computational characterization and prediction of metal ... · characterization and prediction of...

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Coordination Chemistry Reviews 307 (2016) 211ndash236

Contents lists available at ScienceDirect

Coordination Chemistry Reviews

j ourna l h om epage wwwelsev ier com locate ccr

eview

omputational characterization and prediction of metalndashorganicramework properties

ranc ois-Xavier Coudert lowast1 Alain H FuchsSL Research University Chimie ParisTech ndash CNRS Institut de Recherche de Chimie Paris 75005 Paris France

ontents

1 Introduction 2122 Structural properties 212

21 Crystal structure prediction 21222 Large-scale screening enumeration of hypothetical structures 21523 Geometrical properties surface area pore volume and pore size distribution 21524 Advanced geometrical descriptors 21725 Localization of extra-framework ions 217

3 Physical properties 21931 Mechanical properties 21932 Thermal properties 22233 Optical and electronic properties 222

4 Adsorption 22341 Grand Canonical Monte Carlo 22442 Classical interaction potentials 22543 Coadsorption and separation 22644 Beyond classical force fields open metal sites and chemisorption 22745 Adsorption in flexible MOFs 22846 Comparing simulations and experiments 230

5 Perspectives 23051 Modeling of defects and disorder 23052 Databases for high-throughput screening 23153 Stimuli-responsive MOFs 232Acknowledgments 232References 232

r t i c l e i n f o

rticle historyeceived 26 June 2015eceived in revised form 2 August 2015ccepted 3 August 2015vailable online 12 August 2015

a b s t r a c t

In this introductory review we give an overview of the computational chemistry methods commonly usedin the field of metalndashorganic frameworks (MOFs) to describe or predict the structures themselves andcharacterize their various properties either at the quantum chemical level or through classical molecularsimulation We discuss the methods for the prediction of crystal structures geometrical properties andlarge-scale screening of hypothetical MOFs as well as their thermal and mechanical properties A separatesection deals with the simulation of adsorption of fluids and fluid mixtures in MOFs

eywordscopy 2015 Elsevier BV All rights reserved

etalndashorganic framework

olecular simulation

omputational chemistryheoretical chemistryuantum chemistryolecular dynamics

lowast Corresponding author Tel +33 144276599E-mail address fxcoudertchimie-paristechfr (F-X Coudert)URL httpcoudertname (F-X Coudert)

1 fxcoudert

ttpdxdoiorg101016jccr201508001010-8545copy 2015 Elsevier BV All rights reserved

212 F-X Coudert AH Fuchs Coordination Chemistry Reviews 307 (2016) 211ndash236

AASBU automated assembly of secondary building unitsANN artificial neural networkAUA anistropic united atomBET BrunauerndashEmmettndashTellerCC coupled clusterCHelpG charges from electrostatic potentials using a grid-

based methodCSD Cambridge structural databaseCOF covalent organic frameworkCoRE MOF computation-ready experimental MOFDFT density functional theoryGCMC grand canonical Monte CarloHMC hybrid Monte CarloHPC high-performance computingIAST ideal adsorbed solution theoryIRMOF iso-reticular metalndashorganic frameworkMC Monte CarloMD molecular dynamicsMMSV MorsendashMorsendashsplinendashvan der WaalsMOF metalndashorganic frameworkNLC negative linear compressibilityNTE negative thermal expansionOFAST osmotic framework adsorption solution theoryPSD pore size distributionQSPR quantitative structurendashproperty relationshipRAST real adsorbed solution theoryRCSR reticular chemistry structure resourceRESP restrained electrostatic potentialSBU secondary building unitSPC soft porous crystalTDDFT time-dependent density functional theoryUA united atomUFF universal force fieldVST vacancy solution theoryZAG zinc alkyl gateZIF zeolitic imidazolate frameworkZMOF zeolite-like metalndashorganic framework

1

aattmtapocwShcrnwCtca

Table 1List of reviews published on computational characterization of metalndashorganicframeworks

Year Topic Ref

2015 General modeling of MOFs (book) [1]2015 Quantum chemical characterization of MOFs

including catalysis[2]

2014 High-throughput computational screening [3]2014 First-principles force fields for guest molecules [4]2013 Gas separation [5]2012 Screening for adsorption and separation [6]2012 Methane hydrogen and acetylene storage [7]2011 Adsorption in flexible MOFs [8]2011 Energy environmental and pharmaceutical

applications[9]

2011 Screening for separation applications [10]2009 Hydrogen storage [11]2009 Adsorption [12]

These structures can then either be used to guide the synthesis ofnovel materials or to identify materials already synthesized but

Introduction

Since its emergence in the 1950s molecular simulation has seenn ever-growing use in research in the fields of physical chemicalnd materials sciences where it offers an additional dimension tohe characterization and understanding of systems complemen-ary to experimental techniques and pen-and-paper theoretical

odels The development of novel computational methodologiesogether with the exponential increase in computational powervailable to researchers have dramatically expanded the range ofroblems that can be addressed through modeling This is truef resource-intensive calculations performed on high-performanceomputing (HPC) supercomputers but it is also true of desktoporkstations and even now of laptops and mobile devices [1516]

everal of the simulation techniques of computational chemistryave now reached the status of being relatively ldquoroutinerdquo cal-ulations and are nowadays considered an integral part of theesearcherrsquos toolbox just like experimental characterization tech-iques like X-ray diffraction and NMR spectroscopy Among thosee can cite Density Functional Theory calculations and Grandanonical Monte Carlo simulations It is possible to become a user of

hese tools with relatively little training relying either on commer-ial or academic software with user-friendly interfaces Howevers with any technique one should always take great care in

2008 Adsorption and transport [13]2007 Adsorption of small molecules [14]

checking the validity of the tools for the system at hand as wellas in interpreting the results obtained

Given the formidable research effort focused on metalndashorganicframeworks (MOFs) in the past decade with more than 20000papers published (at a current rate of more than 5 MOF papers perday [17]) 15000 structures on record at the Cambridge Crystallo-graphic Data Centre and over 170 review articles dedicated to thistopic the published literature on computational studies of MOFs isin itself abundant Theoretical approaches are in many cases usedin combination with experimental characterization techniques tostudy newly synthesized materials and understand their proper-ties at the microscopic level In this introductory review we givean overview of the computational chemistry methods commonlyused in the field of MOFs to describe the structures themselves andcharacterize (or predict) their various properties It is by no meansa systematic review of existing computational work on MOFs ofwhich there simply is too much to systematically enumerate hereRather we will try to give the reader an idea of what is possiblein theoretical studies of MOFs both at the quantum chemical leveland through classical molecular simulations For more details onspecific areas of interest we refer to existing reviews of compu-tational MOF studies which are listed in Table 12 We finish thereview by pointing out some of the open questions and challengesin the field

2 Structural properties

21 Crystal structure prediction

In most cases the structure of a newly synthesizedmetalndashorganic framework is determined experimentally usingsingle-crystal X-ray diffraction data when possible or solving thestructure from powder diffraction data if single crystals of suffi-cient size or quality cannot be obtained In the latter case it oftenhappens that because of the molecular complexity of the materiala low symmetry or a large unit cell the structure solution is ardu-ous or impossible to solve Moreover in other cases there is a needfor methodologies of true (or ab initio) computational predictionof MOF crystal structures without any input of experimental data

2 In particular we do not address in this review the very specific topic of thecatalytic activity of MOFs on this we refer the reader to the very recent review byOdoh et al [2]

n Che

wc

h[vtba[gifldsm[

abnbpidbfiatbi[art

fbsso

Fr

S

F-X Coudert AH Fuchs Coordinatio

hose crystals structure has not been solved experimentally byomparison of X-ray powder diffraction patterns

In the past decades computational crystal structure predictionas made giant strides in both the fields of molecular crystals18] and inorganic materials (dense and porous alike) [19] A largeariety of methods have been developed and perfect to exploringhe configurational space of these materials including algorithmsased on the simulated annealing approach genetic (or evolution-ry) algorithm methods [2021] and molecular packing approaches22] There have also been techniques developed that are tar-eted specifically at framework materials including both extendednorganic solids (such as zeolites) and hybrid inorganicndashorganicrameworks Indeed framework materials present a specific chal-enge when it comes to structure prediction featuring both strongirectional bonds and weaker dispersive interactions We brieflyummarize here the crystal structure prediction commonly used foretalndashorganic frameworks and refer the reader to existing reviews

23ndash25] for a more comprehensive treatment of the subjectMetalndashorganic frameworks like inorganic framework materi-

ls can be regarded as composed of elementary or secondaryuilding units (SBU) assembled together into three-dimensionaletworks [2627] This fact is exploited in the Automated Assem-ly of Secondary Building Units (AASBU) method for structurerediction First developed for the computational prediction of

norganic extended lattices [28] the AASBU method uses pre-efined SBUs with tailored ldquosticky-atomrdquo interactions potentialsetween them allowing the coordination in corner- edge- andace-sharing modes From these elements the SBUs auto-assemblento three-dimensional frameworks through series of simulatednnealing and energy minimizations This strategy is applicableo MOFs as well as inorganic frameworks as was demonstratedy the ldquopredictionrdquo of experimentally-known structures includ-

ng HKUST-1 and MOF-5 as well as novel hypothetical frameworks29] The AASBU method which directly simulates in silico thessembly of MOFs is rather expensive computationally as itequires series of minimizations and simulated annealings in ordero converge structures

An alternative method is the direct construction of frameworksrom SBUs by direct enumeration of possible topologies compati-

le with the ldquobuilding blocksrdquo available In this top-down approachometimes called the ldquodecoration strategyrdquo the potentially infinitepace of polymorphs of a given composition is explored by dec-rating a list of mathematical nets with the chosen SBUs which

ig 1 Experimental and hypothetical zeolitic imidazolate frameworks (ZIF) generated

elative energy (compared to dense ZIF of zni topology) versus density

ource Adapted from ref [30] with permission from The Royal Society of Chemistry

mistry Reviews 307 (2016) 211ndash236 213

act as vertices and edges of the net [3132] The nets themselvescan be enumerated systematically from mathematical algorithmsgiven certain constraints on their features and complexity [33]They can also be taken from a list of experimentally known struc-tures such as the database of known zeolitic structures (for zeoliticnets) [34] or the broader Reticular Chemistry Structure Resource(RCSR) database [3536] This approach has been used on a largevariety of system including

bull the identification of carboxylate-based MOFs with zeotypetopologies including the complex MIL-100 and MIL-101 struc-tures [3738]

bull the enumeration of hypothetical (or ldquonot-yet-synthesizedrdquo if oneis optimistic) Zeolitic Imidazolate Frameworks (ZIF) [3930] ormore recently of porous zinc cyanide polymorphs [40]

bull hypothetical covalent organic frameworks (COF) [41]

The structures generated through this decoration process thenneed to be ldquorelaxedrdquo through energy minimization relying onclassical force field-based simulations or quantum chemistry calcu-lations in order to confirm their stability and evaluate their relativeenergy (or formation enthalpy) The latter is important in determin-ing the experimental feasibility of structures even if a given MOFstructure is a local minimum in energy if its relative energy is toohigh compared to other polymorphs it cannot be considered a goodtarget for possible synthesis This process is exemplified on Fig 1in the case of hypothetical ZIFs [3930] Starting with a given com-position (in this case Zn2+ cations and unsubstituted imidazolateanions) zeolitic nets from the IZA database [34] are decorated withthe metal centers (replacing the silicon atoms) and organic linkers(replacing the oxygen atoms) These ldquoidealrdquo starting structures areenergy-minimized through DFT calculations The resulting struc-tures can then be further studied and their formation enthalpy(here their energy relative to dense polymorph ZIF-zni) give insightinto their experimental feasibility In the case of ZIFs a general cor-relation between enthalpy and density is found but the relativelysmall dispersion of the enthalpy values between hypothetical andexperimental energies hints that the currently hypothetical frame-works should be attainable by solvothermal synthesis

