laagste activeringsenergie (89.3

kJ/mol) heeft. De activeringsenergieën voor de vorming van een 2-butoxy complex zijn

gelegen tussen deze twee waarden. Deze resultaten liggen volledig binnen de lijn van de

verwachtingen aangezien de structuur van de transitietoestanden sterk lijkt op die van

carbeniumionen. Zo zal de vorming van een t-butoxy complex bijvoorbeeld aanleiding geven

tot een op een tertiair carbeniumion lijkende transitietoestand. Omwille van de gekende

stabiliteit van een tertiair carbeniumion ten opzichte van secundaire en primaire

carbeniumionen, zal de corresponderende transitietoestand dan ook gekenmerkt worden door

de laagste activeringsenergie. Omgekeerd zal er de transitietoestand voor de vorming van een

isobutoxy complex, die qua structuur dicht aanleunt bij een primair carbeniumion,

gekenmerkt worden door een hoge activeringsenergie. Voor de chemisorptie-energieën tot

slot worden waarden gevonden die liggen tussen -56.6 kJ/mol en -79.8 kJ/mol: het meeste

stabiele σ-complex is het 2-butoxy complex terwijl als minst stabiele gechemisorbeerde

structuur het isobutoxy complex gevonden wordt.

3.2 Dubbelebindingsisomerisatie

De dubbelebindingsisomerisatie is een belangrijke reactie in het reactienetwerk voor de

productie van lineaire alkylbenzenen. In de literatuur worden twee reactiemechanismen

vermeld voor de dubbelebindingsisomerisatie van alkenen met zeolieten als katalysator.

Enerzijds is er een direct mechanisme, anderzijds een mechanisme dat verloopt via

adsorptie/desorptie van de alkenen. Beide mechanismen worden bestudeerd voor de

dubbelebindingsisomerisatie van 1-buteen naar 2-buteen.

Direct mechanisme Bij het direct mechanisme verloopt de dubbelebindingsisomerisatie in één stap, vertrekkende

van de gefysisorbeerde toestand van 1-buteen. De geoptimaliseerde transitietoestand voor dit

mechanisme is afgebeeld in Figuur 3 samen met enkele belangrijke afstanden.


Figuur 3: Transitietoestand voor het directe mechanisme van de dubbelebindingsisomerisatie van 1-buteen naar 2-buteen

Terwijl het zure proton (H1) van het zeoliet het koolstofatoom C1 van de dubbele binding van

het gefysisorbeerde 1-buteen protoneert, wordt tegelijkertijd een proton (H6), afkomstig van

het C3 atoom, geabstraheerd door de naburige zuurstof (O2) van het zeoliet, zodat opnieuw

een zuur centrum gevormd wordt in het zeoliet. De activeringsenergie voor dit mechanisme is

119 kJ/mol en het totale reactiediagram wordt weergegeven in Figuur 4.

Figuur 4: Energieën voor het direct mechanisme van de dubbelebindings-isomerisatie


Mechanisme via adsorptie/desorptie Dit mechanisme voor de dubbelebindingsisomerisatie gebeurt in twee stappen. In de eerste

stap wordt het gefysisorbeerde 1-buteen geprotoneerd met vorming van een alkoxy complex,

meer bepaald 2-butoxy. In de tweede stap vindt deprotonering van dit alkoxide plaats,

aanleiding gevend tot het 2-buteen π-complex. Het mechanisme is voorgesteld in Figuur 5.

O+

Si Al-

O+

Si Al-

H

O+

Si Al-

H

Figuur 5: Mechanisme voor de dubbelebindingsisomerisatie van adsorptie/desorptie

Het reactiediagram wordt getoond in Figuur 6. De activeringsenergieën vereist voor de eerste

stap en tweede stap zijn respectievelijk 93 kJ/mol en 147 kJ/mol. Hieruit volgt duidelijk dat

de dubbelebindingsisomerisatie bij voorkeur zal verlopen via het direct mechanisme omdat de

activeringsenergie daar ongeveer 30 kJ/mol lager is dan diegene hier vereist voor de tweede

stap. De hoge activeringsenergie van de tweede stap (deprotonering) in dit mechanisme is een

gevolg van de stabiliteit van het gevormde alkoxy intermediair.

π 1-butene

1-butene (gas

phase) + 3T

cluster

-34

TS protonation

1-butene

93

σ 2-butoxy

-52

TS protonation

2-butene

147

π 2-butene

107 2-butene (gas

phase) + 3T

cluster

-28

Figuur 6: Reactiediagram voor het mechanisme via adsorptie/desorptie van de dubbelebindingsisomerisatie


3.3 Conclusie

Clusterberekeningen zijn uitgevoerd met de bedoeling om inzicht te verwerven in de structuur

van stabiele intermediairen en transitietoestanden alsook in de mogelijke reactiepaden die

kunnen optreden tijdens zuur gekatalyseerde omzettingsprocessen van koolwaterstoffen. Uit

de berekeningen blijkt nochtans dat de activeringsenergie van het direct mechanisme voor de

dubbelebindingsisomerisatie niet overeenstemt met waarden die experimenteel worden

waargenomen. Dit kan eenvoudig verklaard worden door het feit dat de 3T-cluster geen

correcte beschrijving van het reële zeolietrooster weergeeft. Wanner immers het volledige

zeolietrooster wordt beschouwd en de elektrostatische en stabiliserende dispersie-interacties

in rekening worden gebracht, zal dit een belangrijke invloed hebben op de stabiliteit van de

intermediairen en de grootte van de activeringsenergie. We kunnen besluiten dat hoewel bij

clusterberekeningen geen kwantitatief correcte resultaten verkregen worden, ze toch nuttig

zijn om een kwalitatief inzicht te verwerven in mogelijke reactiemechanismen en ze dus

geschikt zijn als startpunt voor de meer geavanceerde QM-Pot berekeningen.

4 Fysisorptie in H-ZSM-5, H-FAU en H-MOR

In Hoofdstuk 4 van deze thesis wordt dieper ingegaan op de fysisorptie van alkenen en

alkanen in zeolieten. Hierbij werd de invloed van zowel de zeolietstructuur als de

koolwaterstofstructuur nagegaan. De fysisorptie-energie wordt gedefinieerd als het

energieverschil tussen het gefysisorbeerd complex enerzijds en het ongeladen zeoliet en

gasfase koolwaterstof anderzijds. In een uitgebreide studie worden de fysisorptie-energieën

bepaald voor C2-C5 alkenen in H-ZSM-5 en H-MOR en voor C2-C8 alkenen in H-FAU.

Bovendien worden ook de C2-C5 alkanen in H-ZSM-5 bestudeerd. In H-ZSM-5 werden twee

kristallografisch verschillende T-posities beschouwd: het Al7-O17(H)-Si4 zure centrum,

gelegen in het sinusoïdaal kanaal, en de Al12-O24(H)-Si12 positie, gelegen aan de kruising van

een recht en een sinusoïdaal kanaal. Voor H-FAU en H-MOR werden respectievelijk Al-

O1(H)-Si en Al4-O2(H)-Si2 als zuur centrum gekozen. Figuur 7 geeft een voorstelling van de

fysisorptie-energieën van de 1-alkenen in de verschillende zeolietstructuren als functie van het

koolstofgetal (carbon number, CN).


Figuur 7: Fysisorptie-energieën van de 1-alkenen in functie van het koolstofgetal in verschillende zeolieten

Figuur 7 toont duidelijk aan dat er een lineair verband bestaat tussen de fysisorptie-energie en

het koolstofgetal. Voor de fysisorptie-energieën van de 1-alkenen werd voor de verschillende

zeolieten een lineaire fit uitgevoerd en deze wordt voorgesteld door de stippellijnen in de

figuur. Ook de vergelijkingen en de correlatiecoëfficiënt (R2) overeenstemmend met deze

lineaire fits zijn weergegeven in de figuur. In H-ZSM-5(Al7), H-ZSM-5(Al12), H-MOR and

H-FAU nemen de fysisorptie-energieën voor de lineaire alkenen af met respectievelijk 14.23

kJ/mol, 8.62 kJ/mol, 12.38 kJ/mol and 6.94 kJ/mol per extra –CH2– groep. Deze daling van

de fysisorptie-energie met stijgend koolstofgetal wordt voornamelijk veroorzaakt door het

toenemend aantal stabiliserende van der Waals interacties tussen het alkeen en de

zeolietwand. Uit Figuur 7 kan eveneens afgeleid worden dat de sterkte van de fysisorptie ook

afhangt van de zeolietstructuur: volgens dalende fysisorptiesterkte wordt als volgorde

gevonden voor de verschillende zeolieten: H-ZSM-5(Al7) > H-ZSM-5(Al12) > H-MOR > H-

FAU. Deze volgorde kan verklaard worden aan de hand van de topologische verschillen

tussen de verschillende zeolietroosters. De kanalen van H-ZSM-5 zijn namelijk

gekarakteriseerd door 10T ringen, terwijl in H-MOR en H-FAU de kanalen bestaan uit 12T

ringen. Deze nauwere kanalen in H-ZSM-5 zorgen voor een grotere stabilisatie van de

-110

-100

-90

-80

-70

-60

-50

-40

1 2 3 4 5 6 7 8Carbon number

∆Ephys (kJ/mol)

H-FAU ∆Ephys = -6.94CN -22.78 R2 = 0.989

H-MOR ∆Ephys = -12.38CN -20.43 R2 = 0.9683

H-ZSM-5(Al12) ∆Ephys = -8.62CN -41.74 R2 = 0.8003

H-ZSM-5(Al7) ∆Ephys = -14.23CN -30.00 R2 = 0.9904


koolwaterstoffen door de zeolietwand, voornamelijk door dispersie interacties. Het verschil

tussen H-MOR en H-FAU, beide gekarakteriseerd door 12T ringen is te wijten aan het feit dat

H-FAU een veel opener structuur is, waarbij de 12T ringen de verbindingen zijn tussen de

karakteristieke superkooien. Er dient ook opgemerkt te worden dat de correlatiecoëfficiënt

voor H-ZSM-5(Al12) een waarde heeft die een stuk lager ligt dan de andere R2-waarden. Dit

komt doordat de fysisorptie-energie van propyleen sterk afwijkt van de waarde die verwacht

wordt uitgaande van de fysisorptie-energieën voor ethyleen en 1-buteen. Dit is te wijten aan

het feit dat propyleen perfect past in het sinusoïdaal kanaal van H-ZSM-5 en daarbij

maximale stabilisering ondervindt door de zeolietwand. Bij ethyleen is dit effect minder

uitgesproken, terwijl de overige 1-alkenen gefysisorbeerd worden in het recht kanaal van H-

ZSM-5.

Een andere factor die een belangrijke invloed uitoefent op de fysisorptie-energie is de

structuur van het koolwaterstof. Om deze invloed na te gaan werden bijvoorbeeld de

fysisorptie-energieën van verschillende C4 alkenen (i.e. 1-buteen, 2-buteen en isobuteen) en

C5 alkenen (i.e. 1-penteen, 2-methyl-1-buteen and 2-methyl-2-buteen) berekend in de

verschillende zeolieten en onderling vergeleken. De berekende fysisorptie-energieën worden

weergegeven in Tabel 2.

Tabel 2: Fysisorptie-energieën in kJ/mol voor verschillende butenen en pentenen in verschillende zeolieten.

∆Efys [kJ/mol]

Alkeen H-ZSM-5(Al7) H-ZSM-5(Al12) H-FAU H-MOR

1-buteen -88.1 -73.1 -48.9 -74.1

2-buteen -91.0 -76.9 -50.2 -69.2

Isobuteen -81.9 -73.9 -54.8 -68.6

1-penteen -99.8 -84.3 -56.7 -79.8

2-Me-1-buteen - -77.9 -56.2 -80.5

2-Me-2-buteen - -82.7 -58.8 -80.7

De resultaten tonen duidelijk dat de fysisorptie-energieën voor alkenen met een zelfde

koolstofgetal maar met een verschillende structuur onderling verschillen en dat de volgorde

van stabiliteit varieert van zeoliet tot zeoliet. Hieruit wordt besloten dat de waarde van de

fysisorptie-energie sterk verbonden is met de mate waarin het alkeen zich kan inpassen in het

zeolietkanaal, waarbij het aantal stabiliserende interacties gemaximaliseerd wordt.


Tot slot werd ook de fysisorptie-energie van C2-C5 alkanen berekend in het H-ZSM-5 zeoliet

(Al12-O24(H)-Si12 als zuur centrum). De fysisorptie van alkanen verschilt fundamenteel van

deze van alkenen door het feit dat er bij alkanen geen π-complex gevormd wordt. Hierdoor

wordt de stabilisatie door van der Waals interacties relatief gezien veel belangrijker voor

alkanen: de van der Waals interacties dragen bij tot 85-95% van de totale fysisorptie-energie

bij alkanen, terwijl deze bijdrage bij alkenen beperkt blijft tot 45-70%. Dit heeft tevens als

gevolg dat de positie van een alkaan in het zeolietkanaal sterk verschilt van deze van een

alkeen: een alkaan zal zich in het midden van een kanaal positioneren, terwijl een alkeen een

π-complex vormt en zich daardoor dichter bij één kant van de zeolietwand bevindt. In Figuur

8 wordt het lineaire verband weergegeven tussen de fysisorptie-energieën voor de 1-alkanen

en het koolstofgetal. Door middel van een lineaire fit van de fysisorptie-energieën van de 1-

alkenen wordt een extra stabilisatie van 13 kJ/mol gevonden per extra –CH2– groep.

y = -13.551x - 8.9R2 = 0.985

y = -8.6206x - 41.7R2 = 0.8003

-90

-80

-70

-60

-50

-40

-30

1 2 3 4 5 6

Carbon number

∆Ephys (kJ/mol)

alkanen

alkenen

Figuur 8: Fysisorptie-energieën van de 1-alkanen en 1-alkenen als functie van het koolstofgetal in H-ZSM-5(Al12)

Algemeen kan besloten worden dat de QM-Pot methode de verschillen in fysisorptie-energie

weergeeft zoals verwacht uit literatuur. Bovendien kunnen de incrementele waarden voor de

verandering van de fysisorptie-energie met het koolstofgetal vergeleken worden met

resultaten verkregen uit experimenten met alkanen. In de literatuur worden volgende


incrementele waarden gerapporteerd voor de fysisorptie van alkanen: -6.4 tot -7.0 kJ/mol voor

H-FAU, -11.0 tot -12.0 kJ/mol voor H-ZSM-5 and -10.1 tot -10.5 kJ/mol voor H-MOR. Deze

experimentele waarden stemmen goed overeen met onze berekende waarden, alhoewel toch

enkele verschillen waar te nemen zijn. Deze verschillen kunnen te wijten zijn aan 1. het feit

dat er in experimenten geen onderscheid gemaakt wordt tussen zure centra op

kristallografisch verschillende posities in het zeolietrooster, maar dat enkel een gemiddelde

waarde wordt verkregen en 2. het verschil in Si/Al verhouding tussen de simulaties en het

experimentele werk.

5 Zuursterkte van zeolieten

In zeolieten zijn de verschillende zure centra gekarakteriseerd door hun katalytische activiteit.

Deze activiteit wordt in grote mate bepaald door de zuursterkte van het zure centrum, die op

haar beurt dan weer afhankelijk is van onder andere de zeolietstructuur, de positie van het

zure centrum in het zeoliet en de Si/Al verhouding van het zeoliet. Als maat voor de

intrinsieke zuursterkte van een zuur centrum wordt gebruik gemaakt van de

deprotoneringsenergie ∆EDP. Deze deprotoneringsenergie is gedefinieerd aan de hand van

onderstaande vergelijking:

)()( OHZEOZEEDP −−−=∆ −

met: )( −− OZE de energie van het gedeprotoneerde zeoliet en

)( OHZE − de energie van het geprotoneerde zeoliet.

De invloed van de zeolietstructuur werd met behulp van QM-Pot bestudeerd door de

deprotoneringsenergie te berekenen voor verschillende zeolieten (ZSM-5, FAU and MOR)

waarbij één aluminium substitutie wordt uitgevoerd. De invloed van de positie van het zure

centrum in het zeoliet werd onderzocht voor het zeoliet ZSM-5 door twee verschillende

posities te bekijken (Al7-O17(H)-Si4 en Al12-O24(H)-Si12). Tot slot werd in ZSM-5(Al7) de

invloed op de deprotoneringsenergie nagegaan van zowel de Si/Al verhouding als de invloed

van de afstand van de extra aluminium substituties tot het zure centrum dat wordt

gedeprotoneerd.


5.1 Invloed van zeolietstructuur

Om de invloed van enerzijds de zeolietstructuur en anderzijds de positie van het zure centrum

in het zeoliet na te gaan werden verschillende kristallografische plaatsen in verschillende

zeolieten bestudeerd: Al7-O17(H)-Si4 en Al12-O24(H)-Si12 in ZSM-5, Al-O1(H)-Si in FAU and

Al4-O2(H)-Si2 in MOR. De deprotoneringsenergie werd voor de verschillende zeolieten

berekend in een eenheidscel waar slechts één aluminium substitutie is in uitgevoerd, zodat

elke eenheidscel een Si/Al verhouding van 95 heeft. De uiteindelijke waarden van de

deprotoneringsenergieën zijn weergeven in Tabel 3. De verkregen deprotoneringsenergieën

werden gecorrigeerd volgens de procedure beschreven in Hoofdstuk 5.

Tabel 3: Deprotoneringsenergieën van de verschillende zeolieten met één Al substitutie in de eenheidscel

Zeoliet ∆EDP [kJ/mol]

ZSM-5(Al7) 1236.6

ZSM-5(Al12) 1228.1

FAU 1205.9

MOR 1230.4

Uit bovenstaande waarden kunnen we afleiden dat het zeoliet FAU het zuurste centrum bezit

met een deprotoneringsenergie van 1205.9 kJ/mol en ZSM-5(Al7) het minst zure centrum met

een deprotoneringsenergie van 1236.6 kJ/mol. De volgorde van de zeolieten naar dalende

zuursterkte de volgende is: H-FAU > H-MOR > H-ZSM-5(Al12) > H-ZSM-5(Al7).

5.2 Invloed van Si/Al verhouding

Deprotoneringsenergieën werden berekend voor H-ZSM-5(Al7) waarbij meerdere

aluminiumsubstituties doorgevoerd werden in het zeolietrooster. De verkregen resultaten

worden weergegeven in Tabel 4 en laten toe de invloed van de Si/Al verhouding en de

invloed van de afstand van de aluminiumsubstituties tot het zure centrum na te gaan. Uit de

literatuur wordt verwacht dat extra aluminium substituties een minieme invloed hebben op de

deprotoneringsenergie, zolang de Si/Al verhouding boven een bepaalde kritische waarde blijft

die correspondeert met de substitutie van aluminium atomen in “next nearest neighbour”

(NNN) positie. Bovendien werd ook de invloed nagegaan van een aluminiumsubstitutie in de

2T of 2T’ NNN plaats. De 2T posities zijn deze posities naburig aan het silicium atoom dat


behoort tot de Si-O(H)-Al brug, terwijl de 2T’ posities alle andere tetrahedrale posities op

afstand 2T van het aluminium atoom zijn. De verkregen deprotoneringsenergieën werden niet

gecorrigeerd volgens de procedure beschreven in Hoofdstuk 5 omdat dit de resultaten enkel

verschuift naar hogere waarden voor de deprotoneringsenergieën, maar niets verandert aan de

onderlinge relatieve waarden.

Tabel 4: Deprotoneringsenergieën voor verschillende Si/Al verhoudingen

Distance to acid site ∆EDP (kJ/mol)

Si/Al 2T 2T’ 3T 4T QM Pot QM-Pot

95 - - - - 1314.1 -109.9 1204.3

47 1 - - - 1303.1 -57.2 1245.9

- 1 - - 1308.2 -86.4 1221.8

- - 1 - 1307.1 -85.9 1221.2

- - - 1 1305.4 -84.2 1221.2

31 1 1 - - 1312.3 -54.8 1257.5

- 2 - - 1306.8 -81.2 1225.6

- 1 1 - 1306.6 -81.7 1224.9

- 1 - 1 1302.7 -73.1 1229.6

- - 2 - 1312.9 -88.9 1224.0

- - 1 1 1309.0 -80.6 1228.4

23 1 2 - - 1300.0 -40.6 1259.4

- 2 1 - 1291.0 -59.3 1231.7

- 1 2 - 1305.5 -61.6 1243.9

- 1 1 1 1304.7 -70.4 1234.3

- - 3 - 1315.6 -84.2 1231.4

- - 2 1 1312.8 -84.9 1227.9

- - 1 2 1304.0 -69.6 1234.4

18.2 1 3 - - 1309.8 -47.4 1262.4

- 3 1 - 1296.7 -48.7 1248.0

- 2 2 - 1290.9 -52.2 1238.7

- 1 3 - 1307.7 -76.0 1231.7

- 2 1 1 1281.9 -41.0 1240.9

- 1 2 1 1302.1 -53.5 1248.6

- 1 1 2 1300.0 -61.8 1238.2

Aan de hand van de resultaten weergegeven in Tabel 4 kunnen enkele trends waargenomen

worden. Ten eerste heeft een Al substitutie het grootste effect op de deprotoneringsenergie als

het Al atoom zich op de 2T positie bevindt. Het effect van andere NNN substituties is veel

kleiner. Ten tweede kan men besluiten dat de afstand van de Al substitutie tot het zure


centrum in het algemeen geen invloed heeft op de deprotoneringsenergie, tenzij de substitutie

uitgevoerd wordt op een 2T positie. Ten slotte kan geconcludeerd worden dat de invloed van

de Si/Al verhouding afneemt naarmate het aantal Al atomen in de eenheidscel toeneemt. We

kunnen besluiten dat ondanks het feit dat er duidelijk enkele trends waar te nemen zijn, er

toch nog heel wat variatie optreedt tussen de verkregen resultaten. Daarom is validatie van de

verkregen resultaten zeker een vereiste is. Deze validatie kan gebeuren door de

onafhankelijkheid van de berekende deprotoneringsenergieën na te gaan bij variërende grootte

van de ingebedde cluster.

6 Algemene conclusie en verder werk

Algemeen kan worden geconcludeerd dat clusterberekeningen nuttig zijn om kwalitatief

inzicht te verwerven in de structuur van stabiele intermediairen en mogelijke reactiepaden,

maar dat ze zeker niet leiden tot kwantitatief correcte resultaten. Het beschouwen van het

volledige zeolietrooster heeft immers een belangrijke invloed hebben op de stabiliteit van de

intermediairen. Enerzijds omdat dit aanleiding geeft tot een reële beschrijving van de sterische

effecten die het koolwaterstof ondervindt in het zeoliet en anderzijds omdat op die manier de

elektrostatische en stabiliserende dispersie-interacties in rekening worden gebracht. Daarom

zal het noodzakelijk zijn om voor verdere berekeningen gebruik te maken van een methode,

zoals bijvoorbeeld de QM-Pot methode, die het volledige zeolietrooster beschrijft en dus met

bovenstaande effecten rekening houdt.

De fysisorptie van alkenen in zeolieten, de eerste elementaire stap is in de meeste zuur

gekatalyseerde omzettingsprocessen van koolwaterstoffen, is uitgebreid bestudeerd met het

programma QM-Pot. Protonering van de π-complexen is een andere belangrijke elementaire

reactie die zeker verder onderzocht dient te worden. Er is immers volop discussie of het

gechemisorbeerde intermediair een carbeniumion dan wel een alkoxide is. Verder zullen ook

de dubbelebindingsisomerisatiereactie en alkyleringsreactie deel uitmaken van verder

onderzoek. Aangezien alle simulaties uitgevoerd zijn bij 0K, is het nagaan van de invloed van

het temperatuurseffect een ander belangrijk onderwerp voor verder onderzoek.

Chapter 1: Introduction 16

Chapter 1: Introduction

1.1 Zeolites in general

Zeolites are microporous aluminosilicate crystals that can either be natural or synthesized.

Their framework is composed by assembling of SiO4 and AlO4 tetrahedral units. The zeolitic

framework is very open and is characterized by a well-defined microporous network of

channels and cages of molecular dimensions, which leads to a high internal surface. Therefore

zeolites are very good sorbents. For every aluminium atom present in the zeolite framework, a

negative charge is introduced and to maintain charge neutrality, cations have to be added.

When the cation is a proton, it bounds to a nearby oxygen atom of the Si-O-Al bridge and a

Brønsted acid site is formed. These Brønsted acid sites give rise to the acidic properties of

zeolites and make the protonated zeolites very useful as heterogeneous catalysts. The activity

of these zeolite catalysts is based on the acid strength of the Brønsted sites, or in other words

on their ability to donate a proton to a hydrocarbon. The geometry of the well-defined

micropore structures of the zeolites leads to one of the most important features of this class of

catalyst, namely their shape- and size selectivity. This selectivity is the result of 1. the

difference in diffusivities of reactants and products, 2. the difference in adsorption of reactants

in zeolitic cavities of different size and shape and 3. transition state selectivity. Because of

this separation property, zeolites have been used for many years as molecular sieves. They

have been first introduced on a large scale in the 1950s for petrochemical processes. Zeolites

may be used in catalysis as an inert support for other catalytically active components (Davis

(1998) and Koller et al. (1997)) or they can be used as catalysts as such. Nowadays, zeolites

are widely used in the petroleum and chemical industries as solid catalysts for a number of

commercially important hydrocarbon reactions.

