Computational and Theoretical Chemistry 963 (2011) 403–411

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Computational and Theoretical Chemistry

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A DFT study of the structural units in SBA-15 mesoporous molecular sieve

Zhongxue Wang 1, Daxi Wang ⇑, Zhen Zhao ⇑, Yu Chen 2, Jie Lan 1

The State Key Laboratory of Heavy Oil Processing, Faculty of Chemical Science and Engineering, China University of Petroleum, 18# Fuxue Road,Changping District, Beijing 102249, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 July 2010Received in revised form 3 November 2010Accepted 3 November 2010Available online 5 November 2010

Keywords:SBA-15 mesoporous molecular sieveSilica ringDensity functional theoryModel clusterIR spectrum

2210-271X/$ - see front matter Crown Copyright � 2doi:10.1016/j.comptc.2010.11.004

⇑ Corresponding authors. Address: Faculty of ChemChina University of Petroleum, Beijing, 18#, Fuxue Roa102249, China. Tel.: +86 10 89733733 (D. Wang). FacEngineering, State Key Laboratory of Heavy Oil ProPetroleum, Beijing, 18#, Fuxue Road, Changping DisTel.: +86 10 89731586 (Z. Zhao).

E-mail addresses: wzx19780703@163.com (Z. WWang), zhenzhao@cup.edu.cn (Z. Zhao), chenyu@c0871@163.com (J. Lan).

1 Tel.: +86 10 89733733.2 Tel.: +86 10 89731072.

Geometries of silica rings in SBA-15 mesoporous molecular sieve were investigated by the density func-tional theory (DFT). The stable conformations of model clusters with monocyclic and bicyclic silica ringswere obtained. By comparing the calculated values of Si–O bond length and O–Si–O, Si–O–Si bond angleswith the experimental data of amorphous silica, we found that all monocyclic rings are not the reasonablemodel to represent the structure of SBA-15 mesoporous molecular sieve. After having investigated thebicyclic model clusters theoretically, we inferred that 5-, 6- and 7-membered rings should be the mainstructural elements in the SBA-15 framework. Among the model clusters employed in this study themodel 5–6-s was proved to be the best one for the SBA-15 molecular sieve. A comparison between thecalculated IR frequencies of the model clusters and the measured values of SBA-15 further verified thatthe bicyclic model clusters employed here are reasonable and the model 5–6-s is the most suitable modelcluster for the SBA-15 mesoporous molecular sieve.

Crown Copyright � 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction

Mesoporous SBA-15 molecular sieve is a promising new supportmaterial for catalysts. Its large internal surface area (>800 m2/g)and OH concentration allow the dispersion of a large number ofcatalytically active sites [1]. SBA-15 modified by transition metaloxides has a high activity and selectivity to selective oxidation oflight alkanes to useful oxygenates. It has been widely used in theareas of medicine, environmental catalysis, macromolecular sepa-ration and partial oxidation of alkanes since its first synthesis in1998 [2–9].

The catalytic activity of molecular sieve has a close relation withits structure, so the in-depth study of its microstructure becomesessential and has important theoretical and practical significancefor understanding its catalytic mechanism in various fields anddesigning new ones. Preparation and application of SBA-15 meso-porous molecular sieve have been widely studied, but the study ofits molecular structure is still rare.

010 Published by Elsevier B.V. All

ical Science and Engineering,d, Changping District, Beijingulty of Chemical Science andcessing, China University oftrict, Beijing 102249, China.