Another property of metalndashorganic frameworks which can beleveraged for the computational prediction of new structures is theprinciple of isoreticularity ie the possibility of a family of MOFsto share the same topology and metal centers with variations

by decoration of zeolite topologies by Lewis et al [30] along with a plot of their


predicS istry

iisMfbwaipTrwmt

FM

S

Fig 2 Depiction of the linker replacement strategy for computational

ource Reproduced from ref [24] with permission from The Royal Society of Chem

n their organic linkers both in terms of length and functional-zation This is best exemplified by the famous IRMOF series oftructures [42] which all possess the same topology as the originalOF-5 (aka IRMOF-1) structure [43] Based on a given structure

or a parent MOF it is possible to predict the structures of possi-le isoreticular analogues Gradually replacing the original linkerith longer organic molecules with the same coordination modes

nd performing quantum chemical energy minimizations on eachndividual structure This computational strategy is of interest inroposing structures of expanded versions of known structureshis was demonstrated in the case of the MIL-88 family of mate-

ials a series of iron(III)-based and chromium(III)-based MOFsith linear dicarboxylic acid as linkers There the ligand replace-ent strategy was used for computational structure elucidation of

he MIL-88B MIL-88C and MIL-88D compounds (see Fig 2) [44]

ig 3 Scheme of the reverse topological approach for crystal structure prediction as implOF structures

ource Adapted with permission from ref [47] Copyright 2014 American Chemical Soci

tion of isoreticular MOF structures exemplified on the MIL-88 family

Isoreticularity was also leveraged to design and screen new MOF-5 analogues based on commercially available organic linkers [45]and for the de novo synthesis after computational prediction ofultrahigh surface area MOF NU-100 [46]

As a final example a combination of this linker replacementand functionalization approach with the ldquodecorationrdquo strategyhighlighted above was used by Gomez-Gualdron et al [47] to gen-erate 204 hypothetical MOF structures In this reverse topologicalapproach [41] the authors used as starting SBUs a zirconium-based metal center (Zr6O4) present in widely-studied materialUiO-66(Zr) and 48 organic linkers (12 ditopic and 36 tetratopic

building blocks) These building blocks were then combined in fourpossible topologies fcu ftw scu and csq (see Fig 3) After compu-tational identification of a top performer candidate for methanevolumetric deliverable capacity the predicted MOF NU-800 was

emented by Gomez-Gualdron et al [47] to generate 204 hypothetical (Zr6O4)-based

ety

F-X Coudert AH Fuchs Coordination Che

Fig 4 Scheme of the bottom-up approach for large-scale generation of hypotheticalM

Si

sco

2s

dwasrMMlldhGtfoot

afoisdoibcbgbpdgcA(af

OFs by Wilmer et al [50]

ource Reproduced from ref [3] with permission from The Royal Society of Chem-stry

ynthesized and its high predicted gas uptake properties wereonfirmed by experimental high-pressure isotherm measurementsver a large temperature and pressure range

2 Large-scale screening enumeration of hypotheticaltructures

Although the different methods of crystal structure predictionescribed in the previous section each have different strengths andeaknesses it is clear that they cannot necessarily scale to gener-

te very large numbers of hypothetical structures Yet the constantearch for new metalndashorganic frameworks has lead to an intenseesearch effort to replace the current trial-and-error approach toOF synthesis by enabling computationally-guided design of novelOFs There has thus been an effort in the past few years to enable

arger-scale screening of potential MOF structures by generatingarger number of hypothetical structures and storing them intoatabases along with basic characterization information This effortas been further spurred by being part of the broader Materialsenome Initiative a 100 million dollar effort from the White House

hat aims to ldquodiscover develop and deploy new materials twice asastrdquo as the current methods [4849] In this section we detail somef the recent milestones in the generation of large-scale databasesf hypothetical materials and their screening for specific applica-ions [3]

Hypothetical databases of zeolite structures have been avail-ble for many years [51ndash55] containing up to two-million uniqueeasible structures In the MOF world the first large-size databasef hypothetical material was the pioneering work of Wilmer et aln 2012 [50] a decisive step towards large-scale high-throughputcreening of metalndashorganic frameworks The generation proce-ure followed by Wilmer (depicted on Fig 4) is iterative basedn step-wise combination of predefined building blocks rely-ng on geometric rules of attachment pretty much like LEGOregricks All this information input into the generation procedureomes from the experimental literature the building blocks areased on the reagents used in reported MOF syntheses and theeometric rules for attaching the blocks together are determinedy the crystallographic structures of known compounds using thisarticular coordination This approach is more powerful than theecoration or linker replacement strategies because it is entirelyeneral and does not restrict to known topologies It is also lessomputationally demanding than the assembly approaches such as

ASBU because it does not necessitate the minimization of energy

or scoring function) It thus scales to large number of structuress Wilmer demonstrated by generating 137953 hypothetical MOFsrom a library of 120 building blocks with the constraint that each


MOF could contain only one type of metal node and one or two typesof organic linkers along with a single type of functional group

A second example of the generation of hypothetical MOF struc-tures comes from the family of zeolitic imidazolate frameworks(ZIF) Based on the extensive database of more than 300000hypothetical zeolite structures by Deem [5556] Lin et al have usedthe decoration strategy to obtain a database of Zn(imidazolate)2 ZIFstructures replacing the zeolitesrsquo silicon atoms by zinc cations andthe bridging oxygen atoms by imidazolate linkers [57] In additionto these two hypothetical MOF databases two publicly availabledatabases of MOFs have been constructed from experimental struc-tures The first was gathered and published by Goldsmith et al [58]Derived from the Cambridge Structural Database (CSD) [5960]the database contains computation-ready MOF structures iedisorder-free structures from which solvent has been removed Theauthors originally used it for the screening and selection of optimalhydrogen storage materials as well as highlighting the theoreticallimits of hydrogen storage in MOF materials

A second database was built recently by Chung et al withthe aim of producing ldquoa nearly comprehensive set of porous MOFstructures that are derived directly from experimental data but areimmediately suitable for molecular simulations or visualizationrdquo [61]This database of computation-ready experimental MOF structures(or CoRE MOF database) was produced from the CSD crystallo-graphic structures through a multi-step procedure summarizedin Fig 5 (i) selection of potential MOFs based on chemical bondanalysis (over 60000 candidates after this step) (ii) eliminationof 1-D coordination polymers and 2-D hydrogen bonded networksto retain only three-dimensional MOFs (over 20000) (iii) remov-ing partially occupied crystallographic positions elimination ofstructures with disorder in the framework identification of charge-balancing ions (iv) solvent removal The final CoRE MOF databasecontains over 4700 hypothetical porous MOF structures Its authorsused it to investigate the structural properties of the CoRE MOFsthat govern methane storage capacity in MOFs

All the databases described above whether of experimental andhypothetical structures including zeolites MOFs porous polymernetworks and more have been consolidated as part of The Materi-als Project and available online (upon registration) for browsingas well as systematic data mining through documented Appli-cation Programming Interfaces (APIs) [62] Their use as a basisfor large-scale high-throughput screening of porous materials hastaken off in the past three years Most of the screening studiesproposed so far focus on identifying materials for adsorption-based applications including separation [6364] capture [57] andstorage [5065ndash67] of strategic gases hydrogen [6667] methane[506865] carbon dioxide [57] noble gases [6364] etc In thesehigh-throughput screening approaches the performance of mate-rials are typically evaluated either by geometrical properties (poresize pore volume accessible surface area see Section 23) or byevaluation of the host-guest interactions and adsorption properties(through Grand Canonical Monte Carlo simulations with classicalforce fields see Section 41) Large-scale high-throughput screen-ing of metalndashorganic frameworks targeting other properties orrelying on other descriptors has not developed so far

23 Geometrical properties surface area pore volume and poresize distribution

Once a MOF structure has been determined either crystal-lographically or using a combination of diffraction experimentsand quantum chemistry calculations there are several so-called

geometrical properties that can be calculated based solely onthe unit cell parameters and atomic positions Such geometricalcalculations are straightforward to perform and computation-ally inexpensive ranging from seconds to minutes on a desktop


ion-ReS l Soci

cagvcd

maafdatttiaitiBeh

tasarissvn[ts[

of a reference pore geometry (slit-like cylindrical spherical) andof an approximate chemical composition (though no kernels areavailable specifically for MOF materials) Thus they provide a

Fig 5 Schematic illustration of the CoRE (Computatource Adapted with permission from ref [61] Copyright 2014 American Chemica

omputer They rely on a description of the material where eachtom of the framework is a hard sphere centered on crystallo-raphic coordinates The radii used for these hard spheres are thean der Waals radii of the atoms Probe molecules used in order toalculate guest accessibility are also considered spherical with aiameter equal to the kinetic diameter of the molecule

The most common geometric characterization performed onicroporous solids is that of their accessible surface area and

ccessible pore volume representing the surface (resp volume)ccessible to guest molecules of a given size Three possible sur-aces can be used to measure this as depicted in Fig 6 The vaner Waals surface is that defined by hard spheres centered on eachtom and does not depend on probe size The accessible surface ishat accessible to the center of mass of a probe of radius rp Finallyhe Connolly surface (also called solvent-excluded surface) delimitshe space which is inaccessible to any part of the spherical probe its technically harder to compute Duumlren et al have shown that theccessible surface area is the appropriate surface area to character-ze crystalline solids for adsorption applications [69] In particularhe accessible surface area calculated with a probe size correspond-ng to nitrogen (rp = 3681 A [70]) can be directly compared withET surfaces from experimental nitrogen isotherms [71] (thoughxperimental values might be lower because of blocked pores origher in presence of defects see Section 46)

Sampling methods for the calculation of molecular surface arehe most common numerical methods to evaluate the solvent-ccessible surface of both molecules and periodic crystallineystems This procedure is illustrated on Fig 6rsquos lower panel from

sample of points on each atomrsquos ldquosolvation sphererdquo (of radiusi + rp) the proportion of points that are not buried inside neighbor-ng atoms determines the atomrsquos contribution to the total accessibleurface area This is called the Shrake-Rupley algorithm [72] Aimilar sampling method can be adopted for the accessible poreolume the pore space is sampled eg on a regular mesh and theumber of mesh points falling within the pore volume is counted

73] Other sampling methods exist however for the determina-ion of both accessible surface area and accessible pore volumeuch as the use of ray casting [74] and analytical calculations7576]

ady Experimental) MOF database construction [61]ety

Another tool at our disposal for geometric characterizationof pore space is the pore size distribution (PSD) as illustratedon Fig 7 in the case of metalndashorganic framework HKUST-1 (alsoknown as Cu3(btc)2) Experimentally pore size distributions can beobtained by numerical analysis of experimental low-temperaturenitrogen or argon adsorption isotherms [7879] given the choice

Fig 6 Upper panel definition of the van der Waals surface (black line) Connollysurface (blue line) and accessible surface area (red dashed line) Lower panelscheme of the calculation of accessible surface area contribution by each atomthrough sampling of its ldquosolvation sphererdquo green points are accessible red pointsare buried inside neighboring atoms and thus inaccessible