1.2 Scope and justification

Acid catalyzed hydrocarbon conversion processes such as catalytic cracking of hydrocarbons,

hydrocracking of hydrocarbons, isomerisation of olefins, alkylation of aromatic compounds,


etc. play an important role in the (petro)chemical industry. Since the traditional used

homogeneous catalysts are extremely corrosive and harmful for the environment, there is an

increasing demand for environment friendly heterogeneous catalysts. In addition, zeolites

present the advantages, in comparison with previously used alumina-based catalysts, of

having a better long-term thermal and mechanical stability as well as a higher selectivity.

Using zeolites as catalysts can moreover increase the yield of the required products and thus

reduce the production costs significantly. But, although zeolites are already frequently used in

a wide range of petrochemical processes, there exists a constant tendency to understand and to

improve these chemical processes due to the continually increasing competition in these

industrial sectors and the constantly raising quality requirements.

Simultaneously with the accumulation of experimental data numerous simulation techniques

have been performed to mimic the intrazeolite processes. The variety of intrazeolite

phenomena include processes like (1) diffusion of molecules (reactants) into the zeolite, (2)

physisorption (chemisorption) at the active site, (3) chemical reaction of the conversion, (4)

desorption and (5) diffusion of molecules (products) out of the zeolite. It is important to

realize that the diverse intrazeolite processes span different order-of-magnitude time scales.

So, a single theoretical model can not be applied to describe the entire catalytic cycle.

Diffusion of molecules can be better described using classical dynamic (Yashonath and

Santikary (1993) and Schuring et al. (2000)) or Monte Carlo (Bates et al. (1996), Smit and

Siepmann (1994) and Smit (1995)) simulations, whereas quantum chemical calculations are

necessary to assess the catalytic properties. Only micro-kinetic models lead to the necessary

fundamental modelling of the large number of reactions occurring during these hydrocarbon

conversion processes. Major advantages of these models are 1. the limited number of kinetic

parameters and 2. the fundamental nature of the kinetic parameters which allows their

determination by ab initio calculations. Quantum chemical calculations will contribute to

obtain a quantitative description of the influence of the catalyst characteristics (e.g. zeolite

topology and acid strength) as well as of the influence of the hydrocarbon structure on the

selectivity and reactivity of zeolite catalyzed hydrocarbon conversion reactions (Thybaut et al.

(2005) and Narasimhan et al. (2004)). After implementation in a suitable reactor model, the

kinetic model will be used to simulate an industrial process. The proposed model will be

validated by comparing simulated yields with experimental data obtained on pilot plants

and/or industrial units.


1.3 Objective

An important acid catalyzed hydrocarbon conversion process is the alkylation of aromatics.

My master thesis is performed within the scope of this reaction, especially of the alkylation of

benzene with 1-octene for the formation of linear alkylbenzenes (LAB). The reaction network

of this alkylation reaction developed at the LPT is shown in Figure 1.1.

Figure 1.1: reaction network of the alkylation of benzene with 1-octene for the formation of linear alkylbenzenes

In order to understand the catalytic properties of the zeolites in which these reactions occur,

sufficient information about the adsorption of molecular species is required. The adsorption

and subsequent reactions of hydrocarbons on zeolites have already been carried out for a

number of experimental and theoretical methods in many different types of zeolites with

varying structure and size of micro pores or cages. It appears that the size and structure of the

micro pores as well as the molecular structure of the adsorbent determine the adsorption

energy. Of particular interest in this area of active research are the physisorption and

chemisorption of alkenes because these are the first elementary steps in most acid catalyzed

hydrocarbon conversion processes. Physisorption structures are characterized by the

formation of a π-complex between the acid site of the zeolite and the double bond of the

alkene. Protonation of the π-complex yields a chemisorption complex, the nature of which is

very sensitive to the local geometry of the active site and to the structure of the hydrocarbon


(primary, secondary or tertiary). The debate whether protonation of the π-complex leads to the

formation of a carbenium ion or an alkoxide is still going on. Although static calculations at

0K indicate alkoxides to be more stable, a recent study, using quantum chemical periodic

calculations, revealed that entropy effects play an important role and that carbenium ions are

more stable than alkoxides at higher temperatures (Tuma and Sauer (2005)). As an example,

the physisorption complex (π-complex, I)) and chemisorption complexes, i.e. the carbenium

ion (II-a) and the alkoxide (II-b), of 1-butene are depicted in Figure 1.2.

Figure 1.2: The physisorption complex (I) and the chemisorption complexes carbenium ion (II-a) and alkoxide (II-b) for 1-butene

The objective of this master proof is the ab initio calculation of kinetic parameters and

thermodynamic data, which are characteristic for the acid catalyzed reaction of hydrocarbons

on zeolites. As physisorption occurs in any zeolite catalyzed process before reaction can take

place, this intrazeolite phenomenon will be examined by computational techniques. The

intention is to investigate the influence of 1. hydrocarbon, e.g. hydrocarbon structure and

carbon number and 2. catalyst characteristics, e.g. acid strength and zeolite topology on the

physisorption energy. Simulations for the physisorption on an extensive set of alkenes and

alkanes have been performed, considering several zeolite frameworks (MFI, FAU and MOR),

which are industrially relevant and provide possibility to comparison with experimental data.

Another aim is to understand how different factors such as the aluminium content (Si/Al ratio)

and the zeolite framework affect the acidity of zeolites, since the catalytic performance of the

zeolite is strongly governed by the acid strength of the Brønsted sites as well as by the amount

of acid sites. Major research goals have been to find reliable experimental techniques for

characterizing the acid strength of different sites in different catalysts and to understand the

observed changes of the acidity when varying the structure of the catalyst and their


composition. While in experiments it is not always easy to separate the different factors,

quantum mechanical techniques can provide fundamental data on the acid strength of zeolitic

Brønsted sites which are not easily accessible by experiments. With this theoretical approach

it is possible to separate the influence of different parameters on the acidity of the zeolite

catalyst. First, the influence of the zeolite framework is investigated for the different zeolites

(ZSM-5, FAU and MOR) with only one aluminium substitution. Further, the influence of the

Si/Al ratio and the influence of the distance of the aluminium substitutions to the acid site is

studied in H-ZSM-5.


Reference List

Bates S.P., vanWell W.J.M., Vansanten R.A. and Smit B., Journal of Physical Chemistry, 100, 17573 (1996). Location and conformation of N-alkanes in zeolites: An analysis of configurational-bias Monte Carlo calculations.

Davis M.E., Microporous and Mesoporous Materials, 21, 173 (1998). Zeolite-based catalysts for chemicals synthesis.

Koller H., Overweg A.R., Vansanten R.A. and deHaan J.W., Journal of Physical Chemistry B, 101, 1754 (1997). C-13 and Na-23 solid-state NMR study on zeolite Y loaded with Mo(CO)(6).

Narasimhan C.S.L., Thybaut J.W., Marin G.B., Denayer J.F., Baron G.V., Martens J.A. and Jacobs P.A., Chemical Engineering Science, 59, 4765 (2004). Relumped single-event microkinetic model for alkane hydrocracking on shape-selective catalysts: catalysis on ZSM-22 pore mouths, bridge acid sites and micropores.

Schuring D., Jansen A.P.J. and van Santen R.A., Journal of Physical Chemistry B, 104, 941 (2000). Concentration and chainlength dependence of the diffusivity of alkanes in zeolites studied with MD simulations.

Smit B., Molecular Physics, 85, 153 (1995). Grand-Canonical Monte-Carlo Simulations of Chain Molecules - Adsorption-Isotherms of Alkanes in Zeolites.

Smit B. and Siepmann J.I., Journal of Physical Chemistry, 98, 8442 (1994). Computer-Simulations of the Energetics and Siting of N-Alkanes in Zeolites.

Thybaut J.W., Narasimhan C.S.L., Denayer J.F., Baron G.V., Jacobs P.A., Martens J.A. and Marin G.B., Industrial & Engineering Chemistry Research, 44, 5159 (2005). Acid-metal balance of a hydrocracking catalyst: Ideal versus nonideal behavior.

Tuma C. and Sauer J., Angewandte Chemie-International Edition, 44, 4769 (2005). Protonated isobutene in zeolites: tert-butyl cation or alkoxide?

Yashonath S. and Santikary P., Molecular Physics, 78, 1 (1993). Influence of Non-Geometrical Factors on Intracrystalline Diffusion Role of Sorbate Zeolite Interactions.

Chapter 2: Computational method 22

Chapter 2: Computational method

Physical as well as chemical processes play an important role in catalytic reactions taking

place inside zeolites. Experiments and simulations can help to understand these reactions with

regard to their reaction mechanism, kinetic and thermodynamic data, preferred reaction paths,

selectivity etc. The latter, studying intrazeolite processes by means of simulations, more

specifically by quantum chemical calculations, offers a tool to study elementary steps and

reactions at the catalytically active site of the zeolite. Moreover, insight into the influence of

the zeolite framework and of a varying acid strength, e.g. by varying the Si/Al ratio, is

obtained. The following types of quantum chemical calculations are discussed:

• Cluster calculations

• Periodic calculations

• Hybrid quantum mechanics / interatomic potential functions (QM-Pot) calculations

on embedded clusters

Quantum chemical periodic calculations have not been performed in this Master’s thesis, but

will be discussed shortly because it completes the total picture of the different types of

quantum chemical calculations that are possible on zeolites.

2.1 Cluster calculations

The hydrocarbon to zeolite interaction has been investigated mostly by means of the

molecular cluster approach. This cluster approach is the easiest way to simulate reactions

taking place inside zeolites. A fragment of the zeolite which contains the active site, usually a

3T to 5T cluster (T = Si or Al), is cut out from the zeolite structure (see Figure 2.1 for a 3T

cluster). Since there are some covalent bonds broken by cutting out the cluster, the cluster will

be chemical unstable. Because of the covalent nature of the zeolite lattice, hydrogen atoms are

used to saturate the terminal bonds: the Si-H termination is preferred compared to the SiO-H

termination as free optimization of the latter one causes hydrogen bonding between the

terminating hydrogen atoms and the oxygen atoms of the neighbouring O-H groups. These


gas phase clusters are used as a representative model of the entire zeolite framework. The

major advantage of cluster calculations is the relatively small computational cost. Moreover,

this method can give a quick insight into reaction mechanisms, possible intermediates and

transition state structures. The cluster approach however cannot guarantee a correct

description of the real zeolite framework: a 3T cluster is representative for all zeolite types

and cannot distinguish between different zeolite pore structures. Other problems are related to

the absence of both long-range electrostatic contributions and steric interactions of the closest

zeolite atoms with the reactive molecule. Progress in computer power as well as in

computational methods allows studies with increasingly larger clusters. A larger cluster model

can partly allow for the zeolite framework description. In particular, Zygmunt et al. (2000)

provided studies with large clusters, which led to a deeper insight into reactions catalyzed by

acidic zeolites. These large cluster models can partly describe the effect of the zeolite

framework (Sierka and Sauer (1997a) and Sherwood et al. (1997)). Relaxation of the cluster

during optimization causes the final structure to differ significantly from the starting structure

because the gas phase model allows all atoms to move freely compared to the more rigid real

zeolite structure. A known artefact of cluster calculations, which is a caused by this free

optimization, is e.g. the overestimation of Si-O and Al-O bond lengths. To avoid this, it has

been suggested to freeze terminal atoms of the fragment (Gale (1996), Nicholas (1997), Frash

and van Santen (1999) and Zygmunt et al. (1998)) or to constrain active site atoms in a plane

(Boronat et al. (1998)) to acquire a more realistic cluster model. The idea behind these

constraints is to simulate the rigidity of the zeolite framework or to maintain the zeolite-like

structure of the zeolite molecular fragment.

Figure 2.1: 3T cluster with Si(Al)-H termination, B3LYP/6-31g* optimized with Gaussian03.

Although it has been stated that geometry-optimized zeolitic clusters are good model systems

for the extended zeolite and this method has been extensively used in the past to study various

reactions of hydrocarbons in zeolites (see Kramer et al. (1991) and Kramer and van Santen


(1993)), the cluster approach can only be considered as an approximate model, as the physical

and chemical properties of a zeolite are influenced by short and long range electrostatic

contributions (Sastre et al. (2000a) and Sastre et al. (2000b)). The cluster calculations

performed during this Master’s Thesis are not performed with the intention to obtain

quantitative correct results, but rather to gain comprehension in the structure of the stable

intermediates and transition states and as a start for further, more advanced calculations.

The cluster calculations have been carried out on a 3T-cluster using the Gaussian03 program.

The B3LYP functional and a 6-31g* basis set are used (Frisch et al. (2004)).

2.2 Quantum chemical periodic calculations

Quantum chemical periodic calculations overcome the limitations that arise with the cluster

approach. A zeolite lattice is constructed by multiciplating a unit cell – all zeolites are

characterized by a unique unit cell – in the three spatial dimensions. Within this periodical

approach the topology of the inner surface of zeolites is preserved and no arbitrary cuts of the

periodicity of a structure are necessary. This leads to an accurate description of short- as well

as long-range electrostatic interactions. Moreover, the influence of the zeolite framework and

the steric interactions are properly taken into account. The advantage of the periodic approach

is that the entire system is described at a quantum chemical level. Reaction intermediates and

transition states can be calculated, which allows the study of reactivity in a more realistic

environment. The main disadvantage is the heavy computational effort, which limits the size

of the unit cell and as a consequence this method can difficultly be applied to study reaction

of hydrocarbons in industrially relevant zeolites, such as H-ZSM-5 which is characterized by

a unit cell containing 288 atoms. Figure 2.2 shows a mordenite unit cell doubled in the [001]

direction, which also contains 288 atoms in its SiO2 form: here however one silicon atom is

replaced by an aluminium atom, causing a negative charge in the zeolite framework, and a

hydrogen is added to compensate for this charge. The Vienna ab initio simulation package

(VASP) is used for the quantum chemical periodic calculations developed at the Institut für

Materialphysik of the Universität Wien (Kresse and Hafner (1993), Kresse and Hafner (1994),

Kresse and Furthmuller (1996a), Kresse and Furthmuller (1996b)). VASP performs an

iterative solution of the Kohn–Sham equations of density functional theory (DFT), based on

the minimization of the norm of the residual vector to each eigenstate and an efficient charge-

density mixing. The calculations are performed in a plane-wave basis set, using the projector-


augmented wave method (Kresse and Joubert (1999)) and a certain plane wave cut-off.

Besides the problem of the computational effort, another problem arises from the full DFT

calculations since the weak dispersion interactions (van der Waals interaction) between the

host molecule and the zeolite are not properly described, which leads to a significant

underestimation of the physisorption energies. As one of the main interests in this Master’s

Thesis deals with the study of physisorption of alkenes in different zeolites and because of the

huge computational requirements, this calculation method has not been applied in this work.

Figure 2.2: Mordenite unit cell containing 289 atoms viewed along the c-axis.


2.3 Hybrid QM-Pot calculations on embedded clusters

The increasing demand for computational resources with increasing size of the chemical

systems of interest is the major factor that hampers the application of ab initio methods, such

as periodic DFT calculations, to industrially important zeolites like faujasite, mordenite and

ZSM-5. A possible solution for the problem is to limit the quantum mechanical (QM)

treatment to the “active part” of the system, and to describe its environment by simple

parameterized interatomic potential functions. Such approaches are known as hybrid quantum

mechanics / molecular mechanics (QM/MM) embedded cluster methods. The term “molecular

mechanics” however stresses the force field type of the interatomic potential function such as

CFF91 (Maple et al. (1988)) or CHARMM (Gelin and Karplus (1979)) which are most useful

for organic molecules and biomolecules, while inorganic solids are better described by ion-

pair potential functions (Eichler et al. (1997)). Therefore, we prefer the more general term

combined quantum mechanics / interatomic potential functions approach, QM-Pot.

The QM-Pot approach divides the entire system (S) into two parts: the inner part, which is the

embedded cluster (C) terminated by hydrogen link atoms and the remaining, outer part of the

zeolite unit cell. The QM-Pot energy is calculated using the following subtraction scheme:

CPotSPotCQMSPotQM EEEE ,,,, −+=−

Where: CQME , is the QM-energy of the cluster,

SPotE , is the Pot-energy of he whole system (i.e. zeolite unit cell) and

CPotE , is the Pot-energy of the cluster.

In Figure 2.3 a graphical representation is given of the embedded cluster, treated at quantum

mechanical level and of the remaining part of the zeolite unit cell, treated with interatomic

potential functions. The treatment of the link atoms is very important as their possible

contribution to the total QM-Pot energy should be kept as small as possible. From theoretical

deduction it is found that the better the interatomic potential function fits the quantum

mechanical potential energy surface for the terminating atoms, the smaller the influence of the

link atoms on the total QM-Pot energy is (Sauer and Sierka (2000)). The hydrogen link atoms

play the role of “a quarter of a silicon atom” in case of SiO-H termination or of “one-half of

an oxygen atom” in case of Si-H termination. The electronegativity of H is between that of Si

and O and thus H accepts electrons from Si (as O does), and it donates electrons to O (as Si

does). This explains the success of the H-termination for clusters of zeolites. Of course, the


link atoms only approximately simulate the electronic effect of the outer part (the bulk of a

solid), and there must be taken care of that the cluster is large enough to allow for all

significant charge delocalization effects. It is very important to check how the results

converge with the cluster size, and how they depend on the particular choice of the cluster.

This is also true for all types of combined QM-Pot (hybrid QM/MM) calculations.

In the following paragraphs, the QM-Pot method will be discussed more in detail. More

specifically its implementation will be discussed, i.e. the coupling of TURBOMOLE, which is

used for the quantum mechanical calculations and GULP, the program in which the ion-pair

shell potential force field is implemented, to obtain combined QM-Pot results.

Figure 2.3: the QM-Pot scheme representing the QM-part, i.e. embedded cluster terminated by hydrogen link atoms and the Pot (MM in the figure) part, i.e. the remainder of the zeolite unit cell.


2.3.1 QM-Pot computational details

All quantum chemical calculations use the Density Functional Theory (DFT) and the B3LYP

exchange-correlation functional (Becke (1993)). As already mentioned, these DFT

optimisations are performed using the TURBOMOLE program (Ahlrichs et al. (1989) and

Treutler and Ahlrichs (1995)). A T(O)DZP basis set is adopted: a triple-ζ basis set is used for

the oxygen atoms and a double-ζ basis sets for all the other atoms (Si, Al, H and C). The 3T

cluster is mechanically embedded in the zeolite unit cell structure and terminated by OH

groups. The hydrogen atoms are constrained on the broken O-Si bond at a fixed distance of

the oxygen atom, i.e. 0.9666Å in case of SiO-H termination and 0.9628 Å in case of AlO-H

termination. These distances are equilibrium distances obtained by free cluster optimizations

of similar cluster models and are proposed by the developers of the QM-Pot program.

All potential function calculations employ the GULP (General Utility Lattice Program)

program (Gale (1997)). As interatomic potential functions, shell-model ion-pair potentials,

introduced by Dick and Overhauser (1958) are used. The ion-pair potential represents the ions

(often the anions only) by a pair of point charges, the positive core and the negative and mass-

less shell, which are connected by a harmonic spring. In this way, the polarization of the ions

in an electric field is taken into account. The sum of the charges on the core and the shell is

equal to the charge on the ion. All short-range interactions are defined between shells rather

than cores which is consistent with the assumption that the short-range repulsion is caused by

electron repulsion. The full ion-pair potential expression is given by Schroder and Sauer

(1996):

bodyrangeshortshellcoreelec EEEEE −−− +++= 3

The first three terms are pair interactions. The Coulomb energy, Eelec, is a sum that runs over

all point charges, both cores and shells:

∑−=

jijiji

elec rqqE,

1

where rij is the distance between the point charges i en j.

The core-shell interaction runs over all ions for which the shell model is used and acts

between core and shell:

∑=−

iii

shellcore rkE 2


where ri is the actual distance between the ith core and its shell and ki is the spring constant.

The short-range interaction of ions is described by a purely repulsive term between shells and

cations, expressed by the Buckingham potential:

∑−− −=

lkklklkl

rangeshort rAE,

1)exp( ρ

This function is frequently extended by a term which describes the dispersion energy:

∑−−

lkklkl rC

,

6

Between ions of equal charge no short-range repulsion term is defined since the electrostatic

repulsion dominates.

For tetrahedral coordinated atoms often a so-called Three-Body interaction term is added to

the potential expression:

∑∑ −=−

i kjoijkib

body kE,

2,

3 )(2

1 ϑϑ

The indices j en k run over the shells of all oxygen atoms that are bonded to the T atom i. This

term is typical for molecular mechanics potential functions rather than for ionic ones. It gives

the TO4 tetrahedron additional stiffness. The reference angle θ0 usually is 109.47°. It is

assumed that such a term is needed to take into account that the T-O bond is partly covalent

and that the hybridization of the T atom is sp3.

The electrostatic energy is evaluated by the standard Ewald summation technique. For the

summation of short-range interactions, a cut-off radius of 10 Ǻ is chosen. All interatomic

potential functions have been parameterized using DFT results for cluster models of

protonated forms of zeolites by Sierka and Sauer (1997b)and are listed in Table 2.1. Two

types of oxygen atoms are considered, Ob and O: the former is used for the oxygen to which

the acidic proton is bonded or for the oxygen in the alkoxide bond (bonded with carbon

atom), while the latter is used for all other oxygen atoms. Also note that Hb is used for the

acidic proton and Ht for the termination hydrogen link atoms.


Table 2.1: Parameters of the DFT B3-LYP derived shell-model potential.

charges (e)

Core shell

Si 4.0 -

Al 3.0 -

O 1.22858 -3.22858

Ob 0.81753 -2.81753

Hb 1.0 -

Ht 1.0 -

short-range repulsion

A (eV) ρ (Å)

Si-O 1612.45920 0.29955

Si-Ob 997.88097 0.33212

Al-O 1395.77463 0.30449

Al-Ob 1644.88177 0.29139

Ob-Hb 368.64803 0.22511

O-Hb 7614.58003 0.19913

O-Ht 772.06814 0.18524

core-shell interaction

k (eV Å-2)

O 122.47853

Ob 70.15123

three-body interaction

kb (eV rad-2) θ0 (rad)

O-Si-O 0.144703 109.47

Ob-Si-O 0.384711 109.47

O-Al-O 0.893930 109.47

Ob-Al-O 0.686678 109.47

2.3.2 Hydrocarbons in zeolites: extension of the zeolite force field

The force field described above only describes interactions between zeolite atoms (Si, Al, O,

H). However when studying physisorption and chemisorption of alkenes in zeolites, the

zeolite force field needs to be extended. As well the interactions between the zeolite and the

hydrocarbon as the internal hydrocarbon bonds and angles need to be described.


The interaction of the alkene with the zeolite framework is described by the force field

including point charge interactions, i.e. the Coulomb energy term, and Lennard-Jones terms.

The latter is taken from the original CVFF force field provided with the Discover program of

Accelrys Inc. We use the 6-12 Lennard-Jones potential with a cut-off of 40 Å. The general

form of the Lennard-Jones potential between atom i and atom j is given by:

612ij

ij

ij

ijij

r

B

r

AV −=

In which Aij and Bij are calculated by the following expressions:

jiij

jiij

BBB

AAA

=

=

The Lennard-Jones potential acts between carbon or hydrogen atoms of the hydrocarbon on

the one hand and silicon, aluminium and oxygen atoms of the zeolite on the other hand. The A

and B values for each atom are listed in Table 2.2 and a graphical representation of the

Lennard-Jones potential is given in Figure 2.4. The Lennard-Jones potential accounts for

stabilizing as well as repulsive interactions. The former one is linked with the stabilizing van

der Waals interactions and essential to describe physisorption of alkenes in zeolites in a

proper way as will be shown later. The latter one only acts if the hydrocarbon comes too close

to the zeolite framework and is therefore linked with the steric hindrance.

Figure 2.4: The Lennard-Jones potential.