ang), wdxi@cup.edu.cn (D.up.edu.cn (Y. Chen), lanjie

Zhu et al. [9] investigated the structure of the SBA-15 by X-raydiffraction and their results indicated that there is only a broadpeak in the XRD pattern ascribed to amorphous silica. Zhao et al.[1] and Kruk et al. [10] also studied the structure of the SBA-15by a low-angle X-ray diffraction. The XRD pattern of SBA-15showed four peaks that can be indexed as (1 0 0), (1 1 0), (2 0 0)and (2 1 0) reflections corresponding to p6mm hexagonal symme-try. Moreover, they successfully observed two-dimensionally hex-agonal pore on the surface of SBA-15 by transmission electronmicroscopy. Sonwane and other researchers [2,11,12] presented amethod for evaluating the pore structural parameters of SBA-15materials from the nitrogen adsorption isotherms and they foundthat SBA-15 possesses not only uniform hexagonal channels, whichcan be tuned from 5 to 30 nm, but also a number of irregular poresof which diameters are 0.5–1.5 nm. That is to say, XRD, TEM andthe nitrogen adsorption measurements showed that SBA-15molecular sieve does have not only two-dimensionally hexagonalmesoporous pores, but also irregular microporous pores on thesurface, and its framework wall is composed of disordered SiO4

tetrahedral units.The amorphous materials have more intricate structure than

the corresponding crystals consisting of the same elements suchas the amorphous silica and quartz. The structural parameters ofthese amorphous materials are no longer the precise values andthe statistical distribution of these values can only be determinedby the experimental methods. The physicists already have a roughunderstanding of the structure of the silica. The neutron diffractionhad been used to get the mean values of Si–O bond distance andO–Si–O angle of the amorphous silica by Susman et al. [13]. The

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404 Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411

mean values of Si–O bond distance and O–Si–O angle are0.1624 nm and 109.5�, respectively. The 29Si NMR had also beenused to determine the distribution and mean value of Si–O–Si bondangle by Malfait et al. [14] and the average Si–O–Si bond angle wasestimated to be 150� with the bond angle distribution of 16�. King[15] and Pasquarello and Car [16] studied the structure of amor-phous silica by molecular dynamics and postulated that the frame-work of the amorphous silica consists of 4-, 5-, 6-, 7-, and 8-membered rings. 2- and 3-membered rings only exist in the frame-work of the quenched silica [17,18].

Because of the structural complexity and the difference in com-parison with the amorphous silica, the molecular structure of SBA-15 is still not clear and it is very difficult for the physicists andcatalysis researchers to determine the molecular structure ofSBA-15 through experimental methods. Therefore, it is of great sig-nificance to make a profound study on the framework compositionof the SBA-15 mesoporous molecular sieve by the theoreticalmethod.

In this paper, the quantum-chemical method is used to investi-gate the molecular structure and infrared spectra of model clustersfor SBA-15, and SBA-15 mesoporous molecular sieve is also synthe-sized and measured by a Fourier-transform spectrometer. By com-paring the structural parameters and infrared spectra calculated byDFT method with the experimental results, we determine the geo-metric conformation and statistical distribution of the silica ringsin the framework of SBA-15 and finally present the suitable modelcluster of SAB-15 that can be used to further study on the mecha-nism of catalytic reaction which takes place on the catalysts con-taining SBA-15.

2. Calculation model and method

XRD pattern showed that the framework wall of SBA-15 isformed by amorphous silica. So referring to King and Pasquarello’sfindings [15,16], we firstly construct the monocyclic and bicyclicmodel clusters of SBA-15.

The monocyclic model clusters consist of 4, 5, 6, 7 and 8 siliconatoms and are thus called 4-, 5-, 6-, 7- and 8-membered rings,respectively (see Fig. 1A). Each bicyclic model cluster is composedof two monocyclic silica rings by splicing each other and herebythey are denoted by the number of silicon atoms of two silica ringsand the sites of the hydroxyl attached on the compounds (neigh-borhood and non-neighborhood, see Fig. 1B and C).

As shown in Fig. 1, the model cluster A has a 4-membered ringand its boundary is saturated by hydroxyls. The model clusters Band C are spliced by 5- and 6-membered rings and two hydroxylslink up with the hydrogen bond. The model cluster B is called 5–6-v and the model cluster C is called 5–6-s. 5 and 6 represent the

Fig. 1. Model clus

numbers of silicon of two silica rings. ‘‘v’’ stands for the vicinityof two hydroxyls on the model and ‘‘s’’ means that two hydroxylsof the model are not adjacent, namely separated by other groups.The boundary atoms of the model cluster are saturated by hydro-gen atoms.