F-X Coudert AH Fuchs Coordination Chemistry Reviews 307 (2016) 211ndash236 217

F een) a( o the

S

poatVeib5[

2

tnegafaCcnfmo2

atbc[ifitpotsos

ut

ig 7 Left view on the structure of HKUST-1 (Cu3(btc)2) featuring small pores (grPSD) calculated from the crystal structure of HKUST-1 with peaks corresponding t

ource Adapted from ref [77] with permission from Elsevier

oint of qualitative comparison between the geometric propertiesf the ideal crystal structure and those of the samplersquos pore spaces observed through the adsorption process The standard methodo calculate geometrical pore size distributions was developed forycor glasses by Gelb and Gubbins [80] and its computationalfficiency was later improved by the same group [81] This methods entirely generic applicable to nanoporous materials containingoth micropores (below 2 nm) and mesopores (between 2 nm and0 nm) and has been used with success in several MOF materials8283]

4 Advanced geometrical descriptors

These methods described so far however do not account forhe connectivity of the pore space determined by geometric meansor for its accessibility to guest molecules along a diffusion path Forxample if a nanoporous structure presents a cavity linked to a sin-le channel (side pocket) a guest may fit inside the cavity but not beble to enter in the first place if the channel is too narrow It is there-ore necessary to analyze the pore volume (and associated surfacerea) by breaking it down into pathwise connected componentsomponents of dimensionality equal to zero correspond to isolatedages or unreachable side pockets which sorbate molecules can-ot dynamically enter Once identified these need to be excluded

rom GCMC simulations of adsorption in order to avoid insertion ofolecules where it is not physically realistic [8485] Components

f higher dimensionality are one-dimensional pore channels andD and 3D pore networks

The sampling methods described above for accessible surfacend pore volume determination can be extended to further par-ition the porous network into connected components typicallyy mesh-based propagation methods [87ndash8983] derived from thelassical algorithms developed in the study of percolation theory90] These grid-based methods are computationally expensiven particular for high-accuracy determinations which require veryne mesh spacing An alternative to the use of grid-based samplingo characterize pore accessibility exists based on Voronoi decom-osition (depicted on Fig 8) [9192] which for a given arrangementf atoms in a periodic domain provides a graph representation ofhe void space The analysis of the Voronoi network and the acces-ibility of its nodes can then yield information into the componentsf the pore system the dimensionality of the different channel

ystems and the associated surface area and volume [86]

In addition the analysis of the Voronoi network can yield otherseful geometric descriptors for porous materials Three quanti-ies in particular are of particular relevance to the description of

nd two different types of large pores (green and red) Right pore size distributionthree types of pores

molecular adsorption and transport in porous materials (see Fig 8)[938786]

bull the diameter of the largest included sphere Di which reflectsthe size of the largest cavity within a porous material

bull the diameter of the largest free sphere Df representing thelargest spherical probe that can diffuse fully through a structure(ie the size of the narrowest constriction in the channel system)

bull the largest included sphere along the free sphere path Dif

The definitions of these three diameters are illustrated on Fig 8They can be used in order to better understand adsorption sep-aration and diffusion of guests in nanoporous materials [94] toquantify the similarities (and differences) between pore spaces ofmaterials in a given family as well as for high-throughput screeningof structure databases [863]

From a practical point of view the Voronoi-based analysis ofnanoporous materials described above is implemented in the open-source Zeo++ software package [869596] It allows in one singlerun the calculation of all geometric features of a given system Itis widely used for large-scale studies of zeolite and MOF databasesand the screening of hypothetical novel structures [96]

Finally while Voronoi-based descriptions of pore space appearas the most generic tool for systematic description of pore spacegeometries it is worth noting that other approaches have beendeveloped We will cite here in particular the alternative methodof First et al which aims at fragmenting the pore space and rep-resenting as a set of geometrical blocks such as cylinders andspheres in order to identify portals channels cages and theirconnectivity [9798] Performing this analysis on a large num-ber of available experimental crystal structures First et al builttwo online databases of nanoporous materials ZEOMICS [99] andMOFOMICS [100] aggregating quantitative information on the geo-metrical characteristics of zeolites and MOFs respectively (Fig 9)

25 Localization of extra-framework ions

While most metalndashorganic frameworks possess a neutralframework there is an important subclass of MOFs that featureionic frameworks and charge-compensating extra-framework ionsin their pores These materials present some similarity to cationiczeolites although in the case of MOFs both anionic frameworks(with extra-framework cations) and cationic frameworks (with

extra-framework anions) are possible In the past decade a largenumber of ionic MOFs (sometimes called charged MOFs) syntheseshave been reported in the literature [104] Perhaps the best-knownmaterials in this family are the anionic zeolite-like metalndashorganic


Fig 8 Advanced geometrical characterization of nanoporous materials Top left depiction of the Voronoi decomposition of space in 2D and 3D Top right definition of thediameter of the largest included sphere (Di) diameter of the largest free sphere (Df) and

the pore volume of the DDR zeolitic framework (for a probe of radius 32A) between acce

Source Adapted from ref [86] with permission from Elsevier

Fig 9 Analysis of the pore systems of zeolite MFI and metalndashorganic frameworksNOTT-401 [101] ZIF-7 [102] and Mg-rho-ZMOF [103] by the ZEOMICS [97] andMOFOMICS [98] tools

Source Reproduced from ref [97] with permission from The Royal Society of Chem-istry and the MOFOMICS website [100]

largest included sphere along the free sphere path (Dif) Bottom decomposition ofssible and inaccessible volumes

frameworks or ZMOFs [105] rho-ZMOF and sod-ZMOF synthe-sized by Eddaoudi and coworkers are porous anionic MOFs withzeolitic topologies whose overall neutrality is ensured by charge-balancing 134678-hexahydro-2H-pyrimido[12-a]pyrimidinecations [106]

Both cationic and anionic metalndashorganic frameworks have beenstudied for potential applications Due to the electric fields gener-ated inside their nanopores by the presence of extra-frameworksions ionic MOFs show strong interactions with guest moleculesand specific interactions with polar guests in particular This effectcan in turn be leveraged for applications in gas adsorption andstorage [107108] separation [109] molecular recognition [110]drug delivery [111] ion exchange [112] and catalysis [113ndash115]Since the extra-framework ions in charged MOFs can be exchangedthese materials offer a large versatility and tunability However therational design of novel materials and their post-synthetic opti-mization requires a good understanding of their behavior at themicroscopic level and in particular of the localization of theirextra-framework cations and the nature and strength of theionndashguest interactions

The localization of extra-framework ions in the charged MOFstructures is not always possible in particular because the ionsmay be too delocalized or disordered There molecular simu-lation can play an important role identifying possible bindingsites for ions (ie local energy minima) and their physical char-acteristics binding energy mobility (ie spatial spread of the

site) This can be achieved either at the level of quantum chem-ical calculations or through molecular simulations based onclassical force fields The latter in addition to individual bind-ing sites can also help determine the distribution of cations


Fig 10 Top localization of the two cationic sites (I and II) for Na+ in the anionic rho-ZMOF framework Middle Coadsorption isotherms and selectivity for an equimolarCO2CH4 mixture calculated by Grand Canonical Monte Carlo Bottom Locations ofCO2 molecules adsorbed from the equimolar CO2CH4 mixture at various pressures

SC

bmpCldquoettoipt

mamMiifaBirdmct

Fig 11 Top comparison of the minimal shear modulus of several metalndashorganicframeworks obtained from DFT calculations Bottom representation of the soft

mechanical properties depend on both chemical composition and

ource Reproduced with permission from ref [122] Copyright 2009 Americanhemical Society

etween the various possible sites as a function of the experi-ental conditions number and nature of cations temperature

resence of solvent etc This is typically achieved through Montearlo simulations including large-scale displacement moves (orjumpsrdquo) in order to overcome the formidable energy barri-rs typically involved with movement of a cation from siteo site These simulations can also borrow methodologies fromhe very extensive scientific literature available on the topicf extra-framework cation localization in zeolites [116ndash118]ncluding the use of simulated annealing [119] or parallel tem-ering methods [120121] to reach equilibrium in reasonableime

Once the localization of extra-framework ions has been deter-ined it can then be used as input or basis for the study of

dsorption properties of the ionic MOF [123ndash125109] These areethodologically similar to simulations of adsorption in neutralOFs except for the very large strength of the Coulombic ionndashguest

nteractions While simulations of adsorption are treated in detailn Section 4 we give in Fig 10 a rather typical example of resultsrom molecular simulation in ionic MOFs here in the case of thenionic rho-ZMOF with extra-framework Na+ cations In this studyabarao et al [122] identified two types of binding sites for Na+

ons in the anionic framework with site I in an eight-membereding and site II in the ˛-cage The authors showed that carbonioxide is adsorbed predominantly over other gases including

ethane because of its strong electrostatic interactions with the

harged framework and the presence of Na+ ions acting as addi-ional adsorption sites

shear modes of MOF-5 and HKUST-1

Source Reproduced with permission from ref [126] Copyright 2013 AmericanChemical Society

3 Physical properties

31 Mechanical properties

Compared to structural characterization and adsorption prop-erties studies of the mechanical properties of metalndashorganicframeworks appeared relatively late in the literature both exper-imental and computational The first theoretical calculations ofmechanical properties were predictions of the bulk modulusof MOF-5 (and several analogues) by DFT calculations [127]Fuentes-Cabrera et al calculated the energy vs volume curves foreach of these cubic materials fully relaxing the atomic positionsfor each value of unit cell parameter a then the curves werefitted by the BirchndashMurnaghan equation of state [128] Later workperformed calculations not only of bulk modulus but also theindividual elastic constants (C11 C12 and C44) of the cubic MOF-5[129ndash132] along with its average Youngrsquos and shear moduli Thesecalculations were again performed at the DFT level (either withLDA or GGA exchangendashcorrelation functions) They employedeither the fitting of quadratic ldquoenergy vs strainrdquo curves or linearldquostress vs strainrdquo curves by applying small strains to the relaxedstructure

Since these seminal studies other cubic materials have beenstudied by the same methods including IRMOFs [133] ZIF-8[134] UiO-66 [126] etc In addition to these zero Kelvin quantumchemical calculations other works have reported bulk moduli atfinite temperature through force field-based molecular dynamicssimulations eg for MOF-5 [135] and HKUST-1 [136] The mainconclusion from both experimental and computational work onelastic properties of MOFs [134137ndash139] is that MOFs are farsofter than inorganic nanoporous materials such as zeolites iethey present much lower elastic moduli though their detailed

the frameworkrsquos geometric properties (see Fig 11) In particularmany highly porous MOFs feature very low shear moduli (of theorder of 1 GPa) implying relatively small mechanical stability The


F by quaY tio (

Uud

fsscdfsi

Tsbc

bull

bull

bull

bull

Ptw

fpeasfltF

MOFs [157ndash159] On the computational side it can be studied intwo ways In the linear elasticity regime it can be studied throughthe computation of the elastic stiffness tensor as described aboveas was done for the prediction and subsequent experimental

Fig 13 Anisotropy of the elastic moduli as a signature of soft porous crystals 3Drepresentation of the directional Youngrsquos modulus of ldquobreathingrdquo metalndashorganic

ig 12 Determination of the four-rank tensor C of second-order elastic constants

oungrsquos modulus (E) shear modulus (G) linear compressibility (ˇ) and Poissonrsquos ra

iO-66 family of materials is one of the exceptions with shear mod-lus in the 12ndash14 GPa range due to its strong ZrndashO linkages and highegree of coordination [126]