Table 2.2: Parameters A and B used in the expression for the Lennard-Jones potential.

atom A (eV Å12) B (ev Å6)

Csp3 77636.68281260 22.91719173

Csp2 128737.36099524 57.48815803

H 308.25289998 1.42541402

Si 136561.43622211 30.78857787

Al 136561.43622211 30.78857787

O 11833.86243143 21.63347716

In the zeolite force field, no potentials are available describing the internal hydrocarbon bonds

and bond angles or describing the C-O alkoxide bond. Although this C-O bond is treated

within the quantum chemical calculation, as it is a part of the embedded cluster, the lack of a

C-O bond describing parameter in the force field can cause serious problems with regard to

the treatment of the oxygen cores and shells, which are included to account for polarization

effects. Especially the core-shell distance of the alkoxide oxygen atom is in the force field

calculation unrealistically large. This large dipole influences other oxygen atom dipoles not to

far away from the alkoxy bond and as this region is too large, the errors made are not summed

out by the subtraction scheme (see page 26). The potential function chosen to model the

bonds and the bond lengths are the Morse and the Three-Body potential. The general

expressions for both potentials are:

( )( )( )[ ]( )2

0

20

2

1

1exp1

θθ −=

−−−−=

− bBodyThree

eMorse

kE

rraDE

in which De, a and r0 are parameters to be estimated. In order to estimate C-O and internal

hydrocarbon bond describing parameters, a scheme for assigning the charges on the

hydrocarbon atoms has been proposed (see Appendix 1) and a database containing distorted

and optimized structures has been built up. The ab initio calculations have been performed

with TURBOMOLE using the T(O)DZP basis set. The obtained database consists of the

following structures:

• gas phase hydrocarbons (80 structures)

• physisorption complexes on a 14T cluster (19 structures)

• chemisorption complexes on a 14T cluster (15 structures)


Note that the equilibrium angles θ0 are kept fixed at 120.00 degrees for sp2 hybridization and

at 109.47 for sp3 hybridization. Estimation of the parameters was performed by fitting the

force field calculated gradients (i.e. the 1st derivative of the potential energy to x, y and z) on

all atoms to the ab initio calculated ones. The final parameters are listed in Table 2.3.

Table 2.3: Overview of the parameters estimations for the C-O and hydrocarbon bond describing potentials

Bonds (Morse) De (eV) a (Å−−−−1) r 0 (Å)

Csp2–Csp2 1.9947 2.5977 1.3271

C–H 1.4284 2.2707 1.1172

Csp2–H

Csp3–H

Csp3–C 1.4262 2.2722 1.4814

Csp3–Csp2

Csp3–Csp2

Csp3–O 0.9526 1.3651 1.8288 Angle (Three-Body) K (eV rad−−−−2) θ0 (rad)

H–Csp2–H 1.0074 120.00

H–Csp2–C 1.6048 120.00

H–Csp2–Csp3

H–Csp2–Csp2

C–Csp2–C 1.7965 120.00

Csp2–Csp2–Csp2

Csp2–Csp2–Csp3

Csp3–Csp2–Csp3

H–Csp3–H 1.1704 109.47

H–Csp3–C 1.5839 109.47

H–Csp3–Csp3

H–Csp3–Csp2

C–Csp3–C 2.2766 109.47

Csp2–Csp3–Csp2

Csp2–Csp3–Csp3

Csp3–Csp3–Csp3

C–Csp3–O 1.9585 109.47

Csp2–Csp3–O

Csp3–Csp3–O


2.3.3 Implementation

The implementation of the presented embedding scheme combines ab initio code

TURBOMOLE (Ahlrichs et al. (1989) and Treutler and Ahlrichs (1995)) for the cluster with

the shell model ion-pair potential for the environment of the cluster. These shell model

calculations are carried out with the GULP program (Gale (1997)). Both programs were

discussed in more detail in the previous paragraphs. The coordinate input contains two

separate sections: the first one contains the coordinates of the system, i.e. the whole zeolite

unit cell and the second one the coordinates of the cluster, typically the 3T embedded cluster

and a hydrocarbon. Regarding the QM-Pot subtraction scheme (see page 26) several

calculations need to be performed. For all cluster atoms, both QM and Pot energies and

energy gradients have to be calculated, whereas for all other atoms, i.e. these located in the

outer part, only the Pot contribution has to be evaluated. The use of the shell model requires

the optimisation of the shells of the cluster and the host while the cores are fixed. For the

configurations with the converged shell positions, the energies and energy gradients are

calculated for the cores and then combined with the energies and energy gradients resulting

from the SCF calculation resulting in a combined QM-Pot energy and energy gradient. The

combined energy gradient is then used by an optimizer which updates the structure for the

next cycle until convergence is reached as measured by the change of the total energy. A flow

chart of the implementation is shown in Figure 2.5.

2.4 Conclusions

Compared with non-embedded cluster calculations, the QM-Pot approach is more reliable

since the entire zeolite framework is taken into account. Moreover, the topology of the inner

surface of zeolites is preserved and this makes it possible to study the effect of steric

constraints and electrostatic contributions that arise from the zeolite wall close to the site of

interest. Generally, the part of the zeolite unit cell treated by quantum chemical calculations is

a 3T cluster, which is of the same size of non-embedded cluster calculations. The remaining

part of the unit cell, that may contain more than 200 atoms, is treated by interatomic potential

functions. As this technique is much less time consuming than full ab initio methods, QM-Pot

offers the possibility to include the influence of the zeolite framework and steric hindrance in

a reasonable calculation time that is comparable with the time required for non-embedded

cluster calculations.


Figure 2.5: Implementation of the QM-Pot embedding scheme (Eichler et al. (1997))

Compared with full DFT periodic calculations, the computational effort is significantly

reduced. Apart from this, some extra remarks should be made however:

• Polarization of the outer part atoms by the active part of the system is treated at

interatomic potential level, whereas in periodic DFT calculations this is at quantum

chemical level.

• The link atoms only approximately simulate the electronic effect of the outer part and

therefore care must be taken that the size of the cluster is large enough to allow for all

significant charge delocalization effects.

• The convergence or independency of the results with increasing cluster size should be

checked if possible.


Accounting for these remarks, it is clear that the QM-Pot method and QM/MM methods in

general offer a powerful tool to study catalytic reactions inside zeolites with a very good

balance between the computational power needed and the correctness of the zeolite model.

Moreover, for the particular problem of hydrocarbon reactions in zeolites, the QM-Pot

approach has the additional advantage that adsorption energies are described properly, since

the interatomic Lennard-Jones potentials provide a good description of weak dispersion

forces, the van der Waals interactions.


Reference List

Ahlrichs R., Bar M., Haser M., Horn H. and Kolmel C., Chemical Physics Letters, 162, 165 (1989). Electronic-Structure Calculations on Workstation Computers - the Program System Turbomole.

Becke A.D., Journal of Chemical Physics, 98, 5648 (1993). Density-Functional Thermochemistry .3. the Role of Exact Exchange.

Boronat M., Viruela P. and Corma A., Journal of Physical Chemistry A, 102, 982 (1998). Theoretical study of the mechanism of zeolite-catalyzed isomerization reactions of linear butenes.

Dick B.G. and Overhauser A.W., Physical Reviews, 112, 90 (1958).

Eichler U., Kolmel C.M. and Sauer J., Journal of Computational Chemistry, 18, 463 (1997). Combining ab initio techniques with analytical potential functions for structure predictions of large systems: Method and application to crystalline silica polymorphs.

Frash M.V. and van Santen R.A., Topics in Catalysis, 9, 191 (1999). Quantum-chemical modeling of the hydrocarbon transformations in acid zeolite catalysts.

Gaussian 03, revision B.03, Gaussian, Inc.: Wallingford CT, 2004

Gale J.D., Journal of the Chemical Society-Faraday Transactions, 93, 629 (1997). GULP: A computer program for the symmetry-adapted simulation of solids.

Gale J.D., Topics in Catalysis, 3, 169 (1996). A density functional study of molecular adsorption in zeolites.

Gelin B.R. and Karplus M., Biochemistry, 18, 1256 (1979). Side-Chain Torsional Potentials - Effect of Dipeptide, Protein, and Solvent Environment.

Kramer G.J., Deman A.J.M. and van Santen R.A., Journal of the American Chemical Society, 113, 6435 (1991). Zeolites Versus Aluminosilicate Clusters - the Validity of A Local Description.

Kramer G.J. and van Santen R.A., Journal of the American Chemical Society, 115, 2887 (1993). Theoretical Determination of Proton Affinity Differences in Zeolites.

Kresse G. and Furthmuller J., Physical Review B, 54, 11169 (1996a). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.


Kresse G. and Furthmuller J., Computational Materials Science, 6, 15 (1996b). Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set.

Kresse G. and Hafner J., Physical Review B, 49, 14251 (1994). Ab-Initio Molecular-Dynamics Simulation of the Liquid-Metal Amorphous-Semiconductor Transition in Germanium.

Kresse G. and Hafner J., Physical Review B, 47, 558 (1993). Abinitio Molecular-Dynamics for Liquid-Metals.

Kresse G. and Joubert D., Physical Review B, 59, 1758 (1999). From ultrasoft pseudopotentials to the projector augmented-wave method.

Maple J.R., Dinur U. and Hagler A.T., Proceedings of the National Academy of Sciences of the United States of America, 85, 5350 (1988). Derivation of Force-Fields for Molecular Mechanics and Dynamics from Abinitio Energy Surfaces.

Nicholas J.B., Topics in Catalysis, 4, 157 (1997). Density functional theory studies of zeolite structure, acidity, and reactivity.

Sastre G., Fornes V. and Corma A., Journal of Physical Chemistry B, 104, 4349 (2000a). Preferential siting of bridging hydroxyls and their different acid strengths in the two-channel system of MCM-22 zeolite.

Sastre G., Lewis D.W. and Corma A., Physical Chemistry Chemical Physics, 2, 177 (2000b). The role of the electrostatic potential, electric field and electric field gradient on the acidity of AFI and CHA zeotypes.

Sauer J. and Sierka M., Journal of Computational Chemistry, 21, 1470 (2000). Combining quantum mechanics and interatomic potential functions in ab initio studies of extended systems.

Schroder K.P. and Sauer J., Journal of Physical Chemistry, 100, 11043 (1996). Potential functions for silica and zeolite catalysts based on ab initio calculations .3. A shell model ion pair potential for silica and aluminosilicates.

Sherwood P., de Vries A.H., Collins S.J., Greatbanks S.P., Burton N.A., Vincent M.A. and Hillier I.H., Faraday Discussions, 79 (1997). Computer simulation of zeolite structure and reactivity using embedded cluster methods.

Sierka M. and Sauer J., Faraday Discussions, 41 (1997a). Structure and reactivity of silica and zeolite catalysts by a combined quantum mechanics shell-model potential approach based on DFT.

Sierka M. and Sauer J., Faraday Discussions, 41 (1997b). Structure and reactivity of silica and zeolite catalysts by a combined quantum mechanics shell-model potential approach based on DFT.

Treutler O. and Ahlrichs R., Journal of Chemical Physics, 102, 346 (1995). Efficient Molecular Numerical-Integration Schemes.


Zygmunt S.A., Curtiss L.A., Zapol P. and Iton L.E., Journal of Physical Chemistry B, 104, 1944 (2000). Ab initio and density functional study of the activation barrier for ethane cracking in cluster models of zeolite H-ZSM-5.

Zygmunt S.A., Mueller R.M., Curtiss L.A. and Iton L.E., Journal of Molecular Structure-Theochem, 430, 9 (1998). An assessment of density functional methods for studying molecular adsorption in cluster models of zeolites.

Chapter 3:Cluster Calculations 40

Chapter 3: Cluster Calculations

As already mentioned in Chapter 2 , discussing the different possible simulation methods in

general, the gas phase clusters, terminated by hydrogen atoms are somewhat a rough approach

for modelling a zeolite. This is because of the absence of the long-range contributions and

steric interactions of the closest atoms of the zeolite on the reactive molecule missing.

Nevertheless, cluster calculations are very useful to gain insight in the structure of stable

intermediates and transition states and to do a quick scanning of possible reaction paths.

Moreover, this kind of calculations offers a good starting point for the more advanced

quantum chemical periodic calculations and QM-Pot calculations. The cluster calculations are

performed with the Gaussian03 using a 6-31 g* basis set and a B3LYP functional. Within this

approach the zeolite active site is described by a small fragment of the zeolite framework,

containing only a couple of tetrahedral atoms. This consequently reduces the computational

cost significantly, which is non surprisingly one of the biggest advantages of this method. The

cluster used to simulate the active site of the zeolite consists of one aluminium and two silica

tetrahedral atoms. The dangling bonds that appear due to the Si-O and Al-O bond breaking in

the real zeolite structure are saturated with hydrogen atoms. Si(Al)-H and not Si(Al)O-H

terminations were chosen to avoid formation of unnatural hydrogen bonds which are clearly

not present in the real zeolite. In the simulations, the heavy atoms of the cluster (silicon,

aluminium and the oxygen’s in between) were constrained to be in the same plane to avoid

artificial distortions that would not occur in the zeolite structure. The 3T cluster is the

minimum size the cluster must have to contain both the Brøndsted acidic hydroxyl group and

neighbouring basic oxygen, and therefore, it can correctly model the bifunctional nature of the

zeolite active sites. Because of the fact that 4T or 5T cluster sizes will not change the

qualitative picture and conclusions for these calculations and because of the fact that these

calculations are only a starting point for further calculations, a 3T cluster as model for our

zeolite was considered to be sufficient.


3.1 Physisorption and chemisorption of alkenes

Cluster calculations are performed to study the physisorption of 1-butene, 2-butene and

isobutene. Physisorption structures of alkenes are not only characterized by an interaction of

the hydrocarbon molecule with the highly polarisable oxygen atoms of the zeolite wall, but

also by the formation of a π-complex between the acid site of the zeolite and the alkene

double bond. The former interactions are largely neglected due the choice of a 3T cluster as

zeolite model. Protonation of the physisorption complex leads to the formation of a

chemisorption complex, which are at 0 K covalently bonded alkoxy structures (σ-complexes).

This has been expected since cluster calculations totally neglect possible steric hindrance of

the zeolite wall that could avoid C-O bond formation. Protonation of 1-butene and 2-butene

are both considered to lead to a secondary 2-butoxy complex. For isobutene, formation of the

primary isobutoxy and the tertiary t-butoxy are studied.

For each butene, the optimized geometry of the transition state leading to the formation of an

alkoxy structure was calculated first. For this purpose, the structures and distances mentioned

in literature (e.g. Boronat et al. (1998)) were used as a starting point. It has always been

verified that the transition state was characterized by an imaginary frequency corresponding

with the protonation of the alkene. Once these transition states were found, the reactants (π-

complexes) and products (σ-complexes) were optimized, by introducing small distortions

along the reaction coordinate. When the proton is moved a little in the direction of the zeolite

cluster, the physisorption complexes are found, whereas the chemisorption complexes are

obtained when the proton is displaced in the direction of the butene. Figure 3.1 depicts the

relative energy diagram for physisorption and chemisorption of alkenes in which following

definition have been used:

• physE∆ is the physisorption energy,

• aE is the activation energy and aphyscompa EEE +∆= is the composite activation

energy,

• protE∆ is the protonation energy and

• protphyschem EE ∆+∆=∆ is the chemisorption energy.


Figure 3.1: relative energy diagram for the protonation of an alkene

Al

O2

O1

Si2Si

1

H

C1

C2

R1

R2

R3

R4 (a)

C1 C

2R1

R2

R3

R4

Al

O2

O1

Si2Si

1

H

(b)

C1

R1

R2

H C2

Al

O2O

1

Si2Si

1

R3

R4

(c)

Figure 3.2: nomenclature used for the physisorption (a), transition state (b) and the chemisorption (b) complex on a 3T cluster


The optimized values of the most important geometric parameters of the π-complexes, alkoxy

complexes and transition states for 1-butene, 2-butene and isobutene are given in Table 3.1.

The nomenclature used (Si1, Si2, O1, O2, etc.) is clarified in Figure 3.2.

Table 3.1: The most important geometric parameters of the optimized structures

1-butene (2-butoxy) 2-butene (2-butoxy) isobutene (t-butoxy)

π TS σ π TS σ π TS σ

Distance (Ǻ)

Al-O1 1.99 1.86 1.75 1.99 1.84 1.75 1.98 1.84 1.75

Al-O2 1.75 1.81 2.02 1.75 1.84 2.01 1.76 1.83 2.04

O1-Si1 1.71 1.67 1.63 1.71 1.66 1.64 1.71 1.66 1.63

O2-Si2 1.63 1.64 1.71 1.63 1.65 1.71 1.64 1.65 1.71

O1-H 0.99 1.38 - 0.99 1.39 - 0.99 1.41 -

H-C1 2.25 1.25 1.09 2.25 1.25 1.09 2.19 1.25 1.09

H-C2 2.29 2.03 - 2.18 2.04 - 2.34 2.12 -

C1-C2 1.34 1.39 1.52 1.34 1.41 1.53 1.35 1.41 1.53

O2-C2 3.43 2.46 1.49 3.45 2.23 1.49 3.67 2.40 1.51 Angle (deg)

O1-Al-O2 95.67 97.71 102.81 98.20 97.35 103.07 98.00 98.70 105.03

Al-O1-Si1 129.08 133.27 150.78 123.83 134.72 143.52 126.66 133.04 150.90

Al-O2-Si2 148.82 129.04 116.54 145.25 125.24 115.87 141.46 119.59 110.72

Al-O1-H 113.97 108.73 - 116.78 106.33 - 117.48 107.13 -

Al-O2-C2 - 118.07 126.61 - 120.73 126.41 - 120.75 124.49

O2-C2-C1 119.08 105.53 108.42 125.02 106.33 109.73 116.85 103.47 106.42

For the three physisorption structures, the calculated distances are very similar. In the three π-

complexes, the acid proton of the zeolite cluster is nearly equidistant from the two carbon

atoms of the double bond: all H-Cdouble bond distances are between 2.18Ǻ (2-butene) and 2.34Ǻ

(isobutene). The structural changes when going from the physisorbed structure to the

transition state are similar for the three structures. The most important changes occur in the H-

Cdouble bond distances and the Al-O2-Si2 angles. All H-Cdouble bond distances decrease: the

distance between H and the C1 carbon atom to which H is transferred during the protonation

reaction decreases with 1.0Ǻ for 1-butene and 2-butene and 0.94Ǻ for isobutene, while the

maximum decrease in distance between the C2 atom, which is the other carbon atom of the

double bond, and the acid proton H amounts to 0.26Ǻ (1-butene). The C1-C2 bond lengths

elongate to 1.39Ǻ for 1-butene and to 1.41Ǻ for 2-butene and isobutene, which are distances

situated between the typical bond lengths for a C-C single (~1.52Ǻ) and a C-C double bond


(~1.33Ǻ). The Al-O2-Si2 angles reduce about 20° for the three structures. For the shift from

transition state to alkoxy complex, the changes are again very similar for the three structures.

The most prominent geometric changes are the decreasing distance between the C2 carbon

atom of the double bond and O2 (i.e. the alkoxy formation), the increasing Al-O1-Si1 angle and

the decreasing Al-O2-Si2 angle. The C2-O2 alkoxy bond is formed and the distances equal

1.49Å and 1.51Å for 2-butoxy and t-butoxy respectively. The slightly higher C-O distance in

case of the tertiary t-butoxy may be caused by a somewhat higher repulsion (steric hindrance)

between the hydrocarbon and the 3T-cluster model, although this difference is minimal here

and expected to be more pronounced in more realistic zeolite models, such as the models used

in QM-Pot calculations. The optimized C-C bond lengths of the alkoxy complexes are all

between 1.52 Ǻ and 1.53 Ǻ, typical distances for C-C singles bonds. The Al-O1-Si1 angle

increases from 133° to 150° for the 2-butoxy of 1-butene and t-butoxy, whereas the 2-butoxy

of 2-butene increases from 135 to only 143°. The Al-O2-Si2 angle on the other hand decreases

about 10° for 2-butoxy of 2-butene and t-butoxy, while the 2-butoxy of 1-butene decreases

with 13°. Other remarkable geometric parameters are the angles around the C2 atom: the C1-

C2-C3 angle and the dihedral angle around C2 are considered; the dihedral angle is

characterized by the C2 atom and its three bonding partners. For the π–complexes the C1-C2-

C3 angle amounts to 125.6° for 1-butene and 2-butene and to 121.9° for isobutene, while the

dihedral angle is 179° for the three structures. These values were expected because the C1 and

C2 carbon atom have a sp2 hybridization due to the C1-C2 double bond. The transition states

are carbenium ion like with C1-C2-C3 angles around 120° for the three structures and dihedral

angles of 172°, 157° and 164° for respectively 1-butene, 2-butene and isobutene. Finally, the

angles around the C2 atom of the alkoxy intermediates are between 110° and 116.1°; the

dihedral angle around the C2 atom is 122.7° and 124.5° for 2-butoxy starting from

respectively 1-butene and 2-butene and 123.5° for t-butoxy. These results fulfil our

expectations: the C2 carbon atom of the alkoxy intermediates has a sp3 hybridization and

therefore a C1-C2-C3 angle of around 109° and an dihedral angle of around 120° are expected.

The optimized structures for the π-complex, transition state and σ-complex for isobutene are

depicted in Figure 3.3.


Figure 3.3: optimized structures for the π-complex (a), transition state (b) and σ-complex (c) for isobutene

The calculated physisorption, activation and protonation energies are listed in Table 3.2. The

nomenclature as defined in Figure 3.2 is used.

Table 3.2: physisorption, activation and protonation energies for 1-butene, 2-butene and isobutene on a 3T cluster

alkene type alkoxy Energies [kJ/mol]

complex ∆Ephys Ea Eacomp ∆Eprot ∆Echem

1-butene secondary -28.1 93.4 65.3 -51.7 -79.8

2-butene secondary -34.4 107.3 72.9 -39.8 -74.1

isobutene tertiary -29.2 89.3 60.1 -31.6 -60.8

isobutene primary -28.9 141.7 112.9 -27.8 -56.6

The physisorption energies ∆Ephys for the different butenes vary from -28.1 kJ/mol for 1-

butene to -34.4 kJ/mol for 2-butene. Similar results are obtained by Boronat et al. (1998) with

Gaussian94 using the B3P86 functional and the 6-31G** basis set: they found physisorption

energies of -29.7 kJ/mol for 1-butene, -30.1 kJ/mol for 2-butene and -31.8 kJ/mol for

isobutene. Cluster calculations were also carried out by Li et al. (2005) with Gaussian03 using

the B3LYP functional and the 6-31G** basis set: they found a physisorption energy of -34.0

(c)

(b)

(a)


kJ/mol for 1-butene and -42.8 for 2-butene. The difference with our results may be due to the

fact that they use Si(Al)O-H terminations for the dangling bonds of the cluster.

The activation energies Ea differ a lot for the different butenes: the lowest value was found for

the protonation of isobutene leading to t-butoxy and the highest in case of protonation of

isobutene to isobutoxy. The activation energies for 1-butene and 2-butene are situated

between these two values. These results were expected as the transition states resemble

carbenium ions as already mentioned in the discussion of the geometric parameters. The

protonation transition state of isobutene is very close to a tertiary carbenium ion, which is the

most stable carbenium ion compared to primary and secondary ones, and as a consequence it

is characterized by the lowest activation barrier. The protonation of isobutene leading to the

isobutoxy intermediate on the other hand is characterized by formation of a primary

carbenium ion and has the highest activation barrier as primary carbenium ions are known to

be very unstable and almost impossible to be formed. Finally, protonation of 1-butene and 2-

butene are characterized by secondary carbenium ion like transition state. Their stability is

situated between those of the primary and ternary carbenium ions and consequently their

activation energies are found between the values found for the isobutenes. Boronat et al.

(1998) calculated the activation energy for protonation of 1-butene and isobutene (with

formation of isobutoxy) and found respectively 84.6 kJ/mol and 131.5 kJ/mol. These values

differ from ours by approximately 10 kJ/mol, which may be due to the different functional

and basis set used. It is clear however that their and our results follow the same tendency.

The chemisorption energy ∆Echem varies between -56.6 kJ/mol for isobutoxy and -79.8 kJ/mol

for 2-butoxy. Although the chemisorbed structures of 1-butene and 2-butene are both the

same secondary butoxy complex, the σ-complex of 1-butene is 5.7 kJ/mol more stable than

the σ-complex of 2-butene. This difference is attributed to the fact that 2-butene in the

gasphase 6.7 kJ/mol more stable is than 1-butene. Another remark can be made: the

chemisorption energy of the t-butoxy structure is lower than the energy of the isobutoxy

structure. This strikes with our expectations, because a primary alkoxide is normally more

stable than a tertiary alkoxide. The chemisorption energies obtained by Boronat et al. (1998)

amount to -100.1 kJ/mol for 2-butoxy, -83.3 kJ/mol for t-butoxy and -77.5 kJ/mol for

isobutoxy. Again, the same tendency is observed, but now the energies differ about 20kJ/mol

with our results.

For all optimized structures, a frequency calculation was carried out to verify whether the

intermediates are real minima on the potential energy surface. In case of transition states, one


imaginary frequency, corresponding with the reaction coordinate is expected. In our

calculations however, some small unexpected imaginary frequencies are appearing in the

intermediates and the transition states. These frequencies typically lay in the range of 11i cm-1

to 23i cm-1 and are caused by constraining the heavy atoms (Si, Al and O1 and O2) in a plane.