The geometries of these model clusters were fully optimized atthe level of B3LYP with the 6-31G(d) basis set available in Gaussian03. Their harmonic vibrational frequencies were also evaluated atthe same level.

3. Results and discussion

3.1. Structural properties of the monocyclic model clusters

Fig. 2 shows the optimized geometries of the monocyclic modelclusters calculated at the B3LYP/6-31G(d) level, and Table 1 givesthe optimized structural parameters.

As seen in Fig. 2, the conformations of the compounds are sen-sitive to the number of the silicon atoms. The hydroxyls anchoredon the silicon atoms of the model cluster are combined togetherwith the hydrogen bond and also strongly affect on the conforma-tions of the models. The conformations of these silica rings areirregular. For example, four silicon atoms in 4-membered ringmodel (see Fig. 2A) are connected by bridging oxygen atoms andthe dangling bonds of the surface oxygen atoms are terminatedby hydrogen atoms. This conformation is a puckered form and fourhydroxyls are far away from each other. For 8-membered ring (seeFig. 2E), three non-adjacent hydroxyls are linked up with eachother by H-bond and form an equilateral triangle. Its conformationis neither a chair nor a boat conformation. The other silica ringsemployed here also have the irregular conformations.

Due to the lack of the structural data of SBA-15, we adopt Sus-man and Malfait’ data [13,14] as a criteria to evaluate the reason-ability of the model clusters in this study.

As can be seen from Table 1, the mean values of Si–O bondlength and Si–O–Si bond angle of the monocyclic model clustershave great differences from the measured values of amorphoussilica. These differences in Si–O bond lengths are more than0.004 nm. Especially for the 6-membered ring, the differencecomes to 0.006 nm. The deviations of Si–O–Si bond angles fromthe measured values are even more than 6� except for that of8-membered ring. The largest gap is found to be 15� for 7-mem-bered ring. For 8-membered ring, the mean value of Si–O–Si bondangles agrees well with the measured value of amorphous silica,which can be seen as a remarkable coincidence.

In contrast to the large deviations in Si–O–Si bond angles, thecalculated values of O–Si–O bond angle are in agreement withthe measured value (see Table 1). The largest difference between

ter of SBA-15.

A 4-membered ring B 5-membered ring

C 6-membered ring D 7-membered ring

E 8-membered ring

Fig. 2. Stable conformations of the model clusters.

Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411 405

the calculated values of O–Si–O bond angles and the measuredvalue is only 3�. This result indicates that silicon–oxygen tetrahe-drons in the framework of the silica are not easy to be deformed.

Thus we consider that there are two factors influencing theconformations and structural parameters of the silica rings: (1)the number of silicon atoms and (2) the hydrogen bond of the

Table 1Optimized structural parameters of the model clusters calculated at theB3LYP/6-31G(d) levela.

A B C D E Obs.

Si–O 1.6665 1.6729 1.6837 1.6656 1.6760 1.624 [13]Si–O–Si 157.83 158.01 144.92 165.62 149.82 150 [14]O–Si–O 107.95 106.51 109.32 108.32 108.15 109.5 [13]

a All bond length in 10�1 nm and all angles in degree.

4-4-v

4-6-v

4-8-v

Fig. 3. Stable conformations of

406 Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411

hydroxyls in silica ring. The irregular conformations of the mono-cyclic silica rings and the great difference between the calculatedstructural parameters and the measured values demonstrate thatthe monocyclic silica rings are not the suitable model clusters forSBA-15 molecular sieve. It is because that there are superabundanthydroxyls and excessive boundary effect in the model clusters. Toremedy these deficiencies and find the suitable model clusters forSBA-15 molecular sieve, we also investigate the bicyclic modelclusters in the next section.