Characterization of elastic constants of MOFs can also be per-ormed on crystal structures without cubic symmetry with theame techniques Although the manual generation of strainedtructures by hand makes it more tedious in lower-symmetryrystal classes some quantum chemistry software now handle itirectly (including CRYSTAL14 [140141]) and scripts are availableor others These allow to calculate the full four-rank tensor C ofecond-order elastic constants which relates strain to stress n the tensorial Hookersquos law

ij =sum

kl

Cijklkl (1)

he number of independent nonzero elements of this stiffness ten-or depends on the crystal class It determines the entire elasticehavior of the material and by tensorial analysis can be used toalculate physical properties of interest (see Fig 12) including

the directional Youngrsquos modulus E(u) also known as the tensilemodulus quantifies the deformation of the material in directionu when it is compressed in that same directionthe linear compressibility ˇ(u) which characterizes the com-pression along axis u when the crystal undergoes an isotropiccompressionthe shear modulus (or modulus of rigidity) G(u v) which quan-tifies the materialrsquos response to shearing strains along u in theplane normal to vthe Poissonrsquos ratio (u v) which characterizes the transversestrain (in the v direction) under uniaxial stress (in the u direction)

rograms are available for the calculation of these properties fromhe stiffness tensor such as the ElAM [142] code or the online ELATEeb app [143]

The detailed analysis of the elastic properties of metalndashorganicrameworks has in the last few years been applied to differentroperties In addition to the low elastic moduli of MOFs in gen-ral Ortiz et al [145146] demonstrated that the existence of highnisotropy in elastic properties coupled with directions of very

mall Youngrsquos and shear moduli (sub-GPa) is a signature of theexibility of soft porous crystals [147] determining their ability

o undergo large structural deformations under stimulation (seeig 13) [148] This has allowed the prediction of flexibility for new

ntum chemistry calculations and its analysis to obtain physical properties such as)

structures such as NOTT-300 and CAU-13 [149] (the latter has sincebeen confirmed experimentally [150])

Among the mechanical properties of MOFs that have attractedsome interest Negative Linear Compressibility (NLC) [151] hasdrawn significant attention This property of materials expandingin one or two directions under hydrostatic compression is consid-ered rather exotic in inorganic solids [152] but has been observedin a relatively large number of framework materials [153ndash156] and

framework MIL-47 compared to MOF-5 On the bottom panel are indicated thestiffest and softest directions of deformation (minimal and maximal Youngrsquos mod-ulus)

Source Adapted with permission from ref [144] Copyright 2013 American Chem-ical Society


F inimiu

S istry)

cfescc

dtiiTaoo

ig 14 Examples of in silico compression experiments by DFT-based enthalpy mnder tension Bottom pressure-induced proton jump in ZAG-4

ource Adapted with permission from refs [149] (from The Royal Society of Chem

onfirmation of negative linear compressibility in the MIL-53amily [158] It can also be performed by in silico compressionxperiments studying the influence of finite increments of pres-ure on a MOF structure either through enthalpy minimizationalculations under pressure [157] or through constant-pressureonstant-temperature (N T) molecular dynamics studies [149]

Because computational compression experiments allow theetermination of structure (unit cell parameters and atomic posi-ions) as a function of applied mechanical pressure it yieldsnformation outside of the elastic regime and can provide insightnto the occurrence of pressure-induced structural transitions

wo rather typical examples of these in silico compressionsre shown in Fig 14 using DFT-based enthalpy minimizationf the crystal structures at increasing (or decreasing) valuesf pressure The first is that of CAU-13 [161] demonstrating

zation under pressure Top narrow-to-large-pore structural transition in CAU-13

and [160] (Copyright 2014 American Chemical Society)

linear elastic behavior at positive pressure and the existenceof a narrow-pore-to-large-pore structural transition under ten-sion ie for hydrostatic pressures around P minus500 MPa Althoughexperimentally applying hydrostatic tension is not an option itdoes correspond to the outward stress induced by adsorptionof bulky molecules (such as xylenes) in small nanopores Thesecond example is that of ZAG-4 a Zinc Alkyl Gate material show-ing nonmonotonic behavior under compression as seen fromhigh-pressure single-crystal X-ray crystallography [162] Quan-tum chemical calculations of the compression process showed thatthe nonlinear behavior is associated with a structural transition

namely a reversible pressure-induced proton transfer between anincluded water molecule and the linkerrsquos phosphonate group [160]

Finally it should be noted that in the (relatively rare) case ofmaterials for which a good flexible force field is available such

2 on Che

sdirfpfttwZ[tashe

3

dtbtsarcpthhwt

puedc

˛

wefmwvvrtawp

vv(

22 F-X Coudert AH Fuchs Coordinati

tudies can also be performed using force field-based molecularynamics simulations This approach has been well demonstrated

n the case of the crystal-to-crystal ldquobreathingrdquo transition in mate-ials of the MIL-53 family (including MIL-47) as is discussedully in Section 45 The same approach was used to study theressure-induced amorphization in ZIF-8 and ZIF-4 [163] Thereully-anisotropic constant-pressure molecular dynamics simula-ions were used to calculate the evolution of elastic constants ofhe materials at room temperature as a function of pressure3 Thisas used to show that the pressure-induced amorphization of both

IF-8 and ZIF-4 is due to a shear mode softening under pressure163] leading to mechanical instability at sub-GPa pressures whenhe Born stability conditions are no longer satisfied [165] Thispproach was later extended to a larger database of ZIF structureshowing the very limited mechanical stability of a majority of bothypothetical and experimental structures upon solvent or guestvacuation [166]

2 Thermal properties

Because of its scalar nature and limited practical range theiversity in MOF response to temperature is somewhat narrowerhan their responses to pressure described above Yet there haseen a relatively large number of computational studies on thehermal properties of MOFs and in particular their thermal expan-ion There is among the whole class of metalndashorganic frameworks

prevalence of negative thermal expansion (NTE) and its occur-ence in relatively large temperature ranges often including roomonditions Materials exhibiting NTE contract when heated a rareroperty among dense inorganic materials and usually limitedo certain types of structures [167] Negative thermal expansionowever is quite common among molecular frameworks andas been observed experimentally in many metalndashorganic frame-orks including HKUST-1 [168] MOF-5 [169] other members of

he IRMOF family [170] and many ZIFs [166]One possible way to study the thermal expansion of MOFs is to

erform constant-pressure constant-temperature (N T) molec-lar dynamics simulations for various values of temperature Thevolution of the volume and unit cell parameters then allow a directetermination of both the volumetric and linear thermal expansionoefficients ˛V and ˛ respectively

V = 1V

(partV

partT

)N

˛ = 1

(part

partT

)N

(2)

here is any unit cell parameter This was used to confirm thexistence of NTE in several materials of the IRMOF family (usingorce field-based MD simulations) as well as to shed light onto its

icroscopic origin [135170] The propensity of IRMOFs for NTEas attributed to the presence of many soft (low frequency) trans-

erse vibrational modes in the frameworks and in particular theibration modes of the linkers transverse to the metalndashmetal axesesulting in a shorter average effective length of the linkers evenhough all the bond lengths in the structure increase with temper-

ture In a later study Peterson et al combined neutron scatteringith ab initio molecular dynamics of the metal clusters (copperaddle wheels) of HKUST-1 to elucidate the origin of its NTE involv-

3 The elastic constants Cij can be obtained from the fluctuations of the unit cellectors in constant-stress (N T) molecular dynamics simulations with anisotropicariations of the unit cell using the strain-fluctuation formula [164]

kT

V

)Cminus1

ij= 〈ij〉 minus 〈i〉〈j〉

mistry Reviews 307 (2016) 211ndash236

ing both concerted transverse vibrations as well as local molecularvibrations such as paddle wheel twisting deformation [171]

Another approach to study the lattice dynamics of MOFs andtheir thermal expansion is to calculate the thermal expansion coef-ficients within the quasi-harmonic approximation This requiresthe determination of the phonon modes and frequencies of thestructure and their dependence on unit cell parameters this is typ-ically done by ab initio lattice dynamics calculations of the phononfrequencies at various points throughout the Brillouin zone Foreach phonon mode i and k point a mode-specific Gruumlneisen param-eter ik can be calculated

ik = minus(

part log ωik

part log V

)(3)

The phonon modes with both negative Gruumlneisen parameterand low frequency (and thus large amplitude) drive the negativethermal expansion behavior This approach was used for exampleto study the NTE in MOF-5 first at the -point only [169] thenlater across the full Brillouin zone [172] This allowed to identifyboth optic and accoustic modes contributing to the macroscopicNTE of MOF-5 (as schematized in Fig 15) Unlike the direct molec-ular dynamics approach the quasiharmonic approximation cannotaccount for high anharmonicity but it does give more insight intothe roots of the negative thermal expansion at the microscopiclevel

Finally another thermal property of interest in MOFs is theirheat capacity an important thermodynamic parameter to charac-terize the material itself and also optimized the adsorption processfor practical applications Porous solids with larger heat capacitycan better adsorb the heat generated during adsorption thus limit-ing the undesirable thermal effects (increased temperature leadingto lower adsorption) However very few papers directly addressthis issue whether experimentally [173] or computationally [174]

33 Optical and electronic properties

Optical properties of metalndashorganic frameworks including UV-visible absorption and luminescence have attracted a great dealof attention due to their potential for applications in chemicalbiological and radiation detection medical imaging and electro-optical devices [176177] In addition there is also great interestin the characterization and control of band gaps for applicationsin electronic devices solar energy harvesting and photocatalysis[178ndash180] These optical and electronic properties of MOFs requiremodeling at the quantum chemical level mostly in the DensityFunctional Theory (DFT) approach in order to fully characterizethe electronic structure of the material

A lot of the early work on the modeling of electronic propertiesof MOFs focused on the characterization of their band gaps [129]and the possibilities for tuning these by metal exchange [127181]or ligand functionalization [182] or substitution [183] Probablyone of the most comprehensive examples of this kind of studies isthat of Hendon et al [184] who explored through a combinationof synthetic and computational work the influence of linker func-tionalization on the band gap of MIL-125 a photochromic MOFbased on TiO2 and 14-benzenedicarboxylate [185] By studyingmaterials built from linkers with various functional groups theauthors demonstrated that the diaminated linker bdc-(NH2)2was the most efficient in lowering the band gap from 36 to 13eV They also demonstrated that the introduction of just oneaminated linker per unit cell was sufficient in lowering the band

gap

In addition to the value of band gap more recent work hasshifted focus to a broader range of electronic properties includ-ing detailed analysis of electron density and electrostatic potential


Fig 15 Top MOF-5 unit cell and main NTE-contributing vibration modes of the linkers Bottom phonon dispersion curves and density of states (bottom left) and associatedvalues of Gruumlneisen parameters (bottom right redder = more negative)

Source Adapted from ref [172] with permission from The Royal Society of Chemistry

F pictins

S mical

Otuwgespo

optdeMtau

ig 16 Left calculation of MIL-125rsquos electrostatic reference potential for MOFs deix porous MOFs with respect to a common vacuum level

ource Reproduced with permission from ref [175] Copyright 2014 American Che

ne such example is the recently proposed method by Butler et alo report vertical ionization energy of MOFs with respect to a vac-um level set at the value of the electrostatic potential (for MOFshose pores are large enough) [175] (see Fig 16) Based on band

ap and ionization potential values the authors explain certainlectrochemical optical and electrical properties of the materialstudied This method was also used for the characterization of theiezochromism of MOFs ie their ability to change electronic andptical properties as a function of applied pressure [186187]

Finally another area of interest is that of the luminescencef MOFs The experimental literature on the topic (see for exam-le the reviews in Refs [176] [177] and [188]) largely outweighshe computational studies and this is an area still very much inevelopment Several studies have attempted to determined thelectronic nature of the absorption and emission transitions in

OFs and their dependence on linker functionalization nature of

he metal center and linker-linker interactions and stacking Theccurate determination of the luminescence properties require these of computational intensive time-dependent density functional

g the reference point chosen at the pore center Right vertical ionization energy of