This has been reported in literature as one of the drawbacks of applying constraints (Rigby et

al. (1997)), however it will never change the qualitative interpretation of the results. The

transition states for the formation of an alkoxy structure all have an important, expected

imaginary frequency, namely the vibration modes of 533i cm-1 for 1-butene, 589i cm-1 for 2-

butene and 488i cm-1 and 590i cm-1 for isobutene (formation of t-butoxy and isobutoxy

respectively) were obtained and these are clearly associated with the movement of the acid

proton of the zeolite cluster towards a carbon atom of the double bond of the butene, that is

being protonated.

3.2 Double bond isomerization

The double bond isomerization is an important reaction in the reaction network for the

production of linear alkylbenzenes, as discussed in the introduction. In this work, the double

bond isomerization is studied via small cluster calculations for a few model components,

namely the different butenes, because most experimental data are found for these alkenes. The

double bond isomerization in linear olefins is a fast process that requires relatively weak acid

sites and it can occur through two reaction mechanisms. On the one hand Boronat et al.

(1998) proposed a concerted mechanism, where the double bond isomerization proceeds in a

one-step mechanism from the physisorbed state, on the other hand Kazansky (1991) and

Kazansky (1994) proposed a two-step mechanism that takes place via adsorption/desorption,

where chemisorbed intermediates are formed.

3.2.1 Concerted mechanism

In the concerted mechanism, the double bond isomerization proceeds from the physisorbed

state and does not involve the formation of either ionic or covalent alkoxy intermediates. This

mechanism occurs in one step and the corresponding optimized transition state, with its most

important geometric parameters is shown in Figure 3.4: the proton (H1) of the acid hydroxyl

group of the zeolite protonates the C1-atom of the double bond of the adsorbed 1-butene, and


simultaneously, the neighbouring, basic oxygen-atom (O2) of the zeolite abstracts a hydrogen

atom (H6) from the C3 atom, restoring the catalyst active site and yielding adsorbed 2-butene.

The optimized structures of the reactants and the products, namely the π-structures of 1-

butene and 2-butene are already considered in section 3.1.

Figure 3.4: TS for the one-step double bond isomerization of 1-butene to 2-butene

The two –C-H-O- angles are approximately 180°, the C1-H1 and C3-H6 bond lengths are

shorter than the H1-O1 and H6-O2 distances and the C1-C2 and C2-C3 bond lengths are almost

similar (1.436Å and 1.401Å) and situated between the C-C single (~1.52Å) and double

(~1.33Å) bond lengths.

The imaginary vibration mode obtained from the frequency calculation on the optimized

structure for the transition state is 532i cm-1. This imaginary frequency is associated with the

movement of the hydrogen atoms H1 from the 3T cluster to butene and H6 from butene to the

3T cluster. Two other small imaginary frequencies are not related to the reaction coordinate

but are associated with the movement of the AlH2 and SiH3 groups out of the plane containing

the heavy atoms.

The activation energies and the physisorption energies are shown in Figure 3.5.


Figure 3.5: Energies for the concerted double bond isomerization reaction

The activation energy for the double bond isomerization, i.e. the reaction of 1-butene to 2-

butene, calculated as the energy difference between the transition state and the physisorbed 1-

butene, equals 119.2 kJ/mol. Li et al. (2005) calculated an activation energy of 107.0 kJ/mol.

The activation energy with respect to the separated reactants, which are the 3T-cluster and 1-

butene in the gas phase, is also calculated to make comparison with experimental data

possible. This composite activation energy amounts to 91.1 kJ/mol and is higher than the

experimental activation energies of double bound isomerization reactions in zeolites, which

are situated in the range of 62.8 kJ/mol to 83.7 kJ/mol (Kazansky (1991), Kazansky (1994)

and Corma (1995)).

3.2.2 Mechanism via adsorption/desorption

This mechanism for double bond isomerization involves the formation of a surface alkoxy

group by proton addition from the zeolite to the olefin double bond followed by

decomposition of this alkoxy intermediate. Starting from 1-butene (gas phase) and the 3T-

cluster, the physisorption of 1-butene takes place first leading to a stabilization of 28 kJ/mol.

Then, a secondary butoxy intermediate is formed by protonation of the 1-butene π–complex.

The intermediate has a protonation energy of -52 kJ/mol and is consequently more stable than

the physisorbed form. The activation energy for the formation of this σ-complex was already

mentioned before and amounts to 93 kJ/mol. In the second step deprotonation of the 2-butoxy


structure occurs, not leading to the initial reactant, which also could be a possibility, but to

physisorbed 2-butene. Due to the high stability of the alkoxide, this step is characterized by an

activation energy of 147 kJ/mol. Finally, the desorption of the 2-butene π-complex can be

considered and 2-butene in gas phase is obtained. The mechanism is illustrated in Figure 3.6.

All intermediate structures appearing in this two-step reaction have been discussed in section

3.1. The reaction diagram in Figure 3.7 summarizes the obtained results.

O+

Si Al-

O+

Si Al-

H

O+

Si Al-

H

Figure 3.6: Mechanism for the double bond isomerization via adsoption/desorption.

π 1-butene

1-butene (gas phase) + 3T

cluster

-34

TS protonation 1-butene

93

σ 2-butoxy

-52

TS protonation 2-butene

147

π 2-butene

107 2-butene (gas phase) + 3T

cluster

-28

Figure 3.7: The two-step mechanism for the double bond isomerization of 1-butene to 2-butene via the 2-butoxy chemisorption intermediate.

3.3 Conclusions

Cluster calculations have been performed to gain insight into the structures of the possible

stable intermediates and transition states during acid catalysed hydrocarbon processes. For the

different butenes, starting from the optimized transition states for the protonation reaction,


physisorption (π) and chemisorption (σ) structures were optimized. Furthermore, the double

bond isomerization of 1-butene to 2-butene is studied by two reaction mechanisms. The

results clearly show that the double bond isomerization reaction more favourably occurs

through the concerted mechanism, since the activation energy is almost 30 kJ/mol less than

the highest activation energy in the mechanism via adsorption/desorption. The highest

activation energy for the latter mechanism is required in the second step and is due to the high

stability of the alkoxy intermediate. The calculated acitivation energies obtained by the cluster

calculations are significantly higher than the experimental values reported in literature. A

possible explanation is that the 3T-cluster does not give a correct description of the real

zeolite framework, as a lot of stabilizing interaction by the zeolite framework such as the van

der Waals interactions are not accounted for. It can therefore be expected that the QM-Pot

calculations, which allow accounting for these stabilising dispersion forces, will lead to

results correspond better with the experimental data. The cluster approach cannot assure a

quantitative correct description but is certainly suited to obtain qualitative results and insight

in possible reaction mechanisms in a short time.


Reference List


Corma A., Chemical Reviews, 95, 559 (1995). Inorganic Solid Acids and Their Use in Acid-Catalyzed Hydrocarbon Reactions.

Kazansky V.B., Accounts of Chemical Research, 24, 379 (1991). The Nature of Adsorbed Carbenium Ions As Active Intermediates in Catalysis by Solid Acids.

Kazansky V.B., Advanced Zeolite Science and Applications, 85, 251 (1994). The Catalytic Site from A Chemical Point-Of-View.

Li H.Y., Pu M., Liu K.H., Zhang B.F. and Chen B.H., Chemical Physics Letters, 404, 384 (2005). A density-functional theory study on double-bond isomerization of 1-butene to cis-2-butene catalyzed by zeolites.

Rigby A.M., Kramer G.J. and van Santen, R.A., Journal of Catalysis, 107, 1 (1997). Mechanisms of hydrocarbon conversion in zeolites: a quantum mechanical study.

Chapter 4: Physisorption of C2-C8 alkenes in H-FAU, H-MOR and H-ZSM-5 zeolites 53

Chapter 4: Physisorption of C2-C8 alkenes in H-FAU, H-MOR and H-ZSM-5 zeolites

In this chapter, the physisorption of C2-C5 alkenes is studied H-ZSM-5 and H-MOR and the

physisorption of C2-C8 alkenes is studied H-FAU. It is written in the structure of an article to

submit it to a journal. Therefore, the introduction (chapter 1) and the computational method

(chapter 2) are short and concise repeated here.

Abstract - Physisorption, the first elementary step in most acid catalyzed

hydrocarbon conversion processes, is examined for C2-C8 alkenes in H-

FAU and for C2-C5 alkenes in H-ZSM-5 and H-MOR by computational

methods. A combined quantum mechanics-interatomic potential functions

approach (QM-Pot) is applied, which uses periodic boundary conditions,

treats the entire zeolite structure and takes van der Waals interactions into

account. More specifically, the influence of the zeolite framework, the

alkene carbon number and the hydrocarbon structure are investigated. The

sequence in order of decreasing physisorption strength is found to be as

follows: H-ZSM-5 > H-MOR > H-FAU. Physisorption appears to be the

strongest in H-ZSM-5 due to its smaller channels. The predicted

physisorption energies for 1-alkenes are found to decrease with increasing

carbon number, in agreement with experimental results. Further, the

structure of the hydrocarbon determines the ability of the alkene to fit in the

zeolite pore thereby minimizing the steric hindrance and maximizing the

stabilizing interactions with the zeolite wall. Finally, physisorption of

ethane, propane, n-butane, isobutane, n-pentane and isopentane is studied

in H-ZSM-5.


4.1 Introduction

Zeolites are materials build up from SiO4 and AlO4 tetrahedrals. They have a large internal

surface and are characterized by well defined microporous structures, containing channels and

cages of molecular dimensions. For every aluminium atom present in the zeolite framework, a

negative charge is introduced and to maintain charge neutrality, cations have to be added.

When the cation is a proton, it bounds to a nearby oxygen atom of the Si-O-Al bridge and a

Brønsted acid site is formed. These Brønsted acid sites give rise to the acidic properties of

zeolites and make the protonated zeolites very useful as heterogeneous catalysts. The activity

of these zeolite catalysts is based on the acid strength of the Brønsted sites, or in other words

on their ability to donate a proton to a hydrocarbon. Acid catalyzed hydrocarbon conversion

processes such as catalytic cracking of hydrocarbons, isomerisation of olefins, alkylation of

aromatic compounds, etc. play an important role in the (petro)chemical industry. Since the

traditional used homogeneous catalysts are extremely corrosive and harmful for the

environment, there is an increasing demand for environment friendly heterogeneous catalysts.

Although zeolites are already frequently used in a wide range of petrochemical processes,

there exists a constant tendency to understand and to improve these chemical processes due to

the continually increasing competition in these industrial sectors and the constantly raising

quality requirements.

Physisorption of hydrocarbons is the first elementary step in most acid catalyzed hydrocarbon

conversion processes and therefore it is extensively investigated. Physisorption structures of

alkenes are characterized by the formation of a π-complex, which arises by interaction

between the double bound of the alkene and the acid proton of the zeolite. Another important

interaction occurs between the alkene and the highly polarizable oxygen atoms of the zeolite

wall, mainly due to dispersion forces. Therefore, van der Waals interactions have a significant

role in the stabilization of the alkenes inside the zeolite. In this study physisorption is studied

for C2-C8 alkenes in H-FAU and for C2-C5 alkenes in H-ZSM-5 and H-MOR. Moreover, the

physisorption of C2-C5 alkanes is studied in H-ZSM-5. A schematic representation of a

physisorption complex is given in Figure 4.1.

In literature, a lot is reported about the physisorption of alkanes in zeolites since this subject

has been extensively studied via experimental work (Denayer et al. (1998c),Denayer et al.

(1998d) and Narasimhan et al. (2004)) as well as by the use of force field calculations (Smit

and Siepmann (1994) and Smit (1995)). Dixit and Rao used a mathematical approach to


calculate the physisorption energies of alkanes (Dixit and Rao (1998) and Dixit and Rao

(1999b)). Also quantum chemical calculations, such as cluster calculations (Boronat et al.

(2001) and Kazansky (1999)) and periodic DFT calculations (Benco et al. (2001a) and Benco

et al. (2003b)) have been performed to study the physisorption of hydrocarbons in zeolites.

However, due to the lack of stabilizing dispersion (van der Waals) interactions for both HF

and DFT methods, it is extremely difficult to obtain quantitative correct values for the

physisorption energies.

In our calculations especially the influence of the catalyst characteristics, e.g. acid strength

and zeolite topology as well as the influence of the hydrocarbon structure and carbon number

on the physisorption energy of the hydrocarbon has been studied. A combined quantum

mechanics - interatomic potential functions approach (QM-Pot) is applied for the calculations.

This method limits the QM part to the zeolite active site and the reacting hydrocarbon

molecule, and describes the remaining part of the zeolite unit cell by interatomic potential

functions. This does not only lead to a significant reduce of the computer time, but also to

more reliable physisorption energies compared to e.g. quantum chemical periodic

calculations, because the force fields accounts properly for the important dispersion (van der

Waals) interactions whereas traditional density functional methods don’t. The QM-Pot

method has already been successfully applied in earlier work to study reactions of

hydrocarbons in zeolites (Clark et al. (2002) and Clark et al. (2004)). Comparison with

experimental work has shown a good agreement between simulation and experiment with

regard to the physisorption of alkenes in zeolites (Nieminen et al. (2005)).

Al

O2

O1

Si2Si

1

H

C1

C2

R1

R2

R3

R4

Figure 4.1: Schematic representation of a physisorption complex.


4.2 Method

4.2.1 Computational details

In this study, the hybrid quantum mechanics-interatomic potential function (QM-Pot) method

is applied, which treats the entire zeolite structure (Eichler et al. (1997e), Sauer and Sierka

(2000) and Sierka and Sauer (2000)). With QM-Pot, only the site of interest (i.e. the

hydrocarbon and the Brønsted acid site) is treated at a quantum mechanic (QM) level,

whereas the remainder of the periodic zeolite framework, i.e. the non-reactive but

nevertheless important surrounding environment, is modelled by a computationally less

demanding interatomic potential function (Pot) with periodic boundary conditions. The QM-

Pot method yields reliable predictions for structures and properties of silica and zeolite

catalysts (Sierka and Sauer (1997)).

The QM-Pot approach divides the entire system (S) into two parts: the inner part, which is the

Brønsted acid site and the remaining, outer part of the zeolite unit cell. Since the inner part is

chemically bonded to the outer part, partitioning the system requires the breaking of covalent

O-Si bonds between the inner and outer part. These dangling, unsaturated bonds would give

rise to a charged, high spin QM region which is unrepresentative for the original system.

Therefore, the chemical bonds between inner and outer parts are saturated with hydrogen link

atoms to terminate these dangling bonds of the inner part. The inner part with the link atoms

on the one hand and the physisorbed hydrocarbon, i.e. the alkane or the alkene, on the other

hand form the cluster (C). The QM-Pot energy is calculated using the following subtraction

scheme:

CPotSPotCQMSPotQM EEEE ,,,, −+=−

Where: CQME , is the QM-energy of the cluster,

SPotE , is the Pot-energy of the whole system (i.e. zeolite unit cell) and

CPotE , is the Pot-energy of the cluster.

The calculations are performed using the QM-Pot program which is an implementation of the

QM-Pot method. The QM calculations are carried using the TURBOMOLE program

(Ahlrichs et al. (1989) and Treutler and Ahlrichs (1995)). The Density Functional Theory

(DFT) with the B3LYP exchange-correlation functional (Becke (1993) and Lee et al. (1988))

and a T(O)DZP basis set are employed, which means that a triple-ζ basis set for the oxygen

atoms and a double-ζ basis sets for all the other atoms (Schafer et al. (1992)) are used. The


Brønsted acid site (3T cluster) is mechanically embedded in the zeolite unit cell structure and

terminated by OH groups. The hydrogen atoms are constrained on the broken O-Si bond at a

fixed distance of the oxygen atom, i.e. 96.66 pm in case of SiO-H termination and 96.28 pm

in case of AlO-H termination (Sierka and Sauer (1997)). For the interatomic potential

function on the entire periodic zeolite structure, the GULP program (Gale (1997)) is used. As

interatomic potential function, the shell-model ion-pair potential is used, which describes ions

as a massive core and a mass-less shell connected through a harmonic spring. In this way, the

polarisation of the ions in an electric field is taken into account. The sum of the charges on the

core and the shell is equal to the charge on the ion. These potential functions have been

parameterized on DFT results for cluster models of protonated forms of zeolites. Lennard-

Jones potentials are included in the force field because they provide a good description of the

important dispersion (van der Waals) interactions between the hydrocarbon and the zeolite

framework. It is therefore important to keep the cluster as small as possible. The electrostatic

energy is evaluated by the standard Ewald summation technique and for the summation of

short-range interactions a cut-off radius of 10 Ǻ is chosen. Internal hydrocarbon bonds and

angles are described by a Morse and a Three-Body potential. The estimation of the

corresponding parameters has been described elsewhere (De Moor et al. (2006)).

4.2.2 Details on the zeolite structures studied

Three different, industrially important zeolite frameworks, namely ZSM-5, mordenite (MOR)

and faujasite (FAU) have been selected to study the influence of the zeolite framework on the

physisorption behaviour of alkenes inside its pores. The starting geometries of these three

zeolite structures were taken from the database of the Structure Commission of the

International Zeolite Association (IZA) (Treacy and Higgins (2001)). The numbering of the

T-sites and the oxygen atoms corresponds with Olson (Olson et al. (1981)) for MFI, Alberti

(Alberti et al. (1986)) for MOR and Hriljac (Hriljac et al. (1993)) for FAU. In general, for all

three types of zeolite frameworks, one silicon atom was replaced by an aluminium atom. The

resulting negative charge is compensated for by adding a hydrogen atom to a neighbouring

oxygen atom of the aluminium. The experimental unit cell parameters however are

characteristic for e.g. the siliceous or cation exchanged form and can therefore not be used as

such in the simulations. Therefore a constant pressure optimization of the unit cell with the

shell-model ion-pair potential force field alone (GULP) using the ab initio derived force field


parameters of Sierka and Sauer (1997) is performed. The obtained unit cell then can be used

in the constant volume QM-Pot calculations.

The MFI framework of H-ZSM-5, a medium pore zeolite, consists of 10-membered ring

straight channels parallel with the [010] direction and sinusoidal channels parallel with the

[100] direction. The orthorhombic modification of the unit cell, which has 12 different

crystallographic T-sites, is considered. The unit cell consists of 96 T-atoms, of which 95

silicon atoms and 1 aluminium atom, 192 oxygen atoms and 1 hydrogen atom. The Si/Al ratio

is 95. For ZSM-5, two different tetrahedral positions for the aluminium substitution are

considered, namely the Al7-O17(H)-Si4 and the Al12-O24(H)-Si12. The former is located in the

sinusoidal channel, whereas the latter is situated at the intersection of the straight and the

sinusoidal channel. The Al12-O24(H)-Si12 acidic site is considered in this study because of its

better accessibility by bulky reactants compared to the Al7-O17(H)-Si4 site. The same acidic

sites have been studied by Eichler et al. (1997d) and Brandle and Sauer (1998d).

The large pore H-FAU framework is composed of sodalite cages, which are connected by

double 6-membered rings. This construction gives rise to the characteristic supercages of

faujasite, interconnected through 12-membered ring pores. The non-cubic FAU unit cell (144

atoms) is used instead of the cubic one (576 atoms), although it is doubled in the [100]

direction to ensure sufficient separation between the periodic images of the hydrocarbon. This

simulation cell has only one distinct crystallographic T-site; the position of the charge

compensating proton however has been extensively studied in the past (Brandle and Sauer

(1998c), Sierka et al. (1998) and Simperler et al. (2004a)) and has been chosen on the O1 site.

Like H-ZSM-5, this unit cell contains 289 atoms and has a cell composition HAlSi95O192.

The MOR unit cell has 4 crystallographic different T-sites and contains two types of cavities:

a 12-membered ring main channel, parallel with the [001] direction (large pore zeolite) and

“side channels” in the main channels wall in the [010] direction and characterized by

8-membered rings. The MOR unit cell is doubled in the [001] direction to ensure sufficient

separation between the periodic images of the hydrocarbon. The aluminium substitution was

done at the Al4-O2(H)-Si2 site, following the study of Brandle and Sauer (1998b). The

resulting unit cell again contains 289 atoms and has the same cell composition as H-ZSM-5

and H-FAU.

All three simulation cells contain 289 atoms and are characterized by a Si/Al ratio of 95. This

will allow us to investigate unambiguously the influence of the zeolite framework on the


physisorption energies of alkenes. The optimized cell parameters for all simulations cells are

summarized in Table 4.1.

Table 4.1: Shell-model ion-pair potential optimized cell parameters at constant pressure of H-ZSM-5 (with aluminium on the T7 or on the T12 position), H-FAU and H-MOR.

H-ZSM-5(Al7) H-ZSM-5(Al12) H-FAU H-MOR

a [Å] 20.378 20.358 34.971 18.308

b [Å] 19.830 19.859 17.430 20.195

c [Å] 13.509 13.521 17.493 15.003

α [degree] 90.07 89.90 59.99 90.01

β [degree] 90.01 89.81 59.87 89.82

γ [degree] 90.16 89.97 59.90 90.02

4.3 Results and discussion

4.3.1 Details of the Brønsted acid sites

The Brønsted acid sites of the different zeolites are all characterized by their catalytic activity.

The catalytic performance of these Brønsted acid sites is strongly governed by the intrinsic

acidity, i.e. in absence of a proton acceptor. In this study, the energy of deprotonation, ∆EDP,

is used as a measure for the intrinsic acid strength of the specific Brønsted acid site. It is

defined as the energy difference between the deprotonated zeolite (Z-O-) and the protonated

zeolite (Z-OH):


The calculated energies of deprotonation are shown in Table 4.2; nomenclature according to

Figure 4.1 is used. Calculations of the νOH stretching frequencies were also performed,

because the νOH frequency as well serves as an indicator of acid strength in the unloaded

zeolite and enables direct comparison with experimental data. Furthermore, some geometric

parameters of the considered Brønsted acid sites are shown. No scaling factor was used for

the frequencies.

The considered zeolite unit cells are all characterized by a Si/Al ratio of 95, which ensures

that the periodic acid sites do not affect each other and consequently permits the study of

isolated Brønsted acid sites.


Table 4.2: Comparison of acid sites in H-ZSM-5, H-FAU and H-MOR

H-ZSM-5

(Al7) H-ZSM-5

(Al12) H-FAU H-MOR

∆EDP,QM-Pot [kJ/mol] 1236.6 1228.1 1205.9 1230.4

νOH [cm-1] 3677.2 3685.0 3694.1 3690.8

protonated

O1-H [Ǻ] 0.9761 0.9761 0.9748 0.9757

Al-O1H [Ǻ] 1.9089 1.9028 1.9020 1.9008

Si1-O1H [Ǻ] 1.7236 1.7183 1.7240 1.7063

Al-O2 [Ǻ] 1.7196 1.7225 1.7154 1.7167

Si2-O2 [Ǻ] 1.6068 1.6183 1.6078 1.6082

< Si1-O1H-Al [deg] 131.958 134.078 124.730 128.775

< Si2-O2-Al [deg] 145.290 147.268 133.751 139.715

deprotonated

Al-O1 [Ǻ] 1.7545 1.7458 1.7404 1.7503

Si1-O1 [Ǻ] 1.5967 1.5924 1.5924 1.5891

Al-O2 [Ǻ] 1.7428 1.7400 1.7284 1.7349

Si2-O2 [Ǻ] 1.5886 1.5905 1.5821 1.5837

< Si1-O1-Al [deg] 142.335 136.030 133.553 132.027

< Si2-O2-Al [deg] 146.533 158.699 138.854 146.184

The more acidic the proton is, the higher the proton mobility and thus the lower the energy of

deprotonation (or proton affinity) of the zeolite. According to the calculated deprotonation

energies, H-FAU has the most acidic Brønsted site with a deprotonation energy of 1205.9

kJ/mol while H-ZSM-5(Al7) is the weakest acid site, with an energy of deprotonation of

1236.6 kJ/mol. Sierka and Sauer (1997) report a deprotonation energy of 1198 kJ/mol for

H-FAU. Comparison with HF obtained values is possible, but it must be taken into account

that the DFT method yields lower deprotonation energies than the HF methods, since the

inclusion of electron correlation weakens the O-H bond. A correction factor of -46 kJ/mol was

suggested (Sauer and Ahlrichs (1990)), independent of the zeolite framework. Accounting for

this correction factor, Eichler et al. (1997c) found a deprotonation energy of 1205.3 kJ/mol for

H-FAU and Brandle and Sauer (1998a) have calculated 1235.4 kJ/mol for H-ZSM-5(Al7),

1229.4 kJ/mol for H-ZSM-5(Al12) and 1230.1 kJ/mol for H-MOR for the deprotonation

energies. These values are in excellent agreement with our values, as only differences up to

1.5 kJ/mol are observed. Moreover, the same sequence in order of decreasing intrinsic acidity

is found, namely H-FAU > H-MOR ≈ H-ZSM-5(Al12) > H-ZSM-5(Al7).