4-5-v

4-7-v

5-5-v

the bicyclic model clusters.

Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411 407

3.2. Structural properties of the bicyclic model clusters

The bicyclic model clusters were fully optimized with theabove-mentioned method, the stable geometries are shown inFig. 3 and the values of the corresponding structural parametersare listed in Table 2.

One can find from Fig. 3 that because of the existence of the strainand space resistance the silica rings converted their irregular geom-etries to the ones that present a balance between the strain energyand the space resistance during the fully optimization process. Thatis, all 4-membered rings in the present model clusters havepuckered conformation (see Fig. 3, 4–4-v) and 5-, 6-membered rings

5-6-v

5-8-v

6-7-v

Fig. 3 (cont

have chair conformation (see Fig. 3, 5–6-v). The conformations of4-, 5- and 6-membered rings of the model clusters are similar to thatof the cycloalkane. The conformations of 7- and 8-membered ringsare no longer strict chair ones such as the one of the 8-memberedring in the model cluster 6–8-v (see Fig. 3), which is a boat conforma-tion while the conformation of 6-membered ring is a chair one.

Due to the hydrogen bond between the hydroxyls attached tothe non-adjacent silicon atoms of the model cluster, the conforma-tion of the silica ring becomes more complex. It is neither a regularchair one nor a boat one such as that of the 8-membered ring in themodel cluster 5–8-s (see Fig. 3), which is the twisted boatconformation.

5-7-v

6-6-v

6-8-v

inued)

7-7-v 8-8-v

5-6-s 6-7-s

5-8-s

Fig. 3 (continued)

Table 2Optimized structural parameters of the model clusters calculated at the B3LYP/6-31G(d) level.

4–4-v 4–5-v 4–6-v 4–7-v 4–8-v 5–5-v 5–6-v 5–7-v 5–8-v 6–6-v 6–7-v 6–8-v 7–7-v 8–8-v 5–6-s 6–7-s 5–8-s Obs.

Si–O a 1.6452 1.6457 1.6436 1.6457 1.6434 1.6439 1.6434 1.6566 1.6442 1.6437 1.6438 1.6437 1.6429 1.6470 1.6433 1.6452 1.6433 1.624[13]

Si–O–Si b 144.61 144.93 147.46 144.45 146.18 146.66 148.79 150.85 148.36 148.97 149.12 149.37 150.90 145.67 150.60 148.59 151.13 150[14]

O–Si–O b 110.32 110.02 110.99 110.16 110.46 110.26 110.73 110.53 110.38 110.39 110.70 110.53 110.46 110.31 110.35 109.85 110.26 109.5[13]

a Bond length in 0.1 nm.b Bond angle in degree.

408 Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411

Table 3IR spectral data of the model clusters calculated at the B3LYP/6-31G(d) level.

4–4-v 4–5-v 4–6-v 4–7-v 4–8-v 5–5-v 5–6-v 5–7-v 5–8-v 6–6-v 6–8-v 6–7-v 7–7-v 8–8-v 5–6-s 6–7-s 5–8-s Obs.a

Si–O rocking 357 375 364 382 393 401 400 398 388 410 393 399 398 378 435 433 409 450Si–O bending 842 834 831 830 858 829 839 828 834 833 834 826 836 830 803 832 822 809Si–O stretching 1098 1095 1075 1071 1082 1077 1069 1070 1062 1062 1063 1065 1098 1089 1065 1074 1111 1087SiO–H rocking 843 905 895 893 883 899 910 902 884 905 886 883 903 863 895 907 848 901H–O 3680 3664 366 3665 3664 3663 3669 3666 3667 3666 3664 3670 3667 3676 3659 3656 3759 –H–O� � �Hb 3669 3550 3562 3545 3564 3542 3560 3558 3551 3548 3529 3568 3566 3632 3473 3476 3695 3409

a The experimental IR data were obtained from the characterization of SBA-15 in the next section.b The frequency of H–O� � �H refers to the stretching frequency of the hydrogen-bonded O–H.

Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411 409

Susman and Malfait’s data [14,15] are also adopted as the crite-ria to evaluate the reasonability of the model clusters in thissection.

As can be seen from Table 2, the mean values of Si–O length andO–Si–O angle of the model clusters are in good agreement with themeasured values of amorphous silica. The differences between Si–O bond lengths of the model clusters with the measured value areless than 0.002 nm and the deviations of O–Si–O bond angle of themodel clusters from the experimental value are also very small,less than 2.0�. Especially for the 5–6-s model cluster, the differencebetween the calculated Si–O bond length and that of amorphoussilica is only 0.8�. The results clearly indicate that the model clus-ters adopted in this section are very reasonable.

In general, the values of Si–O–Si bond angles may be used tospeculate the statistical distribution of silica rings in the frame-work of SBA-15. The larger difference between the calculatedSi–O–Si bond angle and the experimental one the silica ring pos-sesses, the lower possibility in the SBA-15 framework its existenceis. The Si–O–Si bond angles of 4–4-v, 4–5-v, 4–6-v, 4–7-v, 4–8-v,5–5-v and 8–8-v have relatively larger difference from the mea-sured value compared with that of other bicyclic model clusters,and the maximum deviation reaches 4.6�. And for the modelclusters 5–6-v, 5–7-v, 5–8-v, 6–6-v, 6–7-v, 6–8-v, 7–7-v, 5–6-s,6–7-s and 5–8-v, the values of Si–O–Si bond angles are in goodagreement with the measured value of amorphous silica and themaximum deviation is only 1.6�.

In summary, Si–O–Si bond angles of the model clusters consist-ing of 4-membered ring have generally greater differences fromthe measured value. It is inferred that 4-membered ring accountsfor a small proportion of all silica rings in the SBA-15 framework.It can also be deduced that the proportion of the silica rings inthe framework of SBA-15 should be in the following descending

500 1000 1500 2000

40

60

80

100

tran

smitt

ance

/ %

wavenum

Fig. 4. FT-IR spectrum of SB

order: 6-membered ring > 5-membered ring > 7-membered ring >8-membered ring.

In all model clusters employed here, the calculated values of thestructural parameters of 5–6-s model are in the best agreementwith the measured values. The difference between the calculatedSi–O band length and the measured one is only 1.2%. Thedeviations between the mean value of bond angles and the mea-sured values are less than 0.8%. Hence it can be employed as themost suitable model cluster of SBA-15 mesoporous molecular sievein the follow-up theoretical study.

3.3. Calculation and measurement of IR spectral data

It is generally accepted that IR spectrum is a direct representa-tion of the structure of a compound. The chemical bonds in differ-ent environments may have different IR absorption band, i.e. thevarious band intensities or at various band frequencies. It is avaluable tool for the molecular structure determination and verifi-cation. Therefore, FT-IR was also used to investigate the structureof SBA-15 in this study.

In order to find the suitable model clusters of SBA-15 molecularsieve and verify the reasonability of these model clusters, wecalculated IR spectral data of the model clusters employed hereand also measured IR spectrum of SBA-15.

3.3.1. Calculation of the IR spectral dataIR spectral data of the model clusters calculated by the above-

mentioned method are presented in Table 3. Calculated frequen-cies were scaled by 0.9614 to account for the overestimation ofvibrational frequencies determined at the B3LYP/6-31G(d) levelof theory [19].

2500 3000 3500 4000

ber / cm-1

A-15 molecular sieve.

Table 4The releasing energies of the silica rings (kJ/mol).

4-Membered ring 5-Membered ring 6-Membered ring 7-Membered ring 8-Membered ring

DEreleasing 2.5786 3.3060 4.0299 4.7528 5.4794

410 Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411

In Table 3, one can find that the Si–O rocks of the model clustersoccur at 357–435 cm�1. Correspondingly, the Si–O bending andstretching frequencies are observed at 803–842 cm�1 and 1062–1111 cm�1, respectively. The SiO–H rocking frequencies are ob-tained at 843–910 cm�1. The O–H stretching frequencies are at3473–3759 cm�1. The single O–H stretching frequency is higherthan that of the hydrogen-bonded O–H.