Society

theory (TDDFT) [189190] with ad hoc exchangendashcorrelation func-tionals and large basis sets in order to describe the excited statesand optical (absorption and emission) spectra of MOFs This hasallowed to determine the nature of the emission transition in a fewluminescent MOFs [191192] including archetypical MOF-5 [193]

4 Adsorption

As nanoporous materials adsorption of molecular fluids insideMOFs is one of their earliest and most studied properties Due totheir well-defined crystalline structure high pore volume largesurface area and tailorable pore sizes MOFs show great promisein becoming the next generation of nanoporous adsorbents Theyare thus natural candidates to supplement or replace zeolites inadsorption-based industrial applications with a specific focus

on energy-related and biomedical applications This includesdrug delivery gas adsorption and capture gas storage and deliv-ery separation in gas and liquid phase purification and sensing[194ndash196] In particular the separation capture and sequestration


F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

ig 17 Schematic diagram of the Monte Carlo simulation of adsorption in a porounsemble (allowing deformation of the material in green)

f carbon dioxide from industrial and automotive emissions hasecently attracted intense research interest in the effort to curbmissions of this greenhouse gas linked to human-induced globalarming [197198]

Adsorption properties of new porous materials are routinelyeported along with the synthesis structure and other physicalnd chemical characterization In addition to the standard nitro-en or argon adsorption at cryogenic temperatures part of theET measurement of surface area [199200] adsorption and des-rption isotherms of gases of strategic interest such as CO2 CH4O N2 and O2 is often performed to assess novel materials Some-hat more specialized topic which are nonetheless of practical

mportance such as adsorption of hydrogen [11201ndash203] polarolecules (such as water [204205] and alcohols [206]) and largerolecules (including hydrocarbons [207]) have all been extensively

tudied in some of the materialsGiven the importance of this field there has been significant

omputational work addressing both the fundamental understand-ng of adsorption in metalndashorganic frameworks and the practicalpplications Molecular simulation of adsorption allows to shedight into the microscopic root of the behaviors observed exper-mentally It can also be a powerful tool for the quantitativerediction of adsorption and coadsorption in MOFs as well as theptimization of materials for adsorption-based processes Reviewsn this topic are refs [12] and [7] Here we summarize the statef the art in molecular simulation of adsorption in metalndashorganicrameworks starting with the classical Grand Canonical Montearlo methods for adsorption and coadsorption of fluids before

isting advanced techniques developed in the last few years for thetudy of specific aspects of MOF adsorption

1 Grand Canonical Monte Carlo

The standard molecular simulation technique to study the ther-odynamics of adsorption in rigid nanoporous materials is to useonte Carlo simulations in the Grand Canonical ensemble or Grand

anonical Monte Carlo (GCMC) [208ndash210] It has been extensivelysed and validated in a large variety of nanoporous materials

ncluding zeolites nanoporous carbons mesoporous materials etchis approach schematized in Fig 17 models the adsorption of

in the Grand Canonical thermodynamic ensemble (in orange) and in the osmotic

molecular fluids or mixtures inside a rigid porous matrix (systemof fixed volume V) for given values of the temperature (T) andchemical potential of the fluid ()

In Monte Carlo simulations series of configurations of thesystem under study are generated in a stochastic process by ran-dom moves accepted according to each configurationrsquos Boltzmannprobability These molecular Monte Carlo moves typically includetranslation and rotation of molecules as well as intramolecular dis-placements ie changes in a given moleculersquos conformation GrandCanonical Monte Carlo simulations go beyond this by simulatingthe exchange of molecules between the interior of a materialrsquospore space and an external reservoir of bulk fluid with additionalmoves consisting of insertion of molecules into the pore volume aswell as deletion (moving them back to the reservoir) This allows thedirect simulation of an open thermodynamic ensemble with ther-modynamic equilibrium between two phases (bulk and adsorbate)without an explicit interface

The conditions of a Grand Canonical Monte Carlo simulationare close to the thermodynamic conditions during experimentaladsorption measurements Each point of an adsorption isothermin GCMC is the result of a simulation at fixed ( V T) andthe full isotherm Nads() is obtained by running simulations atdifferent values of This is close to experimental isothermswhich are typically measured as Nexcess(P) where P is the pres-sure of the external fluid Two differences between simulated andexperimental adsorption isotherms need to be taken into accountfor quantitative comparison The first is to relate the chemicalpotential (used in GCMC) to the pressure P (measured experimen-tally) of the bulk fluid This can be achieved through an equation ofstate as (partpartP)T = Vm(P T) the molar volume of the fluid Thisequation of state for the fluid needs to be obtained from priorMonte Carlo simulations or alternatively obtained from experi-mental data In the specific case of low-pressure adsorption theideal gas law might be used then equating pressure and fugac-ity = 0 + RT ln(PP0) The second important difference betweenisotherms calculated through GCMC and measured experimentally

is that between absolute and excess adsorbed properties respec-tively This can be significant in high-pressure experiment andneeds to be accounted for before any comparison between theo-retical and experimental data [211]

n Che

cwlostweTfmbroIta

4

aiiaicmlTtcIastsvmBFiEn(hCmfi

fmamt(ispp

(at


Finally this short introduction to Grand Canonical Monte Carloan be concluded with the simple question what can one computeith GCMC simulations The output of GCMC includes both equi-

ibrium thermodynamic quantities as well as a representative setf configurations of the system in the given conditions The macro-copic quantities include the absolute adsorption uptake (Nads) iehe average number of adsorbed molecules in the porous systemhich is used in plotting adsorption isotherms It also includes

nergetic quantities such as the isosteric heat of adsorption (qst)hese quantities can be directly compared to experimental dataor validation or used predictively as input for thermodynamic

odels of industrial adsorption-based processes such as fixed-ed adsorption columns In addition Monte Carlo simulations alsoesult in the generation of a sample of representative configurationsf the system from which structural information can be obtainedn adsorption in particular one can thus plot density distribu-ions for adsorbed molecules yielding microscopic insight into thedsorption mechanism

2 Classical interaction potentials

Monte Carlo simulations as described above rely on the evalu-tion of the energy of each generated configuration of the systemn order to evaluate its Boltzmann probability and accept or rejectt In short the accuracy of the averages computed from the GCMCre directly dictated by the accuracy of the description used for thenteractions of the molecules in the system Because such energyalculations of single configurations will be made on the order ofillions of times per GCMC simulation quantum chemical calcu-

ation of the energy of each configuration is out of the picturehus the interactions between the fluid molecules and MOF needo be described using classical models interaction potentials alsoalled force fields are analytical functions of interatomic distancesn this approximation we typically break down the hostndashguestnd guestndashguest interactions into terms with analytical expres-ions and simple physical meaning At the intermolecular levelhese terms include Coulombic interactions long-range disper-ion short-range interatomic repulsion polarizability etc A wideariety of functional forms are available to describe these inter-olecular interactions including the common Lennard-Jones and

uckingham potentials as well as the Morse potential and theeynmanndashHibbs quantum effective potential necessary for includ-ng quantum effects in adsorption of light gases such as hydrogenach ldquoforce centerrdquo on which these intermolecular potentials acteed not necessarily be an atom Approaches such as United AtomUA) [212] and its refinement Anistropic United Atom (AUA) [213]ave shown that it is possible of grouping a functional group (CHH2 CH3 ) into a single force center In addition to the inter-olecular terms intramolecular terms may need to be considered

or all but the smallest rigid molecules Intramolecular terms typ-cally include stretching bending and torsion potentials

The choice of force fields is one between accuracy and trans-erability On the one hand designing ad hoc force fields for every

aterial and guest molecule studied is a very time consuming trial-nd-error process which some consider close enough to a blackagic but it can provide very accurate description of the interac-

ions in the system On the other hand the so-called transferableor universal) force fields which describe the same types of atomsn many different materials with identical parameters are muchimpler to use and adapt to new MOF structures but their sim-licity comes at the cost of a more approximate description of theotential energy surface

When it comes to transferable force fields the most used are UFFUniversal Force Field) [214] and DREIDING [215] Both force fieldsre generic enough to provide potential parameters for elementshroughout the periodic table covering both the organic linkers


and metal atoms of MOFs [216] Some groups have neverthelessworked on extending these universal force fields to handle moretransition metals or to improve the description of certain typesof atoms (like the oxygen atoms in metal oxide clusters) [217] Inaddition when modeling the adsorption of polar guest moleculesthese force fields need to be supplemented with atomic partialcharges to describe the Coulombic interactions Classically sev-eral methods are available for the calculation of partial chargesin molecular systems based on high-level quantum chemical cal-culations grouped broadly in two families population analysisor charge partitioning methods (Mulliken [218] Hirshfeld [219]Bader [220]) and electrostatic potential fitting (such as CHelpG[221] and RESP [222]) Electrostatic potential fitting methods areinherently more suited for the purpose of obtaining partial atomiccharges for interatomic Coulombic potentials but were long limitedto nonperiodic systems The past five years have seen a lot of devel-opments of the state of the art in this area with a new generationof electrostatic potential-based methods for periodic solids such asREPEAT (Repeating Electrostatic Potential Extracted ATomic) [223]and DDEC (Density-Derived Electrostatic and Chemical charges)[224] as well as their later refinements [225226]

Other approaches to the problem of atomic partial chargesdetermination have been proposed If one wants to performrapid calculations at the detriment of quality of the resultsclassical approximations can be used in the form of chargeequilibration methods [50227] These are particularly useful forhigh-throughput characterization of large numbers of materialsAt the other hand of the spectrum it is also worth noting that thedetermination of atomic charges can also be bypassed entirelyusing the full electrostatic potential map in the materialrsquos unit cellas determined from DFT calculations [228] This latter approachcan become however computational quite expensive for materialswith large unit cells

While transferable force fields can lead to reasonable agreementin the case of adsorption of small nonpolar molecules in someMOFs it should be noted again that they are a rather crude ldquofirstorderrdquo approximation of the interatomic interactions Thus thereis a real need for a systematic methodology for developing reliableforce fields for novel or hypothetical MOF structures A large num-ber of such methods have been proposed in the past few yearsusing computationally-demanding high-level quantum chemistrycalculations as a basis for determining force field parameters Thecase of partial charges has been discussed already above but otherterms can also be derived from quantum chemical calculationsshort-range repulsion dispersion polarization interactions etcThese terms are typically optimized by choosing a functional formbeforehand and optimizing all available force field parametersto match certain properties of the high-level calculations Somemethodologies focus on properties of the equilibrium structuresuch as lattice parameters atomic positions forces (ie first deriva-tives of the energy with respect to atomic coordinates) vibrationfrequencies (ie second derivatives) bulk modulus (second deriva-tive of the energy with respect to strain) etc Other methodologiesrely on fitting energy and sometimes atomic forces on a largesample of representative configurations of the system themselvesextracted from prior molecular simulations This sampling canbe performed with MD or GCMC simulation using universal forcefields or ab initio molecular dynamics

In conclusion a lot of methodologies have been proposed forthe development of MOF force fields from first principles manywith great success on limited number of materials Some of therecent work in this area includes MOF-FF [229] BTW-FF [174]

QuickFF [230231] among others [232233] However none of themso far have demonstrated a decisive edge in universality or large-scale predictive power Development of first-principles force fieldsremains for the most part an open challenge in the molecular


coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S

Fig 18 Flowchart of a typical computational study of gas mixture

imulation of MOF adsorption More studies of systematic eval-ation of force field performance are needed [234] and otherptions for parameter determination (such as genetic algorithms235136]) might be necessary to reach a truly universal method-logy