The O1-H bond lengths are nearly the same for all the protonated zeolites, with values

between 0.9748 Ǻ and 0.9761 Å. It is remarkable that all considered bond lengths around the

acid site, for the protonated as well as for the deprotonated form, have nearly the same value

for the different zeolites. In contrast, the bond angles around the acid site are significantly

different for the considered zeolites, as can be seen in Table 4.2. In the SiO2 form of the

considered zeolite framework, the average Si-O bond length equals 1.63Å. Introducing an Al

in the framework causes the Al-O1H, Al-O2 and Si1-O1H bonds to elongate respectively to

1.90Å, 1.72Å and 1.72Å for all the protonated zeolites. The Si2-O2 bond length of the

protonated forms on the other hand decrease a little for all the zeolite structures. The bond

angles, Si1-O1H-Al and the Si2-O2-Al, on the other hand largely differ for the different

protonated zeolite structures: the Si1-O1H-Al angle varies between 124 and 134 deg and the

Si2-O2-Al angle between 139 and 145 deg. Also, Si1-O1H-Al angles are sharper compared to

the siliceous oxide forms of ZSM-5, FAU and MOR for which bond angles of 140-149 deg,

142 deg and 140 deg respectively are found. Deprotonation, causes a few changes in the

geometric parameters of the zeolite structures, due to the relaxation around the acidic site. For

each zeolite, the Al1-O1 and Si1-O1 bond lengths shorten with respectively 0.15Å and 0.13Å,

the Al-O2 bond distance increases a little (0.03Å) and the Si2-O2 bond length decreases

slightly (0.02Å). Further, the Si1-O1-Al and Si2-O2-Al angles all increase, but the magnitude

of these increases depends strongly on the concerned zeolite.

Table 4.2 also shows spectroscopic properties, more specifically the OH stretching frequency,

νOH. Comparison is made with observed data available. The observed wave numbers for the

OH stretching frequency decrease according to following sequence: H-FAU (3694.1cm-1) >

H-MOR (3690.8cm-1) > H-ZSM-5(Al12) (3685.0cm-1) > H-ZSM-5(Al7) (3677.2cm-1). The

OH vibration frequencies for H-FAU (3596cm-1), obtained by Eichler et al. (1997b)., and

these for H-ZSM-5 (3580 cm-1) and H-FAU (3582 cm-1), found by Simperler et al. (2004b),

follow the same order for the different zeolites. Sierka and Sauer (1997)reported a value of

3646cm-1 for the νOH of H-FAU. Experimentally, infrared spectroscopy is used to measure

O-H stretching frequencies. In H-FAU values of 3623cm-1 (for an Si/Al ratio of 21) to

3627cm-1 (Si/Al = 5.4) were observed, in H-ZSM-5 OH stretching frequencies of 3610 cm-1

(Si/Al = 52) to 3612 cm-1 (Si/Al = 12.6) were seen and in H-MOR 3607 cm-1 (Si/Al = 10.7)

was found (Eichler et al. (1997a) and Czyzniewska et al. (2002)). The differences between our

calculated values and the experimentally determined values, are partly due to the fact that no

scaling factor was used for the reported frequencies. Also the difference in Si/Al ratio


between our model structures and experimental materials may have an influence. The

sequential order that we have found with regard to the O-H stretch frequency is in agreement

with experimental work.

4.3.2 Physisorption in H-ZSM-5, H-FAU and H-MOR

In this work physisorption of ethylene, propylene, 1-butene, 2-butene, isobutene, 1-pentene,

2-methyl-1-butene and 2-methyl-2-butene in H-ZSM-5 and H-MOR and of ethylene,

propylene, 1-butene, 2-butene, isobutene, 1-pentene, 2-methyl-1-butene and 2-methyl-2-

butene, 1-hexene, 1-heptene and 1- to 4-octene in H-FAU has been investigated.

Physisorption complexes of alkenes are characterized by the formation of a π-complex: the

interaction of the acidic proton with the alkene double bond leads to a certain stabilization

energy. The largest part of the stabilization however comes from stabilizing dispersion (van

der Waals) interactions. The physisorption energy, ∆Ephys, is calculated using the following

equation:

nhydrocarbozeolitephys EEEE −−=∆ π

Where: πE is the energy of the physisorption complex,

zeoliteE is the energy of the hydrocarbon-free zeolite and

nhydrocarboE is the energy of the hydrocarbon in the gas phase.

Figure 4.2 depicts the physisorption complexes of propylene for the four acidic sites of the

different zeolite structures.

Table 4.3 shows the ranges of the relevant bonds and angles of all physisorption complexes in

the different zeolites. Figure 4.1 explains the used nomenclature. By comparing the geometric

parameters with these of the protonated form (see Table 4.2) it appears that the zeolite

framework undergoes only very slight differences when a hydrocarbon molecule is

physisorbed. The O-H bonds for example increase with only 0.02Ǻ (from 0.97Ǻ -0.98Ǻ to

0.99Ǻ -1.00Ǻ), the Si-OH bond lengths and Al-OH bond lengths hardly change as they stay

respectively in a range of 1.70Ǻ - 1.72Ǻ and 1.88Ǻ - 1.91Ǻ and the Al-O1-Si1 angles

decrease 1-3 deg for the different zeolite frameworks.


Figure 4.2: Physisorption complexes of propylene in H-ZSM-5(Al7) (a), H-ZSM-5(Al12) (b), H-FAU (c) and H-MOR (d)

Further, the hydrocarbon molecules as well experience only small deformations by

physisorption: the bond lengths of the C1-C2 double bond increase a little (about 0.01 Ǻ) and

the angles between the carbon atoms increase with 1- 2 deg. Finally, the H-// distances vary

significantly for the different zeolite structures but also for the different alkenes: from 2.08Ǻ

(2-butene) to 2.27Ǻ (2-Me-1-butene) in H-FAU and from 2.15Ǻ (2-butene) to 2.38Ǻ

(2-Me-1-butene) in H-ZSM-5(Al12). These differences are closely connected with the local

geometry of the acid sites in the zeolite and with the structure of the alkene.

a b

c d


Table 4.3: Ranges for geometric parameters of all physisorption complexes in the different zeolite frameworks.

Distances (Å) H-ZSM-5(Al7) H-ZSM-5(Al12) H-FAU H-MOR

H-// 2.18 – 2.31 2.15 – 2.38 2.08 – 2.27 2.10 – 2.34

C1-C2 1.33 – 1.35 1.34 – 1.35 1.34 – 1.35 1.34 – 1.35

O1-H 0.99 – 1.00 0.99 – 1.00 0.99 – 1.00 0.99 – 1.00

Al-O1 1.90 – 1.91 1.89 – 1.90 1.88 – 1.89 1.89 – 1.90

Al-O2 1.72 1.72 1.72 1.72

O1-Si1 1.71 – 1.72 1.71 – 1.72 1.71 – 1.72 1.70

O2-Si2 1.60 1.61 1.60 – 1.61 1.60 – 1.61

O2-C2 3.58 – 4.04 3.33 – 4.43 3.31 – 3.77 3.63 – 4.07

Angles (degree)

Al-O1-Si1 129.68 – 132.57 131.01 – 131.67 122.70 – 123.85 126.11 – 126.97

Al-O2-Si2 145.82 – 147.36 142.37 – 149.81 134.54 – 135.45 139.21 – 140.00

Al-O1-H 114.06 – 115.73 109.14 – 113.11 113.68 – 119.17 114.60 – 117.17

The physisorption energies for all alkenes in H-ZSM-5, H-FAU and H-MOR are shown in

Table 4.4. The zeolite structure with, if necessary the tetrahedral position of the aluminium

substitution are mentioned. The separate quantum chemical (QM) and interatomic potential

(Pot) contributions to the total physisorption energy are mentioned. The contribution of the

Lennard-Jones interatomic potential, which is an estimate of the van der Waals forces, to the

Pot energy is given between brackets.

In H-ZSM-5, the Al7-O17(H)-Si4 acidic site, which is located in the sinusoidal channel, clearly

is the strongest physisorption site with physisorption energies going from -56.5 kJ/mol for

ethylene to -99.8 kJ/mol for 1-pentene. The physisorption energies for the Al12-O24(H)-Si12

site, located at the intersection of a straight and a sinusoidal channel, vary from -54.7 kJ/mol

for ethylene to -84.3 kJ/mol for 1-pentene. In H-FAU the physisorption energy varies from

-36.7 kJ/mol for ethylene to -79.9 kJ/mol for 1-octene and in H-MOR the physisorption

energy decreases from -44.3 kJ/mol for ethylene to -79.8 kJ/mol for 1-pentene. Apparently

stronger physisorption occurs in the medium pore zeolite, H-ZSM-5 compared to the large

pore zeolites, H-FAU and H-MOR. The two contributions, i.e. the QM-contribution and the

Pot-contribution are analyzed in the following paragraphs.


Table 4.4: Physisorption energies in kJ/mol for different alkenes in different zeolites. The total physisorption energy (∆∆∆∆Ephys,QM-Pot) with its quantum chemical (∆Ephys,QM) and interatomic potential (∆Ephys,Pot) contributions are given, as well as the van der Waals part of the Pot contribution (between brackets).

Zeolite Alkene Physisorption energy [kJ/mol] ∆Ephys,QM-Pot ∆Ephys,QM ∆Ephys,Pot H-ZSM-5(Al7) Ethylene -56.5 -16.3 -40.5 (-36.3) Propylene -74.6 -26.3 -48.4 (-49.0) 1-butene -88.1 -22.8 -65.3 (-63.3) 2-butene -91.0 -24.1 -67.0 (-64.1) Isobutene -81.9 -22.8 -59.0 (-60.1) 1-pentene -99.8 -22.8 -76.9 (-75.9)

H-ZSM-5(Al12) Ethylene -54.7 -7.9 -46.8 (-34.3) Propylene -75.6 -5.3 -70.3 (-51.7) 1-butene -73.1 -16.6 -56.4 (-46.9) 2-butene -76.9 -12.0 -64.9 (-50.2) Isobutene -73.9 -7.2 -66.7 (-46.5) 1-pentene -84.3 -14.2 -70.0 (-61.6) 2-Me-1-butene -77.9 -12.1 -65.8 (-59.4) 2-Me-2-butene -82.7 -14.6 -68.1 (-59.4)

H-FAU Ethylene -36.7 -18.5 -18.2 (-12.8) Propylene -46.0 -24.0 -22.0 (-16.3) 1-butene -48.9 -20.1 -28.9 (-21.6) 2-butene -50.2 -22.0 -28.2 (-21.2) Isobutene -54.8 -23.3 -31.5 (-22.5) 1-pentene -56.7 -17.8 -38.8 (-32.6) 2-Me-1-butene -56.2 -21.0 -35.2 (-26.9) 2-Me-2-butene -58.8 -15.5 -43.4 (-34.4) 1-hexene -62.7 -21.1 -41.6 (-34.6) 1-heptene -71.5 -20.7 -50.7 (-46.7) 1-octene -79.9 -23.3 -56.6 (-51.7) 2-octene -74.4 -18.6 -55.9 (-50.3) 3-octene -71.6 -14.4 -57.2 (-48.2) 4-octene -73.5 -13.8 -59.6 (-52.6)

H-MOR Ethylene -44.3 -10.6 -33.7 (-26.3) Propylene -56.8 -12.4 -44.3 (-34.0) 1-butene -74.1 -18.4 -55.7 (-46.6) 2-butene -69.2 -17.6 -51.6 (-43.6) Isobutene -68.6 -14.1 -54.5 (-44.7) 1-pentene -79.8 -17.4 -62.4 (-55.6) 2-Me-1-butene -80.5 -12.2 -68.3 (-59.0) 2-Me-2-butene -80.7 -12.4 -68.3 (-56.7)


The QM-contribution to the physisorption energy, i.e. the first term on the right hand side of

equation on page 56, varies between -13.8 kJ/mol and -24.0 kJ/mol in H-FAU, between -16.3

kJ/mol and -26.3 kJ/mol in H-ZSM-5(Al7), between -5.3 kJ/mol and -16.6 kJ/mol in H-ZSM-

5(Al12) and between -10.6 kJ/mol and -18.4 kJ/mol in H-MOR. Although for each zeolite

structure, the QM-contribution to the physisorption energy fluctuates in a range of 10 kJ/mol,

a systematic trend as a function of e.g. the carbon number is not observed and therefore can be

considered as independent of the alkene length. This is expected since the main part of this

QM-energy arises from the formation of the π-complex, which is evidently independent of the

alkene length. The variations in the QM-contribution seem to originate from small

geometrical differences in the physisorption complex, such as the proton to double bond

distance (see Table 4.3). The Pot–contribution to the physisorption energy, i.e. the second and

third term on the right hand side of equation 1, on the other hand is clearly dependent of the

alkene length as its contribution to the total physisorption energy increases with increasing

carbon number.. We observe a decrease from -18.2 kJ/mol for ethylene to -59.6 kJ/mol for

4-octene in H-FAU, from -40.5 kJ/mol for ethylene to -76.9 kJ/mol for 1-pentene in

H-ZSM-5(Al7), from -46.8 kJ/mol for ethylene to -70.0 kJ/mol for 1-pentene in

H-ZSM-5(Al12) and from -33.7 kJ/mol for ethylene to -68.3 kJ/mol for 2-methyl-2-butene in

H-MOR. This was also expected, since longer alkenes give rise to more stabilizing dispersion

(van der Waals) interactions with the zeolite wall. These van der Waals interactions are very

important as they averagely account for 80% to 90% of the Pot-contribution of the

physisorption energy, as can be seen in Table 4.4. For ZSM-5(Al7) this amounts even to close

to 100%. Comparing the QM- and Pot-contribution and the van der Waals part in the latter,

we conclude that it is mainly the van der Waals contribution that determines the decrease of

the physisorption energy with the carbon number.

From the results discussed above, it can be concluded that the sequence in order of decreasing

physisorption strength is as follows: H-ZSM-5(Al7) > H-ZSM-5(Al12) > H-MOR > H-FAU.

As already mentioned, H-ZSM-5 is a medium pore zeolite, characterized by 10-membered

straight and sinusoidal channels, whereas H-FAU and H-MOR are large pore zeolites,

characterized by 12-membered rings. The maximum diameter of a sphere that can be included

in the MFI, MOR and FAU framework is 6.3 Å, 6.64 Å and 11.18 Å respectively. The results

agree with the idea that the physisorption energy is a function of the framework density,

which usually increases with decreasing pore size, in such a way that the strongest

physisorption occurs in the zeolites with the highest framework density. This is mainly related


with the amount of stabilizing dispersion interactions that appear between the alkene and the

zeolite wall. In H-ZSM-5(Al7), the physisorption occurs in the small sinusoidal channel and

as a result, the alkene is strongly stabilized by dispersion interactions with the entire zeolite

wall. Physisorption in H-ZSM-5(Al12) on the other hand takes place at the intersection of the

straight and the sinusoidal channel. More space is available here compared to the sinusoidal

channel which will allow physisorption of bulkier species, however, as a consequence this

will also result in less stabilization by dispersion interactions. As the physisorption in H-MOR

occurs in the 12-membered main channel, the alkene is mainly stabilized by only one side of

the zeolite wall of the channel. In H-FAU the alkene will experience even less stabilization by

dispersion interactions since physisorption occurs in the supercage.

Figure 4.3 depicts the physisorption energy of all 1-alkenes in the different zeolite

frameworks as a function of the carbon number (CN). It clearly indicates that a linear

relationship between the physisorption energy and the carbon number exists. The dotted lines

in Figure 4.3 are obtained by linear fits of the physisorption energies of the 1-alkenes for the

different zeolite structures; the equations and the correlation coefficient (R2) corresponding

with these linear fits are also given. The correlation coefficient of H-ZSM-5(Al12) of 0.8003

is because of the large deviation of propylene from the expected value. This hydrocarbon

molecule perfectly fits in the sinusoidal channel thereby experiencing a maximum

stabilization by the zeolite wall, in contrast to ethylene which is less stabilized by dispersion

interactions. The longer alkenes in H-ZSM-5(Al12) on the other hand are physisorbed in the

straight channel. This importance of the van der Waals stabilization is clearly observed in

Table 4.4 for this specific case. In H-ZSM-5(Al7), H-ZSM-5(Al12), H-MOR and H-FAU the

physisorption energies decrease with respectively 14.23 kJ/mol, 8.62 kJ/mol, 12.38 kJ/mol

and 6.94 kJ/mol per extra –CH2– group for the linear alkenes. Thus, for each zeolite structure

the physisorption energy decreases with increasing carbon number. The largest part of this

decrease is caused by the increase of the van der Waals stabilization with higher carbon

numbers.

Another important issue is the influence of the hydrocarbon structure on the physisorption

energy. The results of the different C4 alkenes (i.e. 1-butene, 2-butene and isobutene) and the

different C5 alkenes (i.e. 1-pentene, 2-methyl-1-butene and 2-methyl-2-butene) in the different

zeolite structures are interesting to compare in this respect. In H-FAU the results of the

various C8 (1- to 4-octene) alkenes are also studied. Table 4.4 shows clearly that the

physisorption energies for alkenes with the same carbon number but with a different structure


vary within each zeolite. However, the stability order differs in all zeolites: in

H-ZSM-5(Al12) for example the order of the C4 and C5 alkenes with decreasing physisorption

energy are 1-butene (-73.1 kJ/mol) > isobutene (-73.9 kJ/mol) > 2-butene (-76.9 kJ/mol) and

2-methyl-1-butene (-77.9 kJ/mol) > 2-methyl-2-butene (-82.7 kJ/mol) > 1-pentene (-84.3

kJ/mol) respectively, whereas in H-MOR these sequences are isobutene (-68.6) > 2-butene

(-69.2 kJ/mol) > 1-butene (-74.1 kJ/mol) and 1-pentene (-79.8 kJ/mol) > 2-methyl-2-butene

(-80.5 kJ/mol) > 2-methyl-2-butene (-80.7 kJ/mol). No systematic trends for the non-branched

alkenes are observed. We conclude that the differences in physisorption energy are related to

the ability of the alkene to fit in the zeolite framework thereby minimizing the steric

hindrance and maximizing the stabilization by interaction with the zeolite framework and π-

complex formation.

In addition to the physisorption of alkenes, physisorption of ethane, propane, n-butane,

isobutene, n-pentene and isopentane in H-ZSM-5(Al12) has been studied. Figure 4.4 shows

the physisorption of 1-pentene (a) and 1-pentane (b) in the straight channel. Whereas the 1-

pentene double bond forms a π-complex with the acidic proton, leading to a position close to

one side of the zeolite wall, 1-pentane is located in the centre of the straight channel. The

physisorption energies are shown in

Table 4.5, in which also the results for alkene physisorption are repeated. The total QM-Pot

physisorption energies are listed as well as the calculated van der Waals stabilization

(between brackets). The van der Waals interactions are relatively more important for alkane

stabilization compared to alkene stabilization. In the former, dispersion interactions contribute

for 85-95% to the total alkane physisorption energy, whereas this is only 45-70%. As a

consequence positioning in the centre of a zeolite channel is the most preferred position with

regard to van der Waals stabilization for an alkane. In case of alkene physisorption, this is

hindered by the formation of the π-complex. Linear fitting of the physisorption energies of the

1-alkanes yields an incremental value of the physisorption energy with the carbon number of

13 kJ/mol, in between the incremental values for alkene physisorption at H-ZSM-5(Al7),

14.23 kJ/mol, and at H-ZSM-5(Al12), 8.62 kJ/mol.

Chapter 4: P

hysisorption of C2-C

8 alkenes in H-F

AU

, H-M

OR

and H-Z

SM-5 zeolites

69

Figure 4.3: P

hysisorption energies of the 1-alkenes as a function of the carbon

number.

-110

-100

-90

-80

-70

-60

-50

-40

1 2 3 4 5 6 7 8Carbon number

∆Ephys (kJ/mol)

∆Ephys = -6.94CN – 22.78 R2 = 0.9894

H-FAU

H-MOR ∆Ephys = -12.38CN – 20.43 R2 = 0.9683

H-ZSM-5 (Al12) ∆Ephys = -8.62CN – 41.74 R2 = 0.8003

H-ZSM-5 (Al7) ∆Ephys = -14.23CN - 30,00 R2 = 0,9904


Figure 4.4: Physisorption of 1-pentene (left) and 1-pentane (right) in the straight channel H-ZSM-5

Table 4.5: Total physisorption energy and van der Waals stabilization (between brackets) for different alkanes and alkenes in H-ZSM-5(Al12).

Alkane ∆∆∆∆Ephys,QM-Pot Alkene ∆∆∆∆Ephys,QM-Pot

ethane -34.6 (-31.8) ethylene -54.7 (-26.3)

propane -50.6 (-45.9) propylene -75.6 (-34.0)

1-butene -73.1 (-46.6) n-butane -65.8 (-61.8)

2-butene -76.9 (-43.6)

i-butane -57.8 (-54.7) i-butene -73.9 (-44.7)

n-pentane -74.7 (-67.9) 1-pentene -84.3 (-55.6)

2-Me-1-butene -77.9 (-59.0) i-pentane -72.6 (-68.2)

2-Me-2-butene -82.7 (-56.7)

Our results show that taking into account both the total zeolite framework and the van der

Waals stabilization is necessary to obtain reliable results for the physisorption of alkenes and

alkanes. This is one of the main problems encountered by the small cluster calculations

describing physisorption: although this type of calculations are still very useful and they can

give qualitative insight in the reaction mechanism, especially for reactions in which reactants

and products are stabilized by more or less the same amount of van der Waals. Physisorption

of alkenes has been intensively studied in the past on 1 to 5T clusters: generally the

physisorption energy of ethylene and isobutene only differ by 10 kJ/mol, much less than in

our case where this difference mounts to for example 18 kJ/mol in case of H-FAU and to 25

kJ/mol in case of H-ZSM-5(Al7). Boronat et al. (1998) studied the influence of the cluster


size on the results using HF and B3PW91 calculations. Results change only slightly, except

for isobutene because of the steric constraints which prevent the molecule to physisorb

strongly. The obtained physisorption energies however are too small because neither HF nor

DFT methods are able to describe correctly dispersion interactions. Rigby and Frash (1997)

have shown the importance of these interactions doing single point MP2 calculations, which

account for van der Waals interactions, on the HF obtained structures, as the physisorption

energy decreases by approximately 6-8 kJ/mol only on the small 3T clusters. Although the

dispersion interactions can be taken into account doing post-HF calculations, neglecting the

influence of the zeolite framework is a remaining important problem and causes the

physisorption strength to be underestimated. Periodic quantum chemical calculations

obviously account for the entire zeolite framework: the computational cost however is a

drawback of this type of calculation and it seriously limits the size of the zeolite unit cell. The

physisorption energies however still seem to be underestimated, as the DFT does not account

properly for the dispersion interactions (Benco et al. (2001b) and Benco et al. (2003a)).

Correction schemes for periodic DFT methods to include van der Waals interactions has been

described by Demuth et al. (2001) and Vos et al. (2001). Also QM/MM schemes have been

applied to study physisorption of alkenes in zeolites. Kasuriya et al. (2003) report a

physisorption energy for ethylene in H-FAU of –36.6 kJ/mol, in excellent agreement with our

QM-Pot calculated value of –36.7 kJ/mol. Panjan and Limtrakul (2003) calculated a

physisorption energy for ethylene in H-ZSM-5 of –38.3 kJ/mol, significantly lower than our

values, –56.5 kJ/mol in H-ZSM-5(Al7) and –54.7 kJ/mol in H-ZSM-5(Al12). They used a

2-layer ONIOM method in which an inner part of the system containing the active site is

treated at the B3LYP/6-311++G(d,p) level, and the remaining part of their 46T model system

at HF/3-21G level. In HF calculations however dispersion interactions are not properly

described and as a consequence a less strong physisorption is observed. Boronat et al. (2004)

studied physisorption of ethylene, propylene and isobutene in H-MOR using ONIOM

(B3PW91/6-31G(d,p):MNDO) and computed physisorption energies of respectively -24

kJ/mol, -27 kJ/mol and -23.5 kJ/mol

In literature, there is lack of experimental data on physisorption of alkenes in acidic zeolites,

however a lot of experimental data are available on the physisorption of alkanes in

industrially important zeolites such as MOR, MFI, FER and FAU. Only one experimentally

obtained value for a physisorbed alkene is reported in literature; the physisorption energy for

ethylene on H-Y zeolite amounts –35.1 ± 1.3 kJ/mol (Cant and Hall (1972). This is in good


agreement with our result for ethylene in H-FAU, -36.7 kJ/mol. With regard to the

physisorption of alkanes in zeolites, only incremental values can be compared with our

simulation results for the physisorption of alkenes, since the decrease of the physisorption

energy due to adding extra –CH2– groups is caused by the increase of the dispersion and

coulomb interactions and not by the interaction of the double bond with the acidic proton of

the zeolite. For the physisorption of alkanes Denayer et al. (1998e) and Denayer et al. (1998b)

report -6.4 kJ/mol, -11.0 kJ/mol and -10.5 kJ/mol as incremental values for physisorption in

H-FAU, H-ZSM-5 and H-MOR respectively, whereas Eder et al. (1997), Eder and Lercher

(1997b) and Eder and Lercher (1997a) found -7 kJ/mol for H-FAU and -12 kJ/mol for

H-ZSM-5. Dixit and Rao (1998) and Dixit and Rao (1999c) used a mathematical approach to

calculate the physisorption energy of alkanes in different zeolites: they report a decrease of

6.9 kJ/mol for H-FAU, 10.0 kJ/mol for H-ZSM-5 and 10.1 kJ/mol for H-MOR per extra

carbon number for linear alkanes. Our results agree fairly well with these increments reported

in literature: we have found that the physisorption energies of linear alkenes decrease per

extra –CH2– group with 6.94 kJ/mol in H-FAU, 14.23 kJ/mol in H-ZSM-5(Al7), 9.76 kJ/mol

in H-ZSM-5(Al12) and 12.38 kJ/mol in H-MOR. The experimental value for H-ZSM-5 is

situated in between the values we calculated for the two Brønsted sites of this zeolite: in

experiments however, no distinction is made between acidic sites at different tetrahedral

position in the zeolite framework, only an average incremental value is obtained. The

calculated incremental value for H-MOR differs by ~2.0 kJ/mol from the experimentally

determined value: a possible explanation may be that more physisorption sites should be

considered. See within this respect the largely different physisorption behaviour of alkenes in

H-ZSM-5(Al7) and H-ZSM-5(Al12). Also the difference in Si/Al ratio for the simulations and

the experimental work may have an influence. For H-FAU, an excellent agreement is obtained

with experimental results.