3.3.2. Preparation and measurement of SBA-15 molecular sieveIn this study, the pure mesoporous SBA-15 molecular sieve was

prepared according to the literature [1] using pluronic P123 triblockcopolymer as template under acidic conditions. A solution ofP123:2 M HCl:TEOS:H2O = 2:60:4.25:15 (w/w) was prepared, stir-red for 20 h at 40 �C, and then hydrothermally treated at 100 �C for48 h. The solid products were filtered and dried overnight at100 �C. Finally, the SBA-15 samples were obtained after the calcina-tions of the resulting solid product at 600 �C for 5 h in air.

The IR vibrational spectrum was measured with a fourier-trans-form spectrometer (FTS-3000). The resolution was set at 4 cm�1.The sample was prepared as a KBr pellet. IR spectrum of SBA-15is shown in Fig. 4.

In the measurement presented here (see Fig. 4), we find sixabsorption regions: 395–510 cm�1, 765–862 cm�1, 865–995 cm�1,995–1311 cm�1, 1555–1768 cm�1, 2702–3764 cm�1. And the peaksin these absorption regions are at 450 cm�1, 809 cm�1, 901 cm�1,1087 cm�1 and 3409 cm�1

, respectively.

3.3.3. Assignment of the IR absorption bandsConsulting the calculated results, we analyzed the infrared spec-

trum of the SBA-15 molecular sieve. The band of 395–510 cm�1

matches the Si–O rocking frequency of the model cluster and it canbe attributed to Si–O rocking vibration. In the same way, the bandsof 765–862 cm�1 and 995–1311 cm�1 are assigned to Si–O bendingand stretching vibrations, respectively. The band of 865–995 cm�1 isascribed to the SiO–H rocking vibration. The broad absorption bandfrom 3764 cm�1 down to 2702 cm�1 is attributed to the SiO–Hstretching vibration. The attribution of the infrared spectra of theSBA-15 molecular sieve is consistent with the results reported inthe literature [20–23].

There is also a strong absorption band of 1555–1768 cm�1 inthe measurement with which we cannot find any calculatedfrequencies to match. Davis and co-workers investigated the IRspectrum of the silica and suggested that this absorption band isattributed to the bending vibration of both free H2O and H2O whichis hydrogen-bonded to the proton of silanol groups [24].

3.3.4. Determination of the suitable model cluster of SBA-15From Table 3 and Fig. 4, one can see that all calculated frequen-

cies of the functional groups are included in the correspondingabsorption regions of SBA-15. This verifies that the model clustersemployed here are reasonable. On the other hand, as the calculatedfrequencies of the model clusters are not fully consistent with thepeak of the corresponding absorption bands of SBA-15, we canadopt these differences as an effective parameter to determinethe most suitable model cluster for SBA-15 molecular sieve.

Contrasting IR spectral data of all model clusters (see Table 3)with that of SBA-15 molecular sieve (see Fig. 4), one can find thatfor all model clusters employed here, the calculated frequencies of5–6-s model are in the best agreement with the measured valuesof SBA-15. For the Si–O rocking and bending frequencies, the

differences between the calculated values of 5–6-s model and themeasured valves are only 15 cm�1 and 6 cm�1, respectively. Forthe H–O rocking and stretching frequencies, the deviations be-tween the calculated values and the measured values are only6 cm�1 and 64 cm�1, respectively. All results verify that the 5–6-smodel can be served as a representative model cluster of SBA-15.

4. The releasing energy

It can be seen from Fig. 3 that all bicyclic model clustersemployed in this paper only consist of three kinds of atoms,namely H, O and Si. Accordingly, we hypothesize that H, O and Siatoms combine with each other to form these models and thereleasing energy is a direct quantitative character to show thestability of the model cluster. The higher the releasing energy is,the more stable the model cluster is.