3 Coadsorption and separation

The Grand Canonical Monte Carlo scheme as described abovean model not only the adsorption of pure components but alsoixtures of molecular fluids by specifying the chemical potential

f each component in the mixture (1 2 V T) Like simulationf pure phases Monte Carlo modeling of mixture coadsorption cane performed to provide microscopic insight into the driving forcesor preferential adsorption or separation for example by seeingow the adsorption of one component of the mixture enhances oruppresses the others or by looking at guestndashguest interactions

But probably the greatest interest in the modeling of coad-orption through GCMC is in the computational prediction of fluideparation properties which can be difficult and time-consumingo measure experimentally This is particularly true of coadsorp-ion because of the increased dimensionality of the problemith a larger number of control parameters Even for a binaryixture coadsorption properties are a function of temperature

ressure and mixture composition thus requiring tedious exper-

mental work to map out in large ranges of each parameter Even

ore so for ternary and more complex mixtures with the numberf experimental measurements for different compositions increas-ng exponentially with the number of components There is thus

ig 19 Results from a computational co-adsorption study of xenonkrypton mixtures

ingle component and equimolar XeKr mixture adsorption isotherms adsorption selectermeation selectivities as a function of pressure performance of CPO-27-Ni for XeKr se

ource Adapted with permission from ref [236] Copyright 2012 American Chemical Soc

orption in metalndashorganic frameworks through GCMC simulations

great incentive in using molecular simulation of coadsorptionto map out the separation properties of MOFs finding optimalworking conditions for applications or providing thermodynamicinformation as input for process engineering and optimizationThe process of a typically computational study of gas coadsorp-tion through GCMC simulations of mixtures is schematized inFig 18 Force fields (an input of the computation) are validatedfor each separate gas by comparison between experimental pure-component isotherms and GCMC simulations If the agreementis not satisfactory the MOFndashadsorbate force fields need to beoptimized either adjusted empirically to the experimental dataor based on ab initio reference data Once the force fields havebeen validated for pure components GCMC simulations of themixture at various temperature pressure and composition are per-formed Analyzing these the results obtained include coadsorptionisotherms selectivities heats of (co)adsorption plot of adsorbeddensities for each component etc A rather typical example of thistype of study is shown in Fig 19 for the case of coadsorption ofxenon and krypton in MOF CPO-27-Ni [236]

The other alternative to the modeling of coadsorption in MOFsespecially for gas mixtures is the use of analytical mixture mod-els such as the Ideal Adsorbed Solution Theory (IAST) [237] ormore complex variants such as Real Adsorbed Solution Theory(RAST) [238239] or Vacancy Solution Theory [240241] Whilethose have been shown to present reasonable predictions among

mixtures of small molecules [242ndash244] they can deviate fromGCMC predictions and experiments in the cases of highly competi-tive adsorption tight packing of guest molecules (shape selectivity)or MOF structures with marked chemical heterogeneity [13245]

in metalndashorganic framework CPO-27-Ni by Gurdal et al [236] From left to rightivities at 1 and 10 bar as a function of mixture composition XeKr adsorption andparation compared to other MOFs

iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe

Fig 20 Calculations of the CO2 binding energies on open

ource Adapted from ref [251] with permission from The Royal Society of Chemist

hus analytical mixture theories such as IAST should only be useds a rough estimate of separation properties before more time-onsuming molecular simulations or experiments are performed

4 Beyond classical force fields open metal sites andhemisorption

The molecular simulation of adsorption by Grand Canonicalonte Carlo relying on classical force fields is a very powerful

ool but it is limited by the accuracy of a given force field toescribe hostndashguest interactions in the system There are severalases where the classical approximations are not a realistic descrip-ion of the intermolecular interactions in particular in the case ofhemisorption (ie formation of bond(s) between host and guest)

ithin the field of adsorption in metalndashorganic frameworks theost common feature which classical force fields typically fail to

escribe is the short-range interaction of guest molecules withetal centers ie the interaction with undercoordinated metal

ites (or coordinatively unsaturated metal sites cus) This genericimitation has been evidenced on several pairs of adsorbents anduest molecules including hydrogen [246] methane [247] carbonioxide [248249] propane and propylene [250] etc

In such cases in order to accurately describe specific hostndashguestnteractions (including guest interactions with coordinativelynsaturated metal sites) one needs to use ab initio quantumhemistry methods either in the Density Functional Theory (DFT)pproach using post-HartreendashFock methods or multi-referenceethods The latter two families of methods can be very accurate

nd require no ad hoc parameters they are thus very powerful totudy novel systems for which classical force fields are not avail-ble or where the adsorption mechanism is unknown as well asery specific interactions On this extensive literature we refer theeader to the recent review of Odoh et al [2] on quantum-chemicalharacterization of MOF properties which includes an extensiveection on the investigation of adsorption properties

A rather representative example of this is the calculation of CO2dsorption in metalndashorganic frameworks of the CPO-27 family withifferent metals using a combination of DFT and post-HartreendashFockethods [251] Yu et al have reported very accurate calculations

f the CO2 binding energies on open metal sites in CPO-27-M with = Mg Mn Fe Co Ni Cu or Zn They first performed geom-

try optimizations of the periodic structures (atomic positionsnd lattice parameters) at the DFT level with generalized gradientpproximation (GGA) exchangendashcorrelation functional Adsorptioneometries were determined by geometry optimizations on repre-entative clusters of the materials (see Fig 20) again at the DFTevel Accurate binding energies were then calculated using these

eometries by single point energies at the MP2 level of theory Theyere then further corrected with a QMMM approach where theM energies were from the MP2-level calculations and the MMnergies were calculated with the Dreiding and UFF force fields

sites in CPO-27-M with M = Mg Mn Fe Co Ni Cu or Zn

In contrast with this high-accuracy methodology studies ofadsorption in MOFs with coordinatively unsaturated sites can alsobe performed entirely at the DFT level These are computationallymuch cheaper and have been widely used in the literature Theyneed however to be carefully benchmarked against experimentaldata or highly accurate reference calculations as the choice of DFTexchangendashcorrelation function and dispersion correction schemecan heavily influence the properties calculated such as adsorptionenergies There appears to be no ldquoone size fits allrdquo choice of method-ology in this area and optimal exchangendashcorrelation functionals foreach adsorbateMOF pair need to be found by comparing the per-formance of various functionals on smaller cluster models usingpost-HartreendashFock or multi-reference calculations [253254252]This is shown for example on Fig 21 a comprehensive plot of bind-ing energies for several small molecules (methane carbon dioxidepropane and propene) in HKUST-1 evaluated with various DFTexchangendashcorrelation functionals and compared to DFTCC results[252]

Energy minimization calculations as described above onlydescribe well-defined adsorption sites of a single molecule aswell as the corresponding geometries and low-coverage adsorp-tion enthalpies (ie adsorption enthalpies in the limit of zero gaspressure) They do not account for entropy and guestndashguest inter-actions and thus cannot treat pore filling or packing effects ofthe molecules inside the pores As a consequence they cannotdescribe the adsorption at high uptake or where entropy playsa big role Therefore there has been a very large effort in theliterature to use the insight and data gained from ab initio cal-culations (adsorption sites binding geometries energies forcesetc) in order to parameterize hostndashguest force fields This cantake the form of reoptimizing existing force fields adjusting someof the terms to match the quantum chemistry data typicallystrengthen the metalndashguest potentials to more accurately describethe binding of molecules to the open metal sites of the frameworkIt can mean choosing an entirely altogether functional form forthe metalndashadsorbate interactions or even a numerical descriptionbased on the energy profile as a function of adsorbatendashmetal centerdistance

There are several examples of force field optimization for openmetal site MOFs in the literature including the cases of hydro-gen in HKUST-1 [246] water in copper-based MOFs [255] carbondioxide and water in Mg-MOF-74 [256] and Zn-MOF-74 [257]CO2 adsorption in Fe2(dobdc) [258] etc We detail here by wayof illustration the procedure followed by Chen et al [249] for theab initio parameterization of a force field describing the adsorptionof CO2 in CPO-27-Mg Starting from a Buckhingham-type poten-tial (the CarrandashKonowalow potential) the authors calibrated aMMSV (MorsendashMorsendashsplinendashvan der Waals) piecewise interac-

tion potential for interactions with the MOFrsquos coordinatively unsat-urated metal sites The optimization of the MMSV potential wasperformed against reference ab initio data obtained with a double-hybrid density functional with empirical dispersion correction

228 F-X Coudert AH Fuchs Coordination Che

Fig 21 Errors in the interaction energies calculated for methane carbon dioxidepropane and propene at CUS (open metal site) WIN (cage window) and CTR (cagec

Si

BabC

S

enter) sites of HKUST-1 with respect to the DFTCC reference level of theory

ource Adapted with permission from ref [252] Copyright 2015 American Chem-cal Society

2PLYP-D2 [259260] The optimization itself was performed using multiobjective genetic algorithm [261] and the good agreementetween energy curves and ab initio data is evident (see Fig 22)hen et al then used the optimized force field to perform GCMC

Fig 22 Ab initio parameterization of a force field deource Adapted with permission from ref [249] Copyright 2012 American Chemical Soc


simulations of adsorption isotherms and showed vastly improvedagreement compared to the standard force fields such as UFF

Another solution that has been proposed is to precompute theMOFndashguest interactions on a fine mesh of points within the poresof the MOF at the quantum chemical level Using single-point quan-tum chemistry calculations typically at the DFT level the potentialenergy surface for a single guest molecule can be obtained andthe combined with guestndashguest classical interatomic potentials in aseries of GCMC simulations This approach has been demonstratedby Chen et al on the study of methane adsorption on HKUST-1(also known as Cu3(btc)2) a MOF with coordinatively unsaturatedmetal sites [247] This method combines a DFT level of descrip-tion of the hostndashguest interactions with a full sampling of thephase space of the system thus accounting for entropy It is how-ever only possible for atomic guests (including rare gases) or smallspherical molecules (such as methane) for nonspherical moleculesthe additional rotational degrees of freedom make the approachcomputationally prohibitive

45 Adsorption in flexible MOFs

Although Monte Carlo simulations in the Grand Canonicalensemble as presented at the beginning of this section are con-sidered the gold standard in the simulation of adsorption innanoporous materials they rely on a very strong assumption thatthe host material is rigid This approximation is very reasonablewhen it comes to the thermodynamics of adsorption in most porousinorganic materials such as zeolites where framework flexibilityis limited However because metalndashorganic frameworks are basedon weaker bonds and interactions (coordinative bonds ndash stack-ing hydrogen bonds etc) that are responsible for their intrinsicstructural flexibility The organicndashinorganic connections thereforeallow underconstrained structural linkages that are responsible forsoft mechanical properties and organic linkers with side chainsallow for local dynamics of the host framework This flexibilityof MOFs can be triggered upon adsorption leading to large-scalestructural changes in the MOF framework and subsequent alter-ation of its physical and chemical properties including adsorptionitself Such flexible MOFs sometimes called Soft Porous Crystals[147] are in growing number [148262263] There is therefore aneed for molecular simulations methods describing the interplaybetween adsorption and host flexibility going beyond the GCMC

method When the flexibility occurs in the form of a clear transitionbetween well-defined and identified crystallographic structuresa simple ldquotwo staterdquo solution can be used studying the adsorp-tion in both rigid structures through GCMC [264265] However

scribing the adsorption of CO2 in CPO-27-Mgiety


Fig 23 Left the two metastable phases of ldquobreathing MOFrdquo MIL-53(Cr) large-pore (top) and narrow-pore (down) Right structural transitions observed by Hybrid MonteC re an

S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf

arlo molecular simulations under stimulation by temperature mechanical pressu

ource Adapted with permission from refs [271] and [270] Copyright 2010 2012

ore complex systems require a more direct approach accountingirectly for their flexibility in molecular simulations