With regard to the physisorption of alkanes we found that the physisorption energy of linear

alkanes decreases with 13 kJ/mol per extra –CH2– group and varies from -34.6 kJ/mol for

ethane to -74.7 kJ/mol for n-pentane. This is a somewhat higher value than expected from

literature, where incremental values up to -12 kJ/mol are reported. This discrepancy again

may be caused by the fact that we only consider physisorption in the sinusoidal channel and

with one Brønsted acid site. Moreover the Si/Al of our zeolite model (95) differs a lot from

the Si/Al ratios of the zeolites used in the experiments. The experimental values obtained by

Dixit and Rao (1999a) vary from -32.0 kJ/mol for ethane to -62.1 kJ/mol for pentane and


those found by Denayer et al. (1998a) go form -25.1 for ethane to -58.6 for pentane.

Comparing these values with our calculations, we find that for the shorter alkanes a very good

quantitative agreement is obtained, but for the longer ones an overestimation of the

physisorption strength is modelled.

4.4 Conclusions

A combined quantum mechanics-interatomic potential functions approach (QM-Pot) has been

used to describe physisorption of alkenes in zeolites H-ZSM-5, H-FAU and H-MOR. The

acidic site (3T cluster) and the hydrocarbon are treated at quantum chemical level and the

remainder of the zeolite framework is modelled by an ion-pair shell potential force field in

which interatomic Lennard-Jones potentials are added to account for proper description of the

weak dispersion forces (van der Waals). QM-Pot accounts for steric effects and electrostatic

contributions that arise from the zeolite wall close to the acid site. Different crystallographic

sites in different zeolites have been studied: Al7-O17(H)-Si4 and Al12-O24(H)-Si12 in H-ZSM-5,

Al-O1(H)-Si in H-FAU and Al4-O2(H)-Si2 in H-MOR. According to the calculated

deprotonation energies, following sequence in order of decreasing intrinsic acidity is

observed: H-FAU > H-MOR ≈ H-ZSM-5(Al12) > H-ZSM-5(Al7). All zeolite unit cells have

a Si/Al ratio of 95.

Physisorption energies are calculated for C2-C5 alkenes in H-ZSM-5 and H-MOR and for C2-

C8 alkenes in H-FAU. From the geometric parameters of the physisorbed structures it appears

that both the zeolite framework and the alkene undergo only very slight differences when

physisorption occurs: bond lengths and angles show little changes in comparison with the

protonated zeolite and the alkene. The H-// distances vary significantly for the different

zeolite structures and the different alkenes, because this distance is closely connected with the

local geometry of the acid site in the zeolite and with the structure of the alkene. The

physisorption strength decreases in the following order: H-ZSM-5(Al7) > H-ZSM-5(Al12) >

H-MOR > H-FAU. This different physisorption behaviour in the various zeolite structures is

related with their pore size and the framework density: the smaller the pore sizes the higher

the amount of stabilizing dispersion interactions between the alkene and the zeolite wall. With

regard to the influence of the alkene carbon number we found that the physisorption energy in

H-ZSM-5(Al7), H-ZSM-5(Al12), H-MOR, H-FAU for the 1-alkenes decreases with

respectively 14.23 kJ/mol, 8.62 kJ/mol, 12.38 kJ/mol and 6.94 kJ/mol per extra –CH2– group.


The decrease of the physisorption energy with increasing carbon number is mainly attributed

to the increase of stabilizing van der Waals interactions. Experimentally determined

incremental values for the change of the physisorption energy with the carbon number are -10

kJ/mol to -12 kJ/mol for H-ZSM-5, -10.1 kJ/mol to -10.5 kJ/mol for H-MOR and -6.4 kJ/mol

to -7 kJ/mol for H-FAU. Differences between calculated and experimentally determined

values may be due to 1. difference in Si/Al ratio and 2. the fact that only one physisorption

site is considered. Concerning the H-ZSM-5 results, it is remarkable that the average of the of

the incremental values corresponding with the two different physisorption sites falls into the

experimentally expected range. With regard to the differences in physisorption energy of the

various C4 and C5 alkenes in H-ZSM-5, H-FAU and H-MOR en the various C8 alkenes in

H-FAU, we conclude these are related with their ability to fit in the zeolite pore structure,

thereby minimizing the steric hindrance and maximizing the stabilizing interactions.

Finally, physisorption of C2-C5 alkanes has been calculated in the straight channel of H-ZSM-

5 (acidic site Al12-O24(H)-Si12). The physisorption energy in H-ZSM-5(Al12), for the

1-alkanes decreases with 13.0 kJ/mol per extra –CH2– group. The decrease of the

physisorption energy with increasing carbon number is here also attributed to the increase of

stabilizing van der Waals interactions. In contrast with the alkenes, no π-complex is formed

with the alkanes and consequently, the van der Waals interactions are relatively more

important for alkane stabilization. The most preferred position, with regard to this van der

Waals stabilization, is for the alkanes the centre of the straight channel, whereas the alkenes

are positioned close to one side of the zeolite wall.


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Chapter 5: Zeolite acidity 81

Chapter 5: Zeolite acidity

The diverse Brønsted acid sites of the different zeolites are all characterized by their catalytic

activity. The catalytic performance of the zeolite is strongly governed by the acid strength of

the Brønsted sites as well as by the amount of acid sites. The latter is largely determined by

the Si/Al ratio of the zeolite, since each aluminium substitution results in a negatively charged

framework and a proton is needed to compensate this charge. What one would like to

understand is how different factors such as the aluminium content and the local structure

affect the acidity. For gas-phase molecules, the Brønsted acidity is well understood and

theoretical predictions can be made with an accuracy that matches that of experiments. The

understanding of Brønsted acidity of inorganic solids is much less advanced, in spite of the

important role these materials play as catalysts in industrial processes and the enormous

amount of research that has been made and is being made. Major research goals have been to

find reliable experimental techniques for characterizing the acid strength of different sites in

different catalysts and to understand the observed changes of the acidity when varying the

structure of the catalyst and their composition. While in experiments it is not always easy to

separate the different factors, quantum mechanical techniques can provide fundamental data

on the acid strength of zeolitic Brønsted sites which are not easily accessible by experiments.

With this theoretical approach it is possible to separate the influence of different parameters

on the acidity of the zeolite catalyst, such as the Si/Al ratio and the zeolite framework. In this

chapter, the energy of deprotonation, ∆EDP, is used as a measure for the intrinsic acid strength

of a specific Brønsted site. The intrinsic acid strength is defined as the acid strength in

absence of a proton acceptor and the deprotonation energy is defined as the energy difference

between the deprotonated zeolite (Z-O-) and the protonated zeolite (Z-OH):


First, the influence of the zeolite framework is investigated by calculating the deprotonation

energy for the different zeolites (ZSM-5, FAU and MOR) with only one aluminium

substitution per simulation cell. Further, the influence of the Si/Al ratio on the deprotonation

energies is studied in H-ZSM-5, by calculating the energy of deprotonation for a varying


amount of Al substitutions in the ZSM-5 unit cell. Barthomeuf (1987) previously reported a

limiting value for the Si/Al ratio above which there is no interaction between the acid sites.

This interaction would otherwise result in a decrease of their acid strength. For ZSM-5 this

limit Si/Al ratio amounts to 9.5, which corresponds to 9 aluminium substitutions per unit cell.

This has already been explained by the observation that the activity decreases with an

increasing number of next nearest neighbour (NNN) aluminium atoms with respect to the

aluminium atom of the bridging Si-O(H)-Al site (Zhidomirov and Kazansky (1986)). Next

nearest neighbour atoms are located on a 2T distance of each other, which is the minimum

allowed distance between two aluminium atoms according to the Löwenstein rule. Figure 5.1

shows the distribution of potential acid sites with different Al-NNN values and thus with

different acid strengths in the FAU zeolite.

Figure 5.1: Distribution of the different types of framework Al as a function of the number of Al per FAU unit cell (Corma (1995))

The distribution shows that acid sites of different strengths can be found for FAU zeolites and

that it is possible to prepare a zeolite with the acid strength required for a given reaction, just

by changing the framework Si/Al ratio. Sierka et al. (1998) go another step forward and state

that the main factor governing the acidity is the closest environment of the Brønsted site, i.e.

the number of aluminium atoms in the nearest neighbour position of the Si atom part of the

Si-O(H)-Al bridge. The role of the more distant aluminium atoms is less important and not

uniform.


5.1 Deprotonation and periodicity in QM-Pot

The QM-Pot program is used for calculating the deprotonation energies of the different zeolite

unit cells. Two difficulties, which arise due to the periodicity of the unit cell, will be

discussed first. Applying periodic boundary conditions to the deprotonation process means

that a negative charge is created in every unit cell. Not only does this create a formal problem

insofar as a divergent Coulomb term appears in the energy of the deprotonated lattice but it is

also an unrealistic model: in a catalytic process we do not expect release of a proton in every

unit cell at the same time. Suggestions have been made for approximate solutions of both

problems. Since the calculation of the energy of the negatively charged zeolite framework by

using the traditional Ewald summation technique is not possible because of the infinite

Coulomb repulsion of the charged unit cells, a uniform positive background charge

distribution to the deprotonated unit cell is added. Consequently, this neutralises the zeolite

unit cell charge and the divergence of the Coulomb energy is eliminated (Leslie and Gillan

(1985)). Also, by taking the difference between QM-Pot energies of the neutralized

deprotonated framework and the protonated zeolite, an estimate of the energy for the periodic

deprotonation of a zeolite is obtained, i.e. for the case when the proton is removed in every

single unit cell. This is a rather unrealistic situation, and we are interested in the deprotonation

of a single acidic site in an otherwise perfect infinite crystal. This can be obtained by

removing the interaction between the charged defects in the anionic unit cells, since the

difference between the energy per unit cell for the two situations - periodic defect and isolated

defect - is the interaction between the charges generated by proton removal. It is equivalent to

the electrostatic interaction between the protons. As proposed by Leslie and Gillan (1985) this

can be treated by a macroscopic approximation if the repeating unit of the periodic defects is

large. The compensation is obtained as the Coulomb energy of a periodic array of protons

with a neutralizing background immersed in a structure-less dielectric, whose dielectric

constant, ε0, is equal to that of the perfect protonated zeolite. The potential function

deprotonation energy of a zeolite which releases a single proton is then:

0

,, )(

ε

+

−∆=∆HE

EE periodicCoulperiodicPotDP

singlePot,DP

ECoul,periodic(H+) is obtained by a shell model potential calculation applying the usual Ewald

summation techniques on an array of protons ordered as in the perfect protonated zeolite. The

dielectric constant, ε0, is calculated as one-third of the trace of the static dielectric tensor


obtained from a shell model potential calculation of the protonated zeolite. Further details

about this correction method can be found in Eichler et al. (1997).

5.2 Single aluminium substitution

First, the deprotonation energy, ∆EDP, of an isolated Brønsted site is calculated in different

zeolites and specifically the influence of the zeolite framework type (ZSM-5, MOR and FAU)

and the crystallographic position (Al7 and Al12 in ZSM-5) on the acidity of zeolites is

investigated. The QM-Pot method is able to discriminate between catalytically active sites in

different crystallographic positions of a framework and between different zeolite frameworks.

More details about the zeolites studied can be found in section 4.2.2 All zeolite unit cells are

characterized by a Si/Al ratio of 95 which permits the study of isolated Brønsted sites. The

calculated deprotonation energies ∆EDP, shown in Table 5.1, are corrected to eliminate

interactions between protons in different unit cells, as mentioned in section 5.1. These

correction terms amount to -34.8 kJ/mol for FAU, -32.1 for MOR and -32.3 kJ/mol and -32.4

kJ/mol for ZSM-5(Al7) and ZSM-5(Al12). Nomenclature used for the bonds and bond

lengths is explained in Figure 5.2. Calculations of the νOH stretching frequencies were

performed as well, enabling direct comparison with experimental data. Furthermore, some

geometric parameters of the considered Brønsted acid sites are shown. To make comparison

with the cluster calculations performed with Gaussian03 (Frisch et al. (2004)) possible, the

results for a 3T-cluster are also mentioned.

Al

O2

O1

Si2Si

1

H

Figure 5.2: Nomenclature used for protonated forms of zeolites

The influence of the zeolite framework is already elaborately discussed in section 4.3.1 With

regard to the deprotonation energies, the following sequence in order of decreasing intrinsic

acidity was found: H-FAU > H-MOR ≈ H-ZSM-5(Al12) > H-ZSM-5(Al7), which is in very

good agreement with the results obtained by Eichler et al. (1997) and Brandle and Sauer

(1998).


Table 5.1: Comparison of acid sites in H-ZSM-5, H-FAU and H-MOR

H-ZSM-5 (Al7) H-ZSM-5 (Al12) H-FAU H-MOR 3T-cluster

∆EDP,QM-Pot [kJ/mol] 1236.6 1228.1 1205.9 1230.4 -

∆EDP,QM 1314.1 1346.0 1319.6 1341.3 1301.3

∆EDP,Pot -109.9 -150.3 -148.5 -143.0 -

0

, )(

ε

+HE periodicCoul -32.3 -32.4 -34.8 -32.1 -

νOH [cm-1] 3677.2 3685.0 3694.1 3690.8 3688

protonated

O1-H [Ǻ] 0.9761 0.9761 0.9748 0.9757 0.9762

Al-O1(H) [Ǻ] 1.9089 1.9028 1.9020 1.9008 2.0061

Si1-O1(H) [Ǻ] 1.7236 1.7183 1.7240 1.7063 1.7098

Al-O2 [Ǻ] 1.7196 1.7225 1.7154 1.7167 1.7561

Si2-O2 [Ǻ] 1.6068 1.6183 1.6078 1.6082 1.6369

< Si1-O1-Al [deg] 131.958 134.078 124.730 128.775 139.427

< Si2-O2-Al [deg] 145.290 147.268 133.751 139.715 151.509

deprotonated

Al-O1(H) [Ǻ] 1.7545 1.7458 1.7404 1.7503 1.7876

Si1-O1(H) [Ǻ] 1.5967 1.5924 1.5924 1.5891 1.5987

Al-O2 [Ǻ] 1.7428 1.7400 1.7284 1.7349 1.7899

Si2-O2 [Ǻ] 1.5886 1.5905 1.5821 1.5837 1.6011

< Si1-O1-Al [deg] 142.335 136.030 133.553 132.027 168.233

< Si2-O2-Al [deg] 146.533 158.699 138.854 146.184 158.423

Calculations on a 3T-cluster as zeolite model are now compared with the QM-Pot

calculations. The deprotonation energy of the 3T-cluster amounts to 1301 kJ/mol, whereas the

QM-Pot deprotonation energies of the zeolites calculated vary between 1206 kJ/mol (FAU)

and 1237 kJ/mol (ZSM-5(Al7)). This higher value for the 3T-cluster was expected since no

long range stabilizing interactions are considered in the cluster calculations. The calculated

QM-contribution to the deprotonation energy of the zeolites, varies between 1314 kJ/mol

(ZSM-5(Al7)) and 1346 kJ/mol (ZSM-5(Al12)) and are comparable with the 3T cluster

calculated value. The higher values are due to the fact that in the 3T cluster calculations the

structure is freely optimized, whereas in the QM-Pot calculations the cluster is mechanically

embedded. Moreover, Si(Al)-H termination was used in the free clusters, whereas in QM-Pot

Si(Al)O-H termination is used, which also may cause a difference (Brand et al. (1992)). The

Pot-contribution on the other hand has values between -110 kJ/mol (ZSM-5(Al7)) and -150


kJ/mol (ZSM-5(Al12)) and therefore contributes to the lower deprotonation energies. The OH

stretching frequency of the cluster amounts to 3688 cm-1 and this value is in very good

agreement with the values obtained by QM-Pot calculations. With regard to the geometric

parameters a distinction is made between the protonated and the deprotonated form of the

sites. For the protonated form it is found that the O1-H and Si1-O1(H) bond lengths are very

similar for both the cluster calculations and the QM-Pot calculations. With the cluster

calculation, the Si2-O2 and Al-O2 bond lengths are slightly overestimated (respectively

0.02Ǻ and 0.03Ǻ), whereas the Al-O1(H) bond length shows a deviation of 0.11Ǻ. Finally,

for the Si1-O1(H)-Al and the Si2-O2-Al angles large deviations were also found. Moreover

the 3T cluster model is not able to account for the change of these angles considering different

zeolite frameworks. For the deprotonated form, the same differences between cluster

calculations and QM-Pot calculations are observed. With the cluster calculation, a slight

overestimation of 0.03Ǻ, 0.05Ǻ and 0.01Ǻ was found for the Al-O1(H), Al-O2 and Si-O2

bond lengths respectively. Finally, the values of the Si1-O1(H)-Al and the Si2-O2-Al angles

differ a lot: in the 3T cluster approach these values amount to 168 deg and 158 deg

respectively, whereas variations between 132 deg and 142 deg and between 146 deg and 159

deg when QM-Pot calculations are performed. All these overestimations obtained with cluster

calculations were expected and are due to the fact that the 3T-cluster can undergo more

relaxation during optimization because the gas phase model allows all atoms to move freely

compared to the 3T-cluster which is embedded in the more rigid real zeolite structure for the

QM-Pot calculations.

5.3 Extra aluminium substitutions

In this section both the influence of the Si/Al ratio as well as the influence of the distance of

the aluminium substitutions to the acid site on the deprotonation energy is studied. All the

calculations have been performed in the ZSM-5 zeolite lattice and deprotonation of the Al7-

O17(H)-Si4 site is considered. The correction term (see section 5.1), which eliminates

interactions between the protons in different unit cells, is not taken into account since its value

is situated in the range of 33-35 kJ/mol for all the investigated structures and thus, relative

differences between the deprotonation energies do not change. To examine the influence of

the Si/Al ratio, this ratio is altered between 95 and 18.2 by substituting up to 4 extra

aluminium atoms. Although an influence of Si/Al ratio on the acid properties of the zeolite is


only expected for much lower Si/Al ratios, see Figure 5.3, it is possible to check whether QM-

Pot results are in agreement with experimental observations. Sierka et al. (1998) have shown

that acidity of Brønsted acid sites in faujasite, measured by the energy of deprotonation, is

primarily determined by the Al for Si substitutions in the nearest neighbourhood of the Si

atom of the Al-O(H)-Si bridge, the next nearest neighbour (NNN) atoms. The role of other Al

substitutions is less important. This means that mainly these NNN Al substitutions are

determining for the acid strength of the zeolite. Mention however that in reality the NNN

positions are expected to be occupied at low Si/Al ratios, whereas we simulate this at higher

Si/Al ratios.

Figure 5.3: IR high-frequency OH stretching frequency (right axis), and chemical shift (left axis) of the corresponding line in the lH MAS NMR spectrum as a function of the Si/Al ratio of USY zeolites (Corma (1995)).

The influence of the distance of the aluminium substitution to the acid site Al7-O17(H)-Si4 is

studied by carrying out the substitutions at 2T to 4T positions, where a 2T substitution is

defined as an aluminium substitution at 2T atoms away from the aluminium of the Brønsted

Al7-O17(H)-Si4 site. However, among all next nearest neighbour (NNN) Al sites those are

distinguished (2T) that are the nearest tetrahedral neighbours of the Si atom of the Si-O(H)-Al

bridge, whereas the ones are called 2T’ sites. This is depictured in Figure 5.4.


Figure 5.4: Distinction between a 2T and 2T’ position

All calculated deprotonation energies for H-ZSM-5 with Si/Al ratio from 18.8 to 95 are

shown in Table 5.2. The different 2T, 2T’, 3T and 4T atoms substituted by aluminium are

chosen without considering specific rules for the distribution of them in the unit cell, as no

information with regard to ZSM-5 could be found in literature. We refer to Appendix for

more information on the chosen tetrahedral positions. The deprotonation energies are always

calculated for a 3T embedded cluster in the H-ZSM-5 unit cell, which implies that the extra

Al substitution are treated within the interatomic potential calculation. Both the QM and the

Pot energy contributions to the total QM-Pot energy are listed. Generally the QM contribution

is situated in a range of 1305±10 kJ/mol for most of the calculated positions, although there

are a few deviations. The Pot contribution shows a lot more variation: the values vary from -

109 kJ/mol to -40 kJ/mol.

In the following paragraphs the influence of the 2T or 2T’ next nearest neighbour positions,

the varying Si/Al ratio and the distance to the acid site will be investigated. The relevant data

from the above table will be listed separately.


Table 5.2: Deprotonation energies for different Si/Al ratio.



95 - - - - 1314.1 -109.9 1204.3

47 1 - - - 1303.1 -57.2 1245.9

- 1 - - 1308.2 -86.4 1221.8

- - 1 - 1307.1 -85.9 1221.2

- - - 1 1305.4 -84.2 1221.2

31 1 1 - - 1312.3 -54.8 1257.5

- 2 - - 1306.8 -81.2 1225.6

- 1 1 - 1306.6 -81.7 1224.9

- 1 - 1 1302.7 -73.1 1229.6

- - 2 - 1312.9 -88.9 1224.0

- - 1 1 1309.0 -80.6 1228.4

23 1 2 - - 1300.0 -40.6 1259.4

- 2 1 - 1291.0 -59.3 1231.7

- 1 2 - 1305.5 -61.6 1243.9

- 1 1 1 1304.7 -70.4 1234.3

- - 3 - 1315.6 -84.2 1231.4

- - 2 1 1312.8 -84.9 1227.9

- - 1 2 1304.0 -69.6 1234.4

18.2 1 3 - - 1309.8 -47.4 1262.4

- 3 1 - 1296.7 -48.7 1248.0

- 2 2 - 1290.9 -52.2 1238.7

- 1 3 - 1307.7 -76.0 1231.7

- 2 1 1 1281.9 -41.0 1240.9

- 1 2 1 1302.1 -53.5 1248.6

- 1 1 2 1300.0 -61.8 1238.2

5.3.1 Influence of 2T and 2T’ Al substitution

As mentioned before, the Si/Al ratio is expected to change most if a NNN in 2T position is

included. Therefore, the change of the deprotonation energy has been studied for one Al in 2T

position and zero to three extra Al atoms in the 2T’ position. This causes the Si/Al ratio to

vary between 95 and 18.2. The results are given in Table 5.3. Comparing the deprotonation

energies in the Si/Al range of 95 to 18.2, an increase of the protonation energy is observed

from 1204.3 kJ/mol to 1262.kJ/mol. The Al substitution at the 2T location however clearly

causes the highest part of the increase. Adding another Al atom at the 2T’ location causes the

deprotonation energy to increase with 12 kJ/mol. Together with the results in Table 5.4 (see


further), it is possible to check whether an additivity rule exists. In Table 5.4, the same 2T’

substitution led to an increase of 17 kJ/mol for going from a Si/Al of 95 to 47, whereas here

the influence of the 2T’ substitution is a little weaker (12 kJ/mol). Substitution of two extra

aluminium atoms resulting in a Si/Al ratio of respectively 23 and 18.2 kJ/mol lead to a

consecutive increase of the deprotonation energy of 2 kJ/mol and 3 kJ/mol. These results

show clearly that an aluminium substitution at a 2T position has the largest influence on the

deprotonation energy, as was expected. One extra aluminium substitution at a 2T’ position

reinforces this effect, but the subsequent 2T’ Al substitutions appear to have almost no

additional effect. Further investigation of the influence of 2T and 2T’ Al substitution is

necessary, especially for a higher amount of Al substitutions at the 2T position. Additionally,

the independence of the cluster size should be verified by varying the cluster size and by

choosing the 2T or 2T’ Al atoms as a part of the imbedded cluster.