The releasing energy was determined by the following expres-sion, Eq. (1) and the corresponding results are listed in Table 4.

DEreleasing ¼ �ðE� nEH �mEO � qESiÞ=2 ð1Þ

In Eq. (1), n, m and q are the number of the hydrogen, oxygenand silicon atoms, respectively. E is the single point energy of themodel cluster (4–4-v, 5–5-v, 6–6-v, 7–7-v and 8–8-v) and EH, EO

and ESi are the single point energy of the hydrogen, oxygen atomsand silicon atoms, respectively.

It can be seen from Table 4 that the releasing energies of the silicarings follow the trend of 4-membered ring < 5-membered ring < 6-membered ring < 7-membered ring < 8-membered ring. With thenumber of the silicon atoms increasing in the silica ring, the releasingenergy increases monotonically. 4-membered ring has the smallestreleasing energy, 2.5786 kJ/mol. The releasing energy of 8-mem-bered ring is 5.4794 kJ/mol and is almost twice as much as that of4-membered ring. So it can be deduced that 4-membered ring isthe most unstable one in all silica rings and it accounts for a smallproportion of all silica rings in the SBA-15 framework.

For 7- and 8-membered rings, based on the releasing energydata, we can see that they have the relatively stable structure.But their optimized geometries in the bicyclic model are deformed,as can be seen from Table 3. When they constitute the frameworkof SBA-15, their contorted conformations often lead to the increas-ing of the repulsive force between the silica rings on SBA-15. Thisrepulsion may result in the instability of the framework of SBA-15.So it can also be deduced that 7- and 8-membered rings mayaccount for a small proportion of all silica rings in the SBA-15framework. In this section, we can also come to the conclusion that5- and 6-membered rings are the main structural units to consti-tute the framework of SBA-15, which is also in agreement withthe above statements.

5. Conclusions

The stable conformations of the monocyclic and bicyclic silicarings have been obtained by performing full optimization at theB3LYP/6-31G(d) level. The monocyclic silica rings change into theirregular conformations. The great differences between the calcu-lated structural parameters and the measured ones demonstratedthat the monocyclic silica rings are not the reasonable model clus-ters of SBA-15 molecular sieve.

In the bicyclic model clusters, 4-membered rings in thepresent model clusters have the puckered conformation and

Z. Wang et al. / Computational and Theoretical Chemistry 963 (2011) 403–411 411

5-, 6-membered rings have the chair conformation. A comparisonbetween the calculated values of the structured parameters andthe measured ones showed that the bicyclic model clusters arethe reasonable model clusters of SBA-15 molecular sieve. The pro-portion of the silica rings in SBA-15 was also inferred on the base ofcalculations. The corresponding results ranked in descending orderare as follows: 6-membered ring, 5-membered ring, 7-memberedring, 8-membered ring and 4-memerbed ring. 5-and 6-memberedrings are the main structural elements of SBA-15.

IR spectral data of the model clusters and SBA-15 molecular sievehave been calculated and measured. IR spectrum of the SBA-15molecular sieve was analyzed for the first time by consulting thecalculated frequencies. The band of 395–510 cm�1 is attributed toSi–O rocking vibration, the band of 765–862 cm�1 is assigned toSi–O bending vibration and the band at 920–1327 cm�1 is attributedto Si–O stretching vibration. The very broad absorption band of2702–3764 cm�1 is ascribed to hydrogen-bonded SiO–H groups.The Si–O bending and stretching bands of all model clusters are ingood agreement with the measured value of SBA-15. This verifiedfurther from the experimental point of view that the model clustersemployed here are reasonable.

An important finding of the present work is that in all modelclusters employed in this paper, the model 5–6-s is the mostsuitable model cluster of SBA-15 molecular sieve.

Acknowledgement

This work was supported by the National Natural Science Foun-dation of China (No. 20773163 and No. 21073235).

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