From a thermodynamics point of view the adsorption of molec-lar fluids inside deformable hosts is most appropriately described

n the osmotic thermodynamic ensemble where the controlarameters are the number of molecules of the host frameworkhost the chemical potential of the adsorbed fluid ads the mechan-

cal constraint exerted on the system and the temperature T266] Direct molecular Monte Carlo simulations of adsorption inhis open ensemble are possible where the Monte Carlo movesypically used in GCMC are supplemented with ldquovolume changerdquo

oves (see Fig 17) However the efficiency of these simulationsre greatly improved by performing simulations in a hybrid MCMDetup (also called Hybrid Monte Carlo or HMC) [267ndash269] In HMChort molecular dynamics trajectories are considered as Montearlo moves allowing to better sample the host frameworkrsquos flex-

bility by following its collective motionsMaybe one of the most striking example of osmotic Monte

arlo simulations is that reported by Ghoufi et al on the CO2dsorption-induced breathing of MIL-53(Cr) [270271] This studyhowed that HMC in the osmotic ensemble was able to describeoth thermal mechanical and adsorption-induced structural tran-itions between the two phases of MIL-53(Cr) based on an ad hocorce field describing the material (as depicted in Fig 23) Thistudy also demonstrated the main issue with direct HMC simu-ation namely the widely hysteretic nature of the transitions andhe difficulties in overcoming free energy barriers associated withhe transition and determining the thermodynamic equilibrium ofhe system

Another way to perform molecular simulation in the osmoticnsemble avoiding the convergence issues of the direct Hybridonte Carlo method is to rely on free energy methods to calculate

he osmotic potential of the system for each possible value of chem-cal potential These methods require the use of non-Boltzmannampling in (guest loading volume) parameter space in order toully characterize the adsorption thermodynamics as well as the

d carbon dioxide adsorption

can Chemical Society

materialrsquos response to adsorption In addition they provide infor-mation on both the thermodynamic equilibrium as well as allmetastable states of the system Three different variants have beenproposed via thermodynamic integration based on GCMC simu-lations as performed by Watanabe et al [272273] through theWangndashLandau algorithm as done by Bousquet et al [274275] orsimilarly with the Transition-Matrix Monte Carlo sampling as pro-posed by Shen et al [276] All three methods were demonstratedon model systems and although they appear promising they havenot yet been applied to atomistically-detailed molecular frame-works

Finally a third way to model adsorption in Soft Porous Crystalsis the use of thermodynamics-based analytical models (see Ref[8] for a review on this topic) This is achieved by writing downthe equations for adsorption in the osmotic ensemble and intro-ducing simple approximate expressions for certain quantities suchas describing the adsorption isotherms can be modeled by classi-cal equations such as Langmuir or Langmuir-Freundlich which canbe either fitted from experimental data [266277] computed fromGCMC simulations of rigid frameworks [278ndash280] or calculatedthrough parameterized equations of state [281] This approach wasfirst used to study stepped adsorption isotherms in bistable mate-rials of the gate opening and breathing families [266282] and laterextended to take into account the influence of temperature [283]and mechanical pressure [281] See Fig 24 for the example of theldquobreathingrdquo of MIL-53(Al) upon xenon adsorption as a function oftemperature and guest pressure

Such analytical models not only help rationalized the behaviorsobserved experimentally and shed light into their key thermody-namic factors and driving forces but they can also have predictivevalue This is in particular the case of the OFAST model [284285](osmotic framework adsorption solution theory) extending the

widely-used IAST coadsorption model to the osmotic ensem-ble Based solely on experimental pure component adsorptionisotherms the OFAST model is able to predict coadsorption in flex-ible MOFs and has been fully validated by comparison against


F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4

ig 24 From a set of experimental adsorption isotherms in a flexible MOF here for

he construction of a full (temperature gas pressure) phase diagram

ource Reproduced from ref [283] Copyright 2009 Wiley-VCH Verlag GmbH amp Co

xperimental data eg on the coadsorption of CO2CH4 mixturesn MIL-53(Al) [286]

6 Comparing simulations and experiments

This short review on the computational modeling of adsorp-ion in MOFs cannot be complete without a few words on theomparison between computational and experimental data mdash andhe pitfalls thereof It is always desirable to validate a simulation

ethodology by comparing its results to available experimentalata when possible However the ample literature on MOF adsorp-ion shows that simulation results and experimental data very ofteniffer quantitatively [287] (as was already noted in the early work

n the area [288]) Moreover the differences can be in some casesather large without the simulation being necessarily at fault theres also large variability in experimental measurements of adsorp-ion data and primarily adsorption isotherms The possible causesor this variability are many

Dependence on the measurement technique used volumetricvs gravimetric equilibration times etc [289290] Experimentalisotherms may in some cases not truly represent the thermody-namic equilibrium especially when adsorption kinetics is slow(eg bulky molecules in small pore MOFs or occurrence of struc-tural transitions)

Impact of the activation procedure and dependence on the his-tory of the sample Residual amounts of solvent organic linkeror templates in the pores of a MOF can severely diminish itsaccessible pore volume and specific surface area

Influence of the textural properties with key parameters suchas crystal size distribution nature of the external surfaces crys-tal shape etc Adsorption on MOF samples of nanoscopic sizesoccurs both inside the pores and on the external surface [279] orat crystallographic line or plane defects Molecular simulationsalmost always assume a bulk behavior (ie an infinite crystal)while crystal sizes in MOFs vary widely depending on materialsynthesis conditions etc

Presence of defects in particular missing organic linkers in thecrystalline structure Depending on synthesis conditions someMOFs can present large amounts of defects within their crys-talline structure These defects can have a dramatic impact onadsorption properties typically increasing the pore volume andpore sizes [83126291292] but also affecting the hostndashguestinteractions and the chemical nature of the internal surface of

the material [293] Moreover if the defects are organized ratherthan randomly dispersed throughout the MOF structure (egcorrelated disorder in UiO-66 [294]) the effects on adsorptioncan be expected to be even more important

in the ldquobreathingrdquo framework MIL-53(Al) analytical thermodynamic models allow

Weinheim

For all these reasons it is highly recommended to perform a fullcharacterization of the pore volume of MOFs comparing their geo-metrical properties to the experimentally measured surface areaspore volume pore size distribution etc [29569] This is a necessaryprerequisite to confirm that the simulations performed on a perfectcrystal structure can match the experimental system and that anycomparison of adsorption isotherms is meaningful In some caseswhere the geometrical and experimental surface areas differ it ispossible to adjust the simulation results by scaling the adsorbedquantities by an empirical factor [216296]The reasoning behindthis is to account for changes in pore volumes through blockedpores or missing linkers which are probably the most commonissues The scaling factor is thus dependent on the material stud-ied the synthesis and activation conditions the exact form andtextural properties of the sample used experimentally Scalingfactors used in the literature typically vary between 07 and 1 Theuse of such a scaling procedure allows one to compare or extrapo-late computational data for different guests in the same adsorbentmaterial However this ldquoquick fixrdquo cannot truly replace a betterunderstanding of the origins of the discrepancy

In conclusion caution should be taken in comparing simulatedadsorption results with experimental ones and in particular whenadjusting computational parameters (such as force field parame-ters) to fit certain experiments one should do so not on a fewisolated adsorption isotherms but only based on a comprehensiveexperimental dataset (adsorption isotherms in wide temperatureand pressure ranges heats of adsorption etc)

5 Perspectives

Ending this introductory review of computational studies ofmetalndashorganic frameworks and their properties we highlight someof the very recent work and remaining open questions that seemfrom our perspective to be important challenges for the develop-ment of the MOF field

51 Modeling of defects and disorder

The occurrence of defects and their correlations have long beenrecognized to play a central role in the physical and chemicalproperties of materials The study of defects in crystalline com-pounds forms an important part of solid-state chemistry andphysics as can be seen by the large body of literature con-cerning dense and porous inorganic materials [297298] Yet theimportance of the role of defects and disorder in metalndashorganicframeworks is only starting to emerge and is still rarely studied

in the existing literature both experimental and theoretical Yetthere is evidence that defects and disorder play an important rolein the function of several existing MOFs The poster child for this isthe UiO-66(Zr or Hf) family of structures of high interest because

n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa


f their thermal mechanical and chemical stability Studies in theast three years have shown that UiO-66 materials can contain sig-ificant amount of missing-linker defects [126299] which have

crucial impact on the adsorption and catalytic properties of theaterial [300] The concentration of these defects can be tuned dur-

ng synthesis [126] they do not occur randomly in the structure butre correlated and form nano-scaled domains of well-defined (reo)opology [294] Moreover the introduction of controlled hetero-eneity in MOFs without loss of its ordered structure can lead tohe creation of more complex structures and pore environments301302] introducing additional functions into known topologiesnd structures [4303] A recent review on the topic can be foundn Ref [304]

In stark contrast to the few examples given above most MOFtructures reported in the literature feature a crystallographictructure and basic characterization of porosity as well as someacroscopic study of their function (adsorption catalytic activity

tc) Because computational chemistry techniques are based oneriodic representations of the crystalline structures they modelerfect materials with no defects and no disorder A colleagueummarized this first-order approach tongue-in-cheek as followsor the most part we are dealing with defects by ldquoignoring themut invoking them as reason for any difference between modeling andxperimentsrdquo [305]

Yet some recent studies have used quantum chemistry andolecular simulation techniques to understand and predict the

mpact of defects on the properties of MOFs At the quantum chem-cal level a good example is the study by Chizallet et al usingFT calculations of the catalysis of transesterification in ZIF-8 oncido-basic sites located at defects or at the external surface ofhe material [306] Another one is the influence of defect concen-ration on the structural mechanical and thermal properties ofiO-66(Hf) [294] giving microscopic insight into the occurrencef defect-dependent thermal densification and colossal negativehermal expansion (NTE) measured experimentally [307] At thelassical level Ghosh et al have studied the impact of defects ondsorption properties of water in UiO-66(Zr) through Grand Canon-cal Monte Carlo simulations [293]

Though there have been a few studies (listed above) on thempact of defects on MOF properties it is worth noting that theigger question has not been addressed so far from the theoreti-al point of view what causes certain MOFs to present defectsnd when and why are these defects correlated There is exper-mental evidence that the occurrence of defects in MOFs can beandom in some cases and correlated in others For example struc-ures obtained by linker-exchange [308309] show no correlationetween the substituted linker positions ie the resulting par-ially solvent-exchange MOF is a solid solution of the two parent

OFs and features a random arrangement of linkers [310] Onhe other hand missing-linker defects in UiO-66(Hf) exhibit cor-elated disorder with the occurrence of nano-scaled domains ofell-defined topology [294] Modeling studies have so far beennable to address this kind of very fundamental questions Norave there been any computational studies on noncrystalline dis-rdered MOF structures ie molten glassy and amorphous MOFs138311ndash313]

2 Databases for high-throughput screening

One of the areas that has seen fast-paced development in the lastew years is that of high-throughput computational screening oforous materials in general and metalndashorganic frameworks in par-

icular As described in some more detail in Section 22 this is theesult of the conjunction of a few factors (i) a large number of knowOF structures (ii) the availability of both computational power

nd advanced modeling techniques and (iii) a political incentive


to speed up the discovery of novel materials This has lead to thedevelopment of two different types of large-scale databases ofMOF structures hypothetical MOF structures generated by com-binatorial approaches (of the order of 100k structures) [50] andldquocomputation-readyrdquo structures derived from experimental crys-tallographic data (of the order of 5k structures) [61] The availabilityof these databases offers great opportunities for high-throughputcomputational screening of materials for specific applications ashas already been done for adsorption of hydrogen [6667] methane[5065] carbon dioxide [57] noble gases [6364] etc But this alsoraises some novel questions and challenges about how best toexploit these databases for materials discovery