Table 5.3: Influence of the 2T and 2T’ Al substitution on the deprotonation energy (see also Figure 5.1)



95 - - - - 1314.1 -109.9 1204.3

47 1 - - - 1303.1 -57.2 1245.9

31 1 1 - - 1312.3 -54.8 1257.5

23 1 2 - - 1300.0 -40.6 1259.4

18.2 1 3 - - 1309.8 -47.4 1262.4

5.3.2 Influence of distance to acid site

5.3.2.a Si/Al = 47

To check the influence of the distance of aluminium substitutions to the acid site, results

obtained by doing one extra aluminium substitution at the 2T, 2T’, 3T and 4T site are shown

in Table 5.4. The simulation without extra Al substitutions is the reference case. When the

Si/Al ratio decreases from 95 to 47, the protonation energy increases with approximately 17

kJ/mol for the 2T’ position, while it increases with as much as 41 kJ/mol for the 2T position.

In addition, the deprotonation energies for an extra aluminium substitution at 3T or 4T

distance do not differ from the 2T’ case. These results clearly illustrate that the 2T atom,

which is a nearest tetrahedral neighbours of the Si atom of the Al-O(H)-Si bridge position (see

Figure 5.4), gives rise to a much higher deprotonation energy than the other positions.

Moreover, substituting the aluminium at the 2T’, 3T or 4T position makes no difference at all


to the deprotonation energy. This is in agreement with what Sierka et al. (1998) found, i.e.

that the acidity of Brønsted acid sites in faujasite, measured by the energy of deprotonation, is

preliminary determined by the Al for Si substitutions in the nearest neighbourhood of the Si

atom of the Si-O(H)-Al bridge and that the role of other NNN Al atoms or more distant

aluminium atoms is less important.

Table 5.4: Influence of the distance of the extra aluminium substitutions to the acid site on the deprotonation energy (Si/Al = 47)



95 - - - - 1314.1 -109.9 1204.3

47 1 - - - 1303.1 -57.2 1245.9

- 1 - - 1308.2 -86.4 1221.8

- - 1 - 1307.1 -85.9 1221.2

- - - 1 1305.4 -84.2 1221.2

5.3.2.b Si/Al = 23

Analogously with the preceding paragraph, the influence of the distance of the aluminium

substitution to the acid site has been studied, but now for the H-ZSM-5 zeolite framework

containing 3 extra Al substitutions above the Al7 one. Results are shown in Table 5.5. In each

situation the Si/Al ratio equals 23, but the aluminium substitutions are carried out at different

distances from the acid site. For the first situation, with an aluminium substitution at the 2T

position and two Al substitutions at 2T’ positions, a deprotonation energy of 1259 kJ/mol is

found. This value is a lot higher in comparison with the other values obtained and this is due

to the fact that a substitution at the 2T position, which has a greater influence as already

mentioned in section 5.3.1, is carried out. When comparing the other deprotonation energies,

they are all situated in a close range of 1230±5 kJ/mol except for one. The deprotonation

energy for the zeolite unit cell containing one 2T’ and two 3T Al substitutions amounts

namely to 1244 kJ/mol. No clear explanation for this unexpected large deprotonation energy

could be found. However, considering all except this value we can conclude that the

deprotonation energy is almost independent of the distance of Al substitutions to the acid site,

unless the aluminium is substituted at a 2T position. This is in agreement with the results

reported by Sierka et al. (1998).

For the other Si/Al ratios studied, analogous conclusions can be drawn (see Table 5.1). In case

of Si/Al ratio of 31, the zeolite deprotonation energy varies between 1224.0 and 1229.6

kJ/mol. In case of 4 extra Al substitutions above the Al7 one, we find an unexpected variation


of the deprotonation energy between 1231.7 and 1248.6 kJ/mol. We conclude by saying that

QM-Pot is able to explain observations reported in the literature with regard to the influence

of the distance to the acid site on the acidity of the zeolite. However the large variations of the

zeolite deprotonation energies e.g. in case of a Si/Al ratio of 18.2, indicate that further testing

of the QM-Pot program for a wider range of Si/Al ratios is necessary. Also benchmarking

with results obtained using larger embedded cluster models might be useful.

Table 5.5: Influence of the distance of the extra aluminium substitutions to the acid site on the deprotonation energy (Si/Al = 23)



95 - - - - 1314.1 -109.9 1204.3

23 1 2 - - 1300.0 -40.6 1259.4

- 2 1 - 1291.0 -59.3 1231.7

- 1 2 - 1305.5 -61.6 1243.9

- 1 1 1 1304.7 -70.4 1234.3

- - 3 - 1315.6 -84.2 1231.4

- - 2 1 1312.8 -84.9 1227.9

- - 1 2 1304.0 -69.6 1234.4

5.3.3 Influence of the Si/Al ratio

The preceding paragraphs have shown the relative importance of the 2T tetrahedral positions

when studying the influence of Al substitutions on the zeolite deprotonation energy. In this

paragraph the influence of the Si/Al ratio is studied, not considering the 2T Al substitutions,

as their effect has been described in section 5.3.1. Table 5.6 contains the average zeolite

deprotonation energy corresponding with the respective Si/Al ratios. From literature we

expect a minor change of the zeolite deprotonation energies as the 2T NNN Al substitutions

have not been considered here. When the Si/Al ratio decreases from 95 to 47, the

deprotonation energy increases with approximately 17 kJ/mol, while it increases with only 5

kJ/mol when the Si/Al ratio decreases from 47 to 31. For the next two extra Al substitutions,

the deprotonation energy increases with about 7kJ/mol. An increase of deprotonation energy,

due to an extra Al substitution, weakens as the amount of Al atoms in the unit cell increases.

A systematic increase of the deprotonation energy is clearly observed, although this was not

expected from experimental viewpoint (see Figure 5.3). This again indicates that further

testing of the QM-Pot program is necessary.


Table 5.6: Influence of the Si/Al ratio on the zeolite deprotonation energy.

∆EDP (kJ/mol)

Si/Al QM Pot QM-Pot

95 1314.1 -109.9 1204.3

47 1306.9 -85.5 1221.4

31 1307.6 -81.1 1226.5

23 1305.6 -71.6 1233.9

18.2 1296.6 -55.5 1241.0

5.4 Conclusions

With regard to the study of the isolated Brønsted acid sites in H-ZSM-5 (Al7 and Al12

position), H-FAU and H-MOR it is found that, according to the calculated deprotonation

energies, the sequence in order of decreasing intrinsic acidity is as follows: H-FAU > H-

MOR ≈ H-ZSM-5(Al12) > H-ZSM-5(Al7).

The influence of an increasing number of Al substitutions as well as the influence of the

distance of the Al substitutions to the acid site on the deprotonation energy has been studied

for H-ZSM-5 with the aluminium atom located in the sinusoidal channel of the zeolite (Al7

position). From the obtained results, some obvious trends could be observed. First, an

aluminium substitution at the 2T position has the largest effect on the deprotonation energy,

whereas the effect of a substitution at the 2T’ position is much smaller. Secondly, the distance

to the Brønsted acid site of the aluminium substitution does generally not lead to a variation

of the deprotonation energy, except when the substitution is carried out at a 2T position.

Finally, the influence of the Si/Al ratio to the deprotonation energy weakens as the amount of

Al atoms in the unit cell increases.

Nevertheless, there is still a lot of variation between the results and therefore validation of the

results becomes indispensable. The cluster size can be varied and chosen in such a way that

two or more Al atoms are part of the embedded cluster to check the independence of the

results with regard to the cluster size.


Reference List

Barthomeuf D., Materials Chemistry and Physics, 17, 49 (1987). Zeolite Acidity Dependence on Structure and Chemical Environment - Correlations with Catalysis.

Brand H.V., Curtiss L.A. and Iton L.E., Journal of Physical Chemistry, 96, 7725 (1992). Computational Studies of Acid Sites in Zsm-5 - Dependence on Cluster Size.

Brandle M. and Sauer J., Journal of the American Chemical Society, 120, 1556 (1998). Acidity differences between inorganic solids induced by their framework structure. A combined quantum mechanics molecular mechanics ab initio study on zeolites.

Corma A., Chemical Reviews, 95, 559 (1995). Inorganic Solid Acids and Their Use in Acid-Catalyzed Hydrocarbon Reactions.

Eichler U., Brandle M. and Sauer J., Journal of Physical Chemistry B, 101, 10035 (1997). Predicting absolute and site specific acidities for zeolite catalysts by a combined quantum mechanics interatomic potential function approach.

Gaussian 03, revision B.03, Gaussian, Inc.: Wallingford CT, 2004

Leslie M. and Gillan M.J., Journal of Physics C-Solid State Physics, 18, 973 (1985). The Energy and Elastic Dipole Tensor of Defects in Ionic-Crystals Calculated by the Supercell Method.

Sierka M., Eichler U., Datka J. and Sauer J., Journal of Physical Chemistry B, 102, 6397 (1998). Heterogeneity of Bronsted acidic sites in faujasite type zeolites due to aluminum content and framework structure.

Zhidomirov G.M. and Kazansky V.B., Advances in Catalysis, 34, 131 (1986). Quantum-Chemical Cluster-Models of Acid-Base Sites of Oxide Catalysts.

Chapter 6: Conclusions 95

Chapter 6: Conclusions

6.1 Cluster calculations

Cluster calculations have been performed to study physisorption, chemisorption and double

bond isomerization of 1-, 2- and isobutene. First, transition state calculations have been

performed and by introducing small perturbations along the reaction coordinate, stable

intermediates, e.g. physisorption and chemisorption complexes, have been located on the

potential energy surface. The physisorption energies are found to be similar for the different

butenes. Protonation of these physisorbed complexes leads to the formation of alkoxy

complexes: activation energies for this reaction are found to depend on the primary,

secondary or tertiary character of the carbenium ion like transition state. As a consequence,

the transition state leading to the formation of the tertiary alkoxide, t-butoxy, is found to have

the lowest barrier, whereas formation of isobutoxy, which is characterized by a primary

carbenium ion like transition state, is characterized by a very high activation energy. The

chemisorption complexes are found to be 55-80 kJ/mol stable than the physisorption

complexes. With regard to the double bond isomerization reaction of 1-butene to 2-butene

two reaction mechanisms has been proposed in the literature. On the one hand a concerted

mechanism where reaction takes place from the physisorbed state has been studied, on the

other hand a two-step mechanism via adsorption/desorption with a chemisorbed complex as

stable intermediate. It is found that the double bond isomerization reaction favourably occurs

through the concerted mechanism, since the corresponding activation barrier is almost 30

kJ/mol lower compared to the two-step mechanism. The activation energy of the one-step

mechanism however does not agree with experimentally determined values. This is easily

explained by the fact that the 3T-cluster clearly does not give a correct description of the real

zeolite environment. Moreover, it is known that taking into account the zeolite framework and

including the corresponding electrostatic and dispersion stabilizing interactions may have a

important influence on the stability of the intermediates and on the height of the reaction

barrier. We conclude that small cluster models cannot assure a quantitative correct description

of the reaction, but certainly can give a qualitative insight in possible reaction mechanisms.


6.2 Physisorption in H-ZSM-5, H-FAU and H-MOR

For a better description of the zeolite environment, a combined quantum mechanics -

interatomic potential functions approach (QM-Pot) is applied, which uses periodic boundary

conditions and treats the entire zeolite structure. Physisorption is studied for C2-C8 alkenes in

H-FAU and for C2-C5 alkenes in H-ZSM-5 and H-MOR. In H-ZSM-5, two crystallographic

T-sites were considered: the Al7-O17(H)-Si4 acidic site, which is located in the sinusoidal

channel, and the O24(H)-Si12 site, located at the intersection of a straight and a sinusoidal

channel. It is found that the physisorption strength decreases in the following order: H-ZSM-

5(Al7) > H-ZSM-5(Al12) > H-MOR > H-FAU. This different physisorption behaviour in the

various zeolite structures is related with their pore size and the framework density: stronger

physisorption occurs in the medium pore zeolite H-ZSM-5 compared to the large pore zeolites

H-FAU and H-MOR, as the smaller channels cause higher stabilization energies by dispersion

(van der Waals) interactions between the alkene and the zeolite wall. With regard to the

influence of the alkene carbon number we found that the physisorption energy for the 1-

alkenes decreases with increasing carbon number, which is mainly attributed to the increase

of stabilizing van der Waals interactions. Incremental values for the decrease of the

physisorption energy of the 1-alkenes with increasing carbon number are 14.23 kJ/mol, 8.62

kJ/mol, 12.38 kJ/mol and 6.94 kJ/mol for H-ZSM-5(Al7), H-ZSM-5(Al12), H-MOR and H-

FAU respectively. These calculated values agree considerably well with experimentally

obtained values, for which ranges of 10-12 kJ/mol, 10.1-10.5 kJ/mol and 6.4-7 kJ/mol were

found for H-ZSM-5, H-MOR and H-FAU respectively. Differences between calculated and

experimentally determined values may be due to 1. difference in Si/Al ratio and 2. the fact

that only one physisorption site is considered. Concerning the H-ZSM-5 results, it is however

remarkable that the average of the incremental values corresponding with the two different

physisorption sites falls into the experimentally expected range. Concerning the influence of

the alkene structure, differences in physisorption energy of the various C4 and C5 alkenes in

H-ZSM-5, H-FAU and H-MOR and of the various C8 alkenes in H-FAU are related to their

ability to fit in the zeolite framework thereby minimizing the steric hindrance and maximizing

the stabilizing interactions. In addition, physisorption energies of C2-C5 alkanes have been

calculated in the straight channel of H-ZSM-5. The physisorption energy for the n-alkanes

also decreases with increasing carbon number due to the increase of stabilizing van der Waals

interactions. In contrast with the alkenes, no π-complex is formed with the alkanes and the

van der Waals interactions are relatively more important for alkane stabilization. Mention that


the positioning of alkanes is totally different from those of alkenes: the alkane molecule is

located in the centre of the straight channel, whereas alkenes are positioned closer to the

zeolite wall due to the formation of a π-complex with the acidic proton.

6.3 Zeolite acidity

To understand how different factors affect the zeolite acidity, the influence of the zeolite

framework, the influence of the Si/Al ratio and the influence of the distance of the Al

substitution to the acid site on the acid strength of the Brønsted acid site are examined

calculating the deprotonation energy. With regard to the study of the isolated Brønsted acid

sites in H-ZSM-5 (Al7 and Al12 position), H-FAU and H-MOR it is found that the sequence

in order of decreasing intrinsic acidity is as follows: H-FAU > H-MOR ≈ H-ZSM-5(Al12) >

H-ZSM-5(Al7). Further, the influence of an increasing number of Al substitutions as well as

the influence of the distance of the Al substitutions to the acid site on the deprotonation

energy has been studied for H-ZSM-5 with the aluminium atom located in the sinusoidal

channel of the zeolite. From the obtained results, some obvious trends could be observed.

First, an Al substitution has the largest effect on the deprotonation energy if the Al is bonded

to the Si atom, part of the Si-O(H)-Al bridge (next nearest neighbour, NNN). The effect of

other NNN substitutions is much smaller. Secondly, the distance to the Brønsted acid site of

the Al substitution does generally not lead to a variation of the deprotonation energy, except

when the substitution is carried out at a 2T position. Finally, the influence of the Si/Al ratio to

the deprotonation energy weakens as the amount of Al atoms in the unit cell increases. We

can conclude that still a lot of variation between the results exists and that observed trends do

not always agree with expectations from experimental point of view. Therefore, validation of

the results is indispensable and this can be done verifying the independence of the calculated

deprotonation energies to changes in the embedded cluster size.


6.4 Future work

In this study, cluster calculations have been perform to study 1. physisorption and

chemisorption for the different butenes and 2. the double bond isomerization reaction of 1-

butene to 2-butene. Then, QM-Pot calculations have been carried out to study the

physisorption of alkenes and alkanes in different zeolite structures. Protonation is another

elementary step in many acid catalyzed reactions and will be subject of future research.

Further, double bond isomerization and alkylation are also important reactions in the reaction

network for e.g. the production of linear alkylbenzenes and will also be studied with the QM-

Pot method. Since all the simulations are performed at a temperature of 0K, another important

issue for future research is to verify the influence of temperature effects on all the above-

mentioned reactions.

Appendix: QM-Pot input 99

Appendix: QM-Pot input

This appendix discusses the structure of a coordinate input file, a “.car”-file, and the general

input file (“.inp” file) for the QM-Pot program.

Car-file

In the car-file the host, which is the total zeolite unit cell, and the embedded cluster, which is

calculated at high level, structures are specified. As a consequence, the coordinate input

contains two separate sections: the first one defining the coordinates of the entire zeolite unit

cell and the second one defining the coordinates of the cluster part, typically the 3T embedded

cluster and a hydrocarbon. Each section is ended with the word END and at the end of the

input file another END is written. Below, a car-file is shown for the H-ZSM-5 zeolite with

one aluminium substitution at the T7 position.

!BIOSYM archive 3 PBC=ON QMPOT ITERATION 57 -1264742.7587406 !DATE Fri Sep 23 22:22:05 2005 PBC 20.37820 19.83040 13.50860 90.07070 90.01070 90.15970 (P1) Si1 8.725773628 1.202584799 7.995345722 XXX 1 Si Si 4.000 Si2 1.476602262 18.631422000 1.244190074 XXX 1 Si Si 4.000 Si3 18.762947879 8.798555830 10.158303190 XXX 1 Si Si 4.000 Si4 11.662250320 11.050912512 3.416714382 XXX 1 Si Si 4.000 Si5 11.541506404 18.657656760 3.304193709 XXX 1 Si Si 4.000 Si6 18.835692296 1.206613518 9.994117236 XXX 1 Si Si 4.000 Si7 1.518118411 10.998521549 1.031698557 XXX 1 Si Si 4.000 Si8 8.568446072 8.859112569 7.780070776 XXX 1 Si Si 4.000 Si9 6.375110718 0.546533367 9.977500786 XXX 1 Si Si 4.000 Si10 3.686355544 19.165892594 3.280997377 XXX 1 Si Si 4.000 Si11 16.407660739 9.328900986 8.212770048 XXX 1 Si Si 4.000 Si12 14.011136337 10.561160853 1.450266619 XXX 1 Si Si 4.000 Si13 13.895502698 19.249586411 1.327230366 XXX 1 Si Si 4.000 Si14 16.582219545 0.625758486 7.997192262 XXX 1 Si Si 4.000 Si15 3.835729153 10.478453163 3.007126161 XXX 1 Si Si 4.000 Si16 6.209492419 9.222115163 9.772166761 XXX 1 Si Si 4.000 Si17 5.627434714 0.993943218 12.952824722 XXX 1 Si Si 4.000 Si18 4.393956175 18.848199967 6.290618168 XXX 1 Si Si 4.000 Si19 15.781220492 8.878880887 5.199136277 XXX 1 Si Si 4.000 Si20 14.648308382 10.999530078 11.956945729 XXX 1 Si Si 4.000 Si21 14.672919429 18.812086984 11.870951997 XXX 1 Si Si 4.000 Si22 15.879766625 0.985617979 4.978126047 XXX 1 Si Si 4.000 Si23 4.386581334 10.986142003 6.036499600 XXX 1 Si Si 4.000 Si24 5.557841868 8.686383529 12.732428218 XXX 1 Si Si 4.000 Si25 2.508721910 1.243318574 12.916867414 XXX 1 Si Si 4.000 Si26 7.537463324 18.786257888 6.067573869 XXX 1 Si Si 4.000 Si27 12.613298878 8.607635608 5.243130290 XXX 1 Si Si 4.000 Si28 17.799626939 11.226377987 12.010694286 XXX 1 Si Si 4.000


Si29 17.795977129 18.607665792 11.884150400 XXX 1 Si Si 4.000 Si30 12.731001259 1.185435405 5.132713933 XXX 1 Si Si 4.000 Si31 7.598052640 11.216656758 5.800813934 XXX 1 Si Si 4.000 Si32 2.387958024 8.503080985 12.647342214 XXX 1 Si Si 4.000 Si33 1.493121639 0.655106980 10.044071292 XXX 1 Si Si 4.000 Si34 8.501810433 19.213708263 3.158184371 XXX 1 Si Si 4.000 Si35 11.601884868 9.258000856 8.108634385 XXX 1 Si Si 4.000 Si36 18.879082355 10.561019955 1.342250246 XXX 1 Si Si 4.000 Si37 18.815952369 19.179412045 1.239702204 XXX 1 Si Si 4.000 Si38 11.794794853 0.699704629 8.043100197 XXX 1 Si Si 4.000 Si39 8.697360397 10.446553393 2.927901343 XXX 1 Si Si 4.000 Si40 1.359823193 9.287317790 9.800372266 XXX 1 Si Si 4.000 Si41 3.918915084 1.445750250 8.292368755 XXX 1 Si Si 4.000 Si42 6.056787949 18.402538417 1.462787204 XXX 1 Si Si 4.000 Si43 13.946861666 8.580960027 9.934887117 XXX 1 Si Si 4.000 Si44 16.502167474 11.270973442 3.148819184 XXX 1 Si Si 4.000 Si45 16.400904596 18.389176923 2.977788498 XXX 1 Si Si 4.000 Si46 14.207295015 1.422217148 9.807215688 XXX 1 Si Si 4.000 Si47 6.237423878 11.147365676 1.228969078 XXX 1 Si Si 4.000 Si48 3.786177009 8.517236403 8.036214500 XXX 1 Si Si 4.000 Si49 8.588483212 16.611523465 8.107825499 XXX 1 Si Si 4.000 Si50 1.435520009 3.350932065 1.469203546 XXX 1 Si Si 4.000 Si51 18.680524223 13.353106692 9.958714436 XXX 1 Si Si 4.000 Si52 11.754355108 6.448827102 3.184352946 XXX 1 Si Si 4.000 Si53 11.713460623 3.332671996 3.125318202 XXX 1 Si Si 4.000 Si54 18.788242678 16.467265344 9.838576690 XXX 1 Si Si 4.000 Si55 1.460929301 6.465005074 1.276178961 XXX 1 Si Si 4.000 Al56 8.596157710 13.436817081 8.056641668 XXX 1 Al Al 3.000 Si57 6.189200800 17.251323291 9.984513937 XXX 1 Si Si 4.000 Si58 3.803613675 2.472991218 3.219598688 XXX 1 Si Si 4.000 Si59 16.347139967 12.467722519 8.153767201 XXX 1 Si Si 4.000 Si60 14.096474846 7.416818399 1.408067873 XXX 1 Si Si 4.000 Si61 14.036784960 2.549999089 1.302151685 XXX 1 Si Si 4.000 Si62 16.418318857 17.316405924 8.064340151 XXX 1 Si Si 4.000 Si63 3.906850824 7.338631365 3.010763362 XXX 1 Si Si 4.000 Si64 6.014867258 12.392999211 9.759265424 XXX 1 Si Si 4.000 Si65 5.306222427 16.417989916 12.814633048 XXX 1 Si Si 4.000 Si66 4.744824724 3.338030228 6.028234663 XXX 1 Si Si 4.000 Si67 15.571215358 13.249808411 5.258407533 XXX 1 Si Si 4.000 Si68 14.916015755 6.590709550 12.046468668 XXX 1 Si Si 4.000 Si69 14.971211388 3.371087675 12.003372837 XXX 1 Si Si 4.000 Si70 15.534916356 16.471587504 5.213644706 XXX 1 Si Si 4.000 Si71 4.660708848 6.552770764 5.905636094 XXX 1 Si Si 4.000 Si72 5.328985889 13.195145799 12.678992635 XXX 1 Si Si 4.000 Si73 2.205876847 16.390533987 12.760945569 XXX 1 Si Si 4.000 Si74 7.849682356 3.458952971 6.153140607 XXX 1 Si Si 4.000 Si75 12.477422137 13.289380849 5.361835762 XXX 1 Si Si 4.000 Si76 18.015729525 6.526124325 12.104696231 XXX 1 Si Si 4.000 Si77 18.076758318 3.418055966 12.002205799 XXX 1 Si Si 4.000 Si78 12.422210601 16.400750445 5.212432331 XXX 1 Si Si 4.000 Si79 7.757230111 6.551911507 5.871670422 XXX 1 Si Si 4.000 Si80 2.233935683 13.288066913 12.652442671 XXX 1 Si Si 4.000 Si81 1.383148614 17.348436749 9.875476443 XXX 1 Si Si 4.000 Si82 8.724280259 2.519498410 3.291968917 XXX 1 Si Si 4.000 Si83 11.571255004 12.371784761 8.238002462 XXX 1 Si Si 4.000 Si84 18.912845619 7.429769751 1.459390199 XXX 1 Si Si 4.000 Si85 18.871782085 2.468837307 1.378929576 XXX 1 Si Si 4.000 Si86 11.586796401 17.412752156 8.078620179 XXX 1 Si Si 4.000 Si87 8.751173034 7.291961128 2.995564821 XXX 1 Si Si 4.000 Si88 1.254333334 12.424931864 9.807377811 XXX 1 Si Si 4.000 Si89 3.809813812 16.366728853 8.147519154 XXX 1 Si Si 4.000 Si90 6.329808657 3.353724612 1.466390499 XXX 1 Si Si 4.000 Si91 13.939970275 13.336195698 9.988287054 XXX 1 Si Si 4.000 Si92 16.528953953 6.554302748 3.238202539 XXX 1 Si Si 4.000 Si93 16.451760118 3.457399516 3.115746656 XXX 1 Si Si 4.000 Si94 13.952254014 16.447597304 9.885344831 XXX 1 Si Si 4.000 Si95 6.360493241 6.421845858 1.237159382 XXX 1 Si Si 4.000 Si96 3.567685086 13.286318259 8.016891670 XXX 1 Si Si 4.000 O97 7.789318277 0.977950737 9.302567195 XXX 1 O1 O 1.229 O98 2.422326202 18.419563934 2.560872871 XXX 1 O1 O 1.229 O99 17.589346217 8.573536631 9.047279913 XXX 1 O1 O 1.229 O100 12.836089449 11.300917923 2.313633617 XXX 1 O1 O 1.229 O101 12.562370957 18.641394218 2.037521660 XXX 1 O1 O 1.229 O102 17.883532203 1.343354638 8.675358857 XXX 1 O1 O 1.229 O103 2.647545636 11.238787983 2.188154639 XXX 1 O1 O 1.229 O104 7.455574241 8.575262974 8.930139259 XXX 1 O1 O 1.229 O105 6.495659462 0.766419745 11.588883920 XXX 1 O1 O 1.229