Focusing first on databases of hypothetical structures it mightbe here interesting to draw some parallels with the existingdatabases of hypothetical zeolitic structures [5455] which haveexisted for nearly ten years now and are of similar size (up totwo million structures) There also like for MOFs the overwhelm-ing majority of screening studies have focused on adsorptionproperties relying both on computationally-cheap geometricalcharacterization (pore size distributions pore diameters surfacearea pore volume see Section 23) and GCMC calculations on can-didate structures selected on geometric criteria This approach hasyielded valuable insight into the relationship between geometricproperties and adsorption performances [50] as well as the intrin-sic limits of these materials [65] It is however rather uncertainhow this approach can be extended to the study of other proper-ties either for MOFs or zeolites simple and ldquocheaprdquo descriptorsare hard to identify for other functions such as catalytic activitythermal and mechanical properties luminescence flexibility

Furthermore given the large number of structures available theuse of a few descriptors and their correlation to key propertiesis typically an overdetermined problem Even simply plotting thedata generated can become difficult for multidimensional data setstwo-dimensional correlation plots for example are limited to test-ing hypotheses formulated a priori There is thus a real need to usemore sophisticated data mining tools and to move away frompredetermined descriptors Some steps have been taken alongthis path in the use of quantitative structurendashproperty relation-ship (QSPR) backed by machine learning algorithms for example byFernandez et al to identify high-performing MOFs for carbon diox-ide capture [314] Thornton et al used a combination of molecularsimulation and machine-learning techniques to identify candidatezeolites for catalytic reduction of carbon dioxide from a sample of300 thousand zeolite structures (hypothetical and experimental)[315] At a much smaller scale Yıldız et al have demonstrated thepotential of Artificial Neural Networks (ANN) to predict adsorptionproperties on the case of hydrogen gas storage in thirteen MOFswith high surface areas [316]

Another issue that needs to be addressed is that of the experi-mental feasibility of the hypothetical MOFs Hypothetical zeolitedatabases have existed for quite some time yet from their system-atic exploration no real structure has been synthesized and testedfor practical applications and the question of why so few zeolitesare observed while there are so many hypothetical frameworksremains open [317ndash319] Though MOFs seem to far a little bet-ter here with several examples of materials synthesized after theyhave been selected by computational design [46] the importantquestions of experimental feasibility and computational ratio-nal design remain Among the currently-listed hypothetical MOFstructures which are experimentally accessible to synthesis andpresent sufficient mechanical thermal and chemical stabilityfor practical applications Can we use the tools of theoretical

chemistry to help guide the synthesis of novel MOFs identified fortheir properties Can we help predict the conditions (reagents sol-vents temperature etc) under which a given MOF may be obtainedexperimentally

2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao

afripuatmofinfibcldocba[


Finally databases built from experimental structures such asoRE MOF [61] raise important questions as to the curation ofhe database and the relevance of the ldquocleaned-uprdquo structureso the properties of the original experimental materials Theeneration of computation-ready structures from crystallographicata involves an automated procedure to remove solvent and dis-rdered guests This procedure has severe limits First it assumeshat all coordinated solvent molecules can be removed from thetructure this is true in some cases (water molecules bound toKUST-1 metal centers for example) but not in general Indeed

here exist some MOFs with included solvent where the very sta-ility of the framework is crucially dependent on the presence ofhe solvent molecules (eg water methanol etc) and which cannote activated without loss of crystallinity [320321166] Secondly itssumes that there is no relaxation upon solvent removal which is

rather crude approximation especially in the case of soft porousrystals Nonetheless this large-scale database is the first of its kindnd is likely to prove useful for understanding fundamental princi-les of MOFs and a basis for computational selection of structuresor targeted applications

3 Stimuli-responsive MOFs

With the large number of new MOF structures synthesized andharacterized every year one of the empirical patterns appear-ng is the common occurrence of flexibility of these framework

aterials There is a rapidly increasing number of frameworktructures whose flexibility manifests in the form of large-scaletructural transformations induced by external stimulation ofhysical or chemical nature changes in temperature mechani-al constraints guest adsorption light exposure etc A number ofifferent terms have been used to refer to this behavior includ-

ng smart materials soft porous crystals [147] dynamic frameworksexible frameworks and stimuli-responsive materials [148] The real-zation over the past ten years of the prevalence of these flexible

aterials and their potential for applications has lead to the emer-ence of an entire subfield of computational methods dedicatedo their modeling The existing literature on this topic has beenescribed in Sections 45 (adsorption-induced structural transi-ions) and Section 31 (mechanical properties) This is howevern area in fast development and with many challenges still leftpen

The first is the need for the systematic development of high-ccuracy force fields for highly flexible materials Force fieldsor MOFs with high degree of flexibility such as MIL-53 or ZIFsequire a good accuracy in the description of the intramolecularnteractions of the framework and in particular the low-frequencyhonons modes For this two categories of force fields have beensed so far The first and dominant category is the use of transfer-ble intramolecular force fields for organic molecules (eg fromhe AMBER parameter database [322]) along with hand-tuned

etalndashorganic bending and torsion potentials The later are thenptimized to reproduce known structural properties and vibrationrequencies [323ndash325] or experimental data such as adsorptionsotherms and structural transitions [326ndash328] This approach isot entirely generalizable and the quality of the resulting forceeld is only validated on limited experimental data and cannote systematically improved as the optimization problem is typi-ally underconstrained (too many parameters fitted on relativelyittle data) On the other hand force fields derived from ab initioata (as described in Section 44) show clear but that methodol-gy is rather hard to apply to flexible materials especially when it

omes to the intramolecular terms Still some recent progress haseen made in this area giving hope that generic methodologies forb initio force fields of flexible MOFs can be a reality in the future231]


The second area of development we want to highlight hereis the recent trend towards better insight into the microscopicmechanisms of stimuli-responsiveness with particular focus onspace-resolved time-resolved and in operando experimental mea-surements Those are crucial to provide a better fundamentalunderstanding of the fundamental nature of the transformationstriggered by complex stimuli and have practical consequences forthe design of novel materials in working conditions Yet relativelylittle theoretical and computational effort has been spent on thismost probably due to the very difficult nature of the issue The ques-tions that need to be answered include how do stimuli-inducedtransformations occur and propagate at the scale of the crys-tal What is their kinetics and dependence on the history ofthe material What determines the possible metastable states ofthe system How do crystal size shape and textural propertiesaffect their physical and chemical properties and ultimately theirresponsivity

Some of the recent studies both experimental and theoret-ical have started to address this issue On the experimentalside one striking such example was the recent observation ofan transient state in the adsorption-induced structural transitionof pillared MOF Zn2(ndc)2(dabco) [329] by using synchrotrongrazing incidence diffraction measurements to determine sep-arately the structures of a crystalrsquos bulk and surface [330]Kondo et al demonstrated that upon adsorption of bulky slow-diffusing molecules the MOF featured a heterostructure with aguest-induced sheared phase at the surface coexisting with anunperturbed MOF structure in the core of the crystal On the the-oretical point of view we presented some time ago a multiscalephysical mechanism and a stochastic model of breathing transi-tions [331] which is to our knowledge still the only example ofsuch ldquoupscalingrdquo trying to address computationally the dynam-ics of structural transitions at the level of the crystal itself Basedon a simple Hamiltonian that describes the physics of hostndashhostand hostndashguest interactions we showed how the behavior ofunit cells is linked to the transition mechanism at the crys-tal level through three key physical parameters the transitionenergy barrier the cell-cell elastic coupling and the system size[332]

Along a similar line but on the different topic of MOF crystalgrowth Yoneya et al have recently used coarse-grained moleculardynamics to investigate the MOF self-assembly and the influenceof metalndashligand coordination in this process [333] This is a firststep toward a better understanding of MOF synthesis and growthat the microscopic scale a topic that has proven crucial but diffi-cult to address so far in MOFs as well as in other porous materials[334335]

Acknowledgments

We thank Anne Boutin for a long-standing and continuing col-laboration on the fascinating topic of modeling of nanoporousmaterials We thank Romain Gaillac and Thomas Manz for criticalreading of the pre-print FXC acknowledges PSL Research Univer-sityrsquos financial support (projects DEFORM and MECADS) and GENCIfor high-performance computing CPU time allocations although nocalculations were performed in the writing of this review a largepart of the work reviewed here requires access of scientists in thefield to large supercomputer centers

References

[1] J Jiang Metal-Organic Frameworks Materials Modeling towards PotentialEngineering Applications Pan Stanford 2015

[2] SO Odoh CJ Cramer DG Truhlar L Gagliardi Chem Rev 115 (2015)6051ndash6111

[3] YJ Coloacuten RQ Snurr Chem Soc Rev 43 (2014) 5735ndash5749

n Che


[4] H Fang H Demir P Kamakoti DS Sholl J Mater Chem A 2 (2014) 274ndash291[5] Q Yang D Liu C Zhong J-R Li Chem Rev 113 (2013) 8261ndash8323[6] T Watanabe DS Sholl Langmuir 28 (2012) 14114ndash14128[7] RB Getman Y-S Bae CE Wilmer RQ Snurr Chem Rev 112 (2012)

703ndash723[8] F-X Coudert A Boutin M Jeffroy C Mellot-Draznieks AH Fuchs

ChemPhysChem 12 (2011) 247ndash258[9] J Jiang R Babarao Z Hu Chem Soc Rev 40 (2011) 3599

[10] R Krishna JM van Baten Phys Chem Chem Phys 13 (2011) 10593[11] SS Han JL Mendoza-Corteacutes WA Goddard III Chem Soc Rev 38 (2009)

1460[12] T Duumlren Y-S Bae RQ Snurr Chem Soc Rev 38 (2009) 1237[13] S Keskin J Liu RB Rankin JK Johnson DS Sholl Ind Eng Chem Res 48

(2009) 2355ndash2371[14] M Nagaoka Y Ohta H Hitomi Coordination Chem Rev 251 (2007)

2522ndash2536[15] MolSim 2010 (version 13) Mobile application software httpsitunesapple

comusappmolsimid377661062mt=8[16] J Feldt RA Mata JM Dieterich J Chem Inf Model 52 (2012) 1072ndash1078[17] MOF papers a Twitter bot that surveys the literature on metal-organic

frameworks httpstwittercomMOF papers[18] SL Price Chem Soc Rev 43 (2014) 2098ndash2111[19] SM Woodley R Catlow Nat Mater 7 (2008) 937ndash946[20] S Kirkpatrick CD Gelatt MP Vecchi Science 220 (1983) 671ndash680[21] J Pannetier J Bassas-Alsina J Rodriguez-Carvajal V Caignaert Nature 346

(1990) 343ndash345[22] JR Holden Z Du HL Ammon J Comput Chem 14 (1993) 422ndash437[23] C Mellot-Draznieks B Slater R Galvelis Materials Modeling towards Engi-

neering Applications Pan Stanford 2015 pp 1ndash52[24] C Mellot-Draznieks J Mater Chem 17 (2007) 4348[25] S Atahan-Evrenk A Aspuru-Guzik Prediction and Calculation of Crystal

Structures Springer International Publishing 2014[26] M Eddaoudi DB Moler H Li B Chen TM Reineke M OrsquoKeeffe OM Yaghi

Acc Chem Res 34 (2001) 319ndash330[27] DJ Tranchemontagne JL Mendoza-Corteacutes M OrsquoKeeffe OM Yaghi Chem

Soc Rev 38 (2009) 1257[28] C Mellot Draznieks JM Newsam AM Gorman CM Freeman G Feacuterey

Angew Chem Int Ed 39 (2000) 2270ndash