O106 3.555341300 18.970272944 4.892984446 XXX 1 O1 O 1.229 O107 16.572956276 9.070214740 6.612830141 XXX 1 O1 O 1.229 O108 13.831219373 10.838529771 13.365803430 XXX 1 O1 O 1.229 O109 13.778250474 19.065480500 13.216974571 XXX 1 O1 O 1.229 O110 16.686244558 0.808495274 6.383362898 XXX 1 O1 O 1.229 O111 3.649241194 10.710569375 4.609686080 XXX 1 O1 O 1.229 O112 6.417218914 8.926604734 11.364857577 XXX 1 O1 O 1.229 O113 4.085809223 1.284886449 12.503320774 XXX 1 O1 O 1.229 O114 5.957457156 19.168239083 5.958527465 XXX 1 O1 O 1.229 O115 14.176045886 9.008330738 5.440176184 XXX 1 O1 O 1.229 O116 16.242395572 10.812748951 12.244416601 XXX 1 O1 O 1.229 O117 16.234322288 18.713135231 12.335067803 XXX 1 O1 O 1.229 O118 14.291024765 0.735803808 5.244979012 XXX 1 O1 O 1.229 O119 5.980915774 11.200242306 5.769797259 XXX 1 O1 O 1.229 O120 3.980010652 8.621720634 12.356362628 XXX 1 O1 O 1.229 O121 1.573570777 1.193333876 11.583097640 XXX 1 O1 O 1.229 O122 8.168687088 18.500870070 4.588495138 XXX 1 O1 O 1.229 O123 11.882839137 8.496393290 6.691169174 XXX 1 O1 O 1.229 O124 18.562921286 11.313823613 13.447853030 XXX 1 O1 O 1.229 O125 18.741061579 18.612730814 13.212789205 XXX 1 O1 O 1.229 O126 12.097976498 1.431336145 6.614816681 XXX 1 O1 O 1.229 O127 8.279541423 11.192502069 4.320501008 XXX 1 O1 O 1.229 O128 1.617373576 8.520973012 11.215752249 XXX 1 O1 O 1.229 O129 2.502274103 1.504534145 9.092388605 XXX 1 O1 O 1.229 O130 7.595192471 18.608446540 1.946736969 XXX 1 O1 O 1.229 O131 12.430219922 8.573008091 9.338296302 XXX 1 O1 O 1.229 O132 18.020254911 11.206058647 2.568205586 XXX 1 O1 O 1.229 O133 17.845187892 18.319646637 2.225031527 XXX 1 O1 O 1.229 O134 12.681478218 1.324525002 9.258072681 XXX 1 O1 O 1.229 O135 7.797174911 10.995564067 1.687795824 XXX 1 O1 O 1.229 O136 2.265513984 8.706426397 8.574997000 XXX 1 O1 O 1.229 O137 5.153207121 1.425903556 9.357846645 XXX 1 O1 O 1.229 O138 5.098979031 18.504964168 2.784338808 XXX 1 O1 O 1.229 O139 14.954637751 8.741965426 8.658454450 XXX 1 O1 O 1.229 O140 15.473591944 11.134127517 1.886547480 XXX 1 O1 O 1.229 O141 15.215660538 18.462389709 1.860722110 XXX 1 O1 O 1.229 O142 15.205509257 1.335366576 8.516021667 XXX 1 O1 O 1.229 O143 5.304464212 11.061112485 2.575595640 XXX 1 O1 O 1.229 O144 4.810146809 8.515865500 9.305639914 XXX 1 O1 O 1.229 O145 7.599798051 16.667186411 9.446432804 XXX 1 O1 O 1.229 O146 2.459214065 3.264796030 2.743900662 XXX 1 O1 O 1.229 O147 17.620214237 13.309926965 8.717962467 XXX 1 O1 O 1.229 O148 12.839569041 6.545197634 1.968599382 XXX 1 O1 O 1.229 O149 12.644573733 3.252067345 1.782510716 XXX 1 O1 O 1.229 O150 17.765532502 16.545611119 8.564086025 XXX 1 O1 O 1.229 O151 2.651213515 6.518196907 2.390669833 XXX 1 O1 O 1.229 O152 7.163930422 13.151379301 8.970104152 XXX 1 O1 O 1.229 O153 6.168203480 17.094469258 11.606838901 XXX 1 O1 O 1.229 O154 3.941816683 2.570737690 4.836428775 XXX 1 O1 O 1.229 O155 16.326831240 12.564727460 6.529719560 XXX 1 O1 O 1.229 O156 14.125438714 7.277962577 13.296733009 XXX 1 O1 O 1.229 O157 14.120607778 2.636084767 13.187986388 XXX 1 O1 O 1.229 O158 16.316005224 17.195211528 6.445590606 XXX 1 O1 O 1.229 O159 3.881231007 7.195074135 4.628026510 XXX 1 O1 O 1.229 O160 6.101339504 12.601730657 11.379345343 XXX 1 O1 O 1.229 O161 3.753274693 16.917858114 12.687098645 XXX 1 O1 O 1.229 O162 6.320111567 2.905438047 5.965961557 XXX 1 O1 O 1.229 O163 14.015245605 12.745435135 5.236901079 XXX 1 O1 O 1.229 O164 16.474978065 7.078083772 12.089893439 XXX 1 O1 O 1.229 O165 16.530272174 2.897406594 12.132758674 XXX 1 O1 O 1.229 O166 13.968068999 16.937180943 5.237817937 XXX 1 O1 O 1.229 O167 6.210204959 7.091327258 5.876664397 XXX 1 O1 O 1.229 O168 3.765909707 12.710660778 12.656052515 XXX 1 O1 O 1.229 O169 1.508745576 16.573917213 11.303086566 XXX 1 O1 O 1.229 O170 8.685769268 3.176726202 4.783253473 XXX 1 O1 O 1.229 O171 11.961351153 13.246853838 6.896060266 XXX 1 O1 O 1.229 O172 18.611938675 6.555174191 0.114228648 XXX 1 O1 O 1.229 O173 18.814758703 3.187919559 13.433528729 XXX 1 O1 O 1.229 O174 11.738581975 16.605153238 6.670610736 XXX 1 O1 O 1.229 O175 8.347172975 6.484672570 4.352756163 XXX 1 O1 O 1.229 O176 1.604304728 13.275310967 11.152818856 XXX 1 O1 O 1.229 O177 2.314071352 16.675744941 8.723752518 XXX 1 O1 O 1.229 O178 7.760180554 3.328507878 2.257125705 XXX 1 O1 O 1.229 O179 12.437634595 12.938767723 9.511505009 XXX 1 O1 O 1.229 O180 18.048945596 6.876900763 2.729373029 XXX 1 O1 O 1.229 O181 17.932149774 3.204444009 2.482443595 XXX 1 O1 O 1.229 O182 12.472222847 16.705389411 9.248944610 XXX 1 O1 O 1.229


O183 7.891760784 6.717699992 1.734281855 XXX 1 O1 O 1.229 O184 2.024119275 13.073691697 8.521309756 XXX 1 O1 O 1.229 O185 4.890282941 16.460964616 9.372617699 XXX 1 O1 O 1.229 O186 5.135319812 3.128318132 2.549379062 XXX 1 O1 O 1.229 O187 14.945440632 13.071020938 8.722967552 XXX 1 O1 O 1.229 O188 15.521518494 6.879348627 1.990806552 XXX 1 O1 O 1.229 O189 15.346876103 3.300186908 1.922258367 XXX 1 O1 O 1.229 O190 15.071646487 16.668654996 8.716163137 XXX 1 O1 O 1.229 O191 5.345361293 6.785778102 2.469861756 XXX 1 O1 O 1.229 O192 4.512577644 12.864189872 9.277944464 XXX 1 O1 O 1.229 O193 6.022152668 18.823765006 9.567136970 XXX 1 O1 O 1.229 O194 3.700207168 0.901024852 2.796710653 XXX 1 O1 O 1.229 O195 16.514317720 10.910515766 8.622102270 XXX 1 O1 O 1.229 O196 13.880873386 8.976673555 1.844911714 XXX 1 O1 O 1.229 O197 14.051103709 0.988808146 1.788714424 XXX 1 O1 O 1.229 O198 16.518644784 18.891545361 8.480420866 XXX 1 O1 O 1.229 O199 3.739289708 8.903272270 2.581901314 XXX 1 O1 O 1.229 O200 6.138234594 10.797883391 9.412516121 XXX 1 O1 O 1.229 O201 1.854896293 18.903613139 10.034320481 XXX 1 O1 O 1.229 O202 8.209655086 0.973306657 3.311032690 XXX 1 O1 O 1.229 O203 12.048501498 10.820022316 7.955283689 XXX 1 O1 O 1.229 O204 18.487681883 8.979930333 1.174382931 XXX 1 O1 O 1.229 O205 18.384827658 0.914176802 1.254550835 XXX 1 O1 O 1.229 O206 12.119614318 18.946373994 7.883117252 XXX 1 O1 O 1.229 O207 8.380247411 8.871525869 3.183289344 XXX 1 O1 O 1.229 O208 1.719028410 10.870234207 9.994430171 XXX 1 O1 O 1.229 O209 8.553732122 2.727748233 7.428157770 XXX 1 O1 O 1.229 O210 1.394807790 17.241226056 0.391302413 XXX 1 O1 O 1.229 O211 18.882786057 7.474430650 11.107891225 XXX 1 O1 O 1.229 O212 11.536481055 12.355835333 4.397681975 XXX 1 O1 O 1.229 O213 11.596316906 17.215485252 4.067750769 XXX 1 O1 O 1.229 O214 18.852368811 2.614692381 10.818166888 XXX 1 O1 O 1.229 O215 1.364463582 12.352767003 0.135117562 XXX 1 O1 O 1.229 O216 8.643737633 7.596333288 6.749326580 XXX 1 O1 O 1.229 O217 8.369541207 0.223270432 6.738529534 XXX 1 O1 O 1.229 O218 2.133669926 19.778787476 0.302030903 XXX 1 O1 O 1.229 O219 18.533250211 10.097215388 11.105627105 XXX 1 O1 O 1.229 O220 11.856207529 9.733185053 4.345663885 XXX 1 O1 O 1.229 O221 11.846534746 19.824678880 4.398773939 XXX 1 O1 O 1.229 O222 18.245610908 0.051041584 10.967007124 XXX 1 O1 O 1.229 O223 1.882664666 9.746897135 0.067584270 XXX 1 O1 O 1.229 O224 8.221356450 10.193368370 6.895009961 XXX 1 O1 O 1.229 O225 7.747534459 17.437778657 6.934563216 XXX 1 O1 O 1.229 O226 2.197869786 2.636975736 0.215718168 XXX 1 O1 O 1.229 O227 17.947153713 12.675608312 11.261354098 XXX 1 O1 O 1.229 O228 12.432281984 7.171092269 4.485292020 XXX 1 O1 O 1.229 O229 12.567471897 2.581852967 4.302377197 XXX 1 O1 O 1.229 O230 18.034493320 17.209974851 11.083542958 XXX 1 O1 O 1.229 O231 2.035210441 7.094609575 13.397913294 XXX 1 O1 O 1.229 O232 8.115406986 12.772245001 6.332933297 XXX 1 O2 O 0.818 O233 4.089363783 2.822340363 7.427654482 XXX 1 O1 O 1.229 O234 5.904691808 16.938307766 0.745846302 XXX 1 O1 O 1.229 O235 14.227574278 7.155339550 10.680678606 XXX 1 O1 O 1.229 O236 16.290979242 12.707365446 3.898372828 XXX 1 O1 O 1.229 O237 16.211261031 17.009850036 3.832006381 XXX 1 O1 O 1.229 O238 14.396531401 2.859630590 10.563487519 XXX 1 O1 O 1.229 O239 6.046067784 12.594631317 0.506671388 XXX 1 O1 O 1.229 O240 3.920736125 7.085595944 7.257462323 XXX 1 O1 O 1.229 O241 3.893607876 0.125328751 7.339031986 XXX 1 O1 O 1.229 O242 5.593173705 19.499123606 0.354367606 XXX 1 O1 O 1.229 O243 14.150610760 9.821664777 10.962051390 XXX 1 O1 O 1.229 O244 16.245497299 10.054686752 4.190220995 XXX 1 O1 O 1.229 O245 16.376809860 19.703984957 3.935596819 XXX 1 O1 O 1.229 O246 14.559177276 0.230053536 10.852853401 XXX 1 O1 O 1.229 O247 5.795754414 9.952949962 0.227926344 XXX 1 O1 O 1.229 O248 4.207188005 9.690245664 6.985487311 XXX 1 O1 O 1.229 O249 4.207351659 17.352881172 6.913031156 XXX 1 O1 O 1.229 O250 6.280863160 2.254865954 0.271024175 XXX 1 O1 O 1.229 O251 14.378167051 12.463320819 11.297193804 XXX 1 O1 O 1.229 O252 16.144547208 7.426406508 4.558237465 XXX 1 O1 O 1.229 O253 16.138569391 2.476821691 4.375149053 XXX 1 O1 O 1.229 O254 14.201578532 17.429087305 11.157223556 XXX 1 O1 O 1.229 O255 6.026847146 7.291424693 13.424584883 XXX 1 O1 O 1.229 O256 3.821610432 12.352983130 6.700794100 XXX 1 O1 O 1.229 O257 20.345966105 0.842125296 9.504520191 XXX 1 O1 O 1.229 O258 10.041880981 18.920286199 2.727341979 XXX 1 O1 O 1.229 O259 10.017883909 9.090863626 8.471839701 XXX 1 O1 O 1.229


O260 0.076101384 10.707283920 1.736136023 XXX 1 O1 O 1.229 O261 -0.017526440 19.052811220 1.742105421 XXX 1 O1 O 1.229 O262 10.250734336 0.937736259 8.480577517 XXX 1 O1 O 1.229 O263 10.248120800 10.825709604 2.617715993 XXX 1 O1 O 1.229 O264 20.181318863 9.034080664 9.380564412 XXX 1 O1 O 1.229 O265 20.184317023 17.228744378 9.453411794 XXX 1 O1 O 1.229 O266 10.287565444 2.596310475 2.819554801 XXX 1 O1 O 1.229 O267 10.004101285 12.513192944 8.513242380 XXX 1 O1 O 1.229 O268 0.132130025 7.276776122 1.786008131 XXX 1 O1 O 1.229 O269 0.056800713 2.558103368 1.851922855 XXX 1 O1 O 1.229 O270 10.007060063 17.409853286 8.471736426 XXX 1 O1 O 1.229 O271 10.351985287 7.151930771 2.721661082 XXX 1 O1 O 1.229 O272 20.022913679 12.515938939 9.556476038 XXX 1 O1 O 1.229 O273 8.863790418 15.090576719 7.668805814 XXX 1 O1 O 1.229 O274 1.079575739 4.892086909 1.074398167 XXX 1 O1 O 1.229 O275 19.074940330 14.911986159 10.242865809 XXX 1 O1 O 1.229 O276 11.444477624 4.887202541 3.534969135 XXX 1 O1 O 1.229 O277 3.816243560 14.836867124 7.573059749 XXX 1 O1 O 1.229 O278 6.185177806 4.852063435 0.831090229 XXX 1 O1 O 1.229 O279 14.026991481 14.908571910 10.416922535 XXX 1 O1 O 1.229 O280 16.398510935 4.989472629 3.669276470 XXX 1 O1 O 1.229 O281 5.426159210 14.808317226 12.707950188 XXX 1 O1 O 1.229 O282 4.600618197 4.938093465 5.821783817 XXX 1 O1 O 1.229 O283 15.659778094 14.863404258 5.371102984 XXX 1 O1 O 1.229 O284 14.809831959 4.977636152 12.151431736 XXX 1 O1 O 1.229 O285 2.201823881 14.820946873 13.201073593 XXX 1 O1 O 1.229 O286 7.815361859 5.053274582 6.502330983 XXX 1 O1 O 1.229 O287 12.379073187 14.821629314 4.808859871 XXX 1 O1 O 1.229 O288 18.066667076 4.988987270 11.571918362 XXX 1 O1 O 1.229 H289 8.366301554 13.382077795 5.613220956 XXX 1 H2 H 1.000 end Si31 7.598052640 11.216656758 5.800813934 XXX 1 Si Si 4.000 Si49 8.588483212 16.611523465 8.107825499 XXX 1 Si Si 4.000 Al56 8.596157710 13.436817081 8.056641668 XXX 1 Al Al 3.000 O232 8.115406986 12.772245001 6.332933297 XXX 1 O2 O 0.818 O273 8.863790418 15.090576719 7.668805814 XXX 1 O1 O 1.229 H289 8.366301554 13.382077795 5.613220956 XXX 1 H2 H 1.000 O224 8.221356450 10.193368370 6.895009961 XXX 1 O1 O 1.229 H8 8.426139371 9.406157279 7.417195954 XXX 1 H1 H 1.000 O127 8.279541423 11.192502069 4.320501008 XXX 1 O1 O 1.229 H39 8.526686057 10.751265017 3.496762606 XXX 1 H1 H 1.000 O119 5.980915774 11.200242306 5.769797259 XXX 1 O1 O 1.229 H23 5.035816230 11.073326589 5.927894742 XXX 1 H1 H 1.000 O270 10.007060063 17.409853286 8.471736426 XXX 1 O1 O 1.229 H86 10.945051736 17.411574533 8.238317876 XXX 1 H1 H 1.000 O225 7.747534459 17.437778657 6.934563216 XXX 1 O1 O 1.229 H26 7.621947644 18.243939921 6.416251023 XXX 1 H1 H 1.000 O145 7.599798051 16.667186411 9.446432804 XXX 1 O1 O 1.229 H57 6.757520732 17.015978559 9.767724749 XXX 1 H1 H 1.000 O152 7.163930422 13.151379301 8.970104152 XXX 1 O1 O 1.229 H64 6.466775135 12.691257781 9.448901115 XXX 1 H1 H 1.000 O267 10.004101285 12.513192944 8.513242380 XXX 1 O1 O 1.229 H83 10.948664056 12.427962693 8.347348393 XXX 1 H1 H 1.000 end end

In the heading of the car-file it is shown that periodic boundary conditions are used

(PBC=ON) and that 57 QM-Pot iterations were needed to obtain the final energy. Obviously,

the cell parameters are given, i.e. the lengths of the three sides (a, b and c) and the three

angles (α, β and γ) of the unit cell. For each atom 9 columns are given. To be able to

distinguish easily all atoms from each other, a unique name was given to every atom. We

have chosen here very logically to use the atom abbreviation followed by a number which 1

for the first atom, 2 for the second atom, etc.. Since the ZSM-5 unit cell of the protonated

form of the zeolite with one aluminium substitution contains 289 atoms, these specific

numbers go form 1 to 289. Column 2, 3 and 4 specify respectively the x, y and z coordinates


of the atom in the unit cell. Column 5 and 6 are standard columns, which do not give any

special information about the atoms. The seventh column however again is very important as

it contains the information of the used the force field type atom. Different types of hydrogen

(H1, H2 and H3), oxygen (O1 and O2) and carbon (C3 and C4) atoms exist, all used in

specific cases. The different atom types in the force field and their meaning are given in Table

1. Column 8 one again shows the atom name and column 9 gives the core-charge of the atom.

This last column in particular is very important if hydrocarbon species are present in the

zeolite structure: in that case the charges used in the force field calculation on the different

hydrocarbon atoms should be mentioned here. Generally, in physisorption complexes, for all

hydrocarbon hydrogen atoms a charge 0.1 has been used, whereas the charge on the carbon

atoms depends on the number of bonds with hydrogen atoms. A charge of -0.1 times the

number of bonded hydrogens has been used. In that way the physisorption complexes always

have charge zero, which is necessary for the force field calculations.

Table 1: Function of the H, O and C atoms

Atom type Function

H1 terminating proton

H2 acid proton

H3 proton of the hydrocarbon

O1 oxygen bonded with 4 T atoms

O2 oxygen bonded with acid proton H2

C3 C atom with sp2 hybridization

C4 C atom with sp3 hybridization

In Chapter .., deprotonation energies are calculated for the ZSM-5 zeolite with aluminium

substitutions at different positions. The choices for the different 2T, 2T’, 3T and 4T atoms

substituted by an aluminium atom have been chosen freely, without following specific rules

for selection of T-position, of course taking the Löwenstein rule into account. Additionally to

the choices of the T-positions, a choice of the oxygen for adding the charge compensating

proton had to be made. All choices for Al substitutions and oxygen atoms are shown in Table

2.


Table 2: The different Si atoms substituted by an Al atom and the O atom to which the proton is bonded.

Distance to the acid site

2T 2T’ 3T 4T

Si39-O207 Si35-O123 Si87-O183 Si71-O282

Si72-O281 Si89-O177 Si11-O99

Si26-O122 Si20-O116

The Al7-O17(H)-Si4 acidic site considered for protonation corresponds with substitution of

silicon Si56 by an aluminium atom and addition of a proton H298 to oxygen O232.

Input file

In the input file the input data and several options made for the QM-Pot calculations are

specified. Below, an input file is shown for the type of calculations, which are mostly done in

this master thesis. $type optim $mode global $structure mfi_Al7_3T.car $hi_program turbo $hi_energy dscf $hi_gradient grad $lo_program newgulp $lo_energy gulp1.3.2_LINUX_bart $lo_gradient gulp1.3.2_LINUX_bart $lo_hessian gulp1.3.2_LINUX_bart $max_cycles 500 $init_hess lolevel $hess_update bfgs $tr_rad 0.15 $rad_max 0.3 $rad_min 1.e-4 $gdiis off $opt_history true $en_change 1.0e-5 $max_grad 1.0e-3 $max_step 1.0e-3 $rms_grad 5.0e-3 $rms_step 1.0e-3 $Al core 3.00000 $Si core 4.00000 $O1 core 1.22858 shel -3.22858 $O2 core 0.81753 shel -2.81753 $H2 core 1.00000 $H1 core 1.00000


The ‘type’ keyword specifies the calculation type. In this input file it is a structure

optimization (optim). Other possibilities are, for example, vibrational analysis (phonon). The

‘mode’ keyword specifies the calculation mode. Here, the value "global" means that QM-Pot

calculation is performed and QM and Pot regions are optimized simultaneously. The

‘structure’ keyword specifies the .car file where the host and cluster structures are specified.

Next, the TURBOMOLE interface function is specified for high-level (QM) calculation and

the following two keywords specify the TURBOMOLE executables needed to calculate

energy and gradient. Then the GULP interface function is specified for low-level (Pot)

calculation. The next three keywords specify the GULP executables needed to calculate

energy, gradient, and the Hessian matrix. Below the options controlling the optimization

procedure are indicated. For example, the maximum amount of iteration cycles is 500, the

initial Hessian matrix is calculated at the Pot level and updated using the bfgs method. Below

that some default program parameters are defined which need not to be changed.

Also 5 convergence criteria for the calculations are specified for the energy change, maximum

gradient, maximum step, rms gradient and rms step. The charges on the zeolite atoms,

including a core and shell charge for the oxygen atoms, as used in the force field calculations

are defined at last in the input file.

ab initio modelling of acid catalyzed hydrocarbon...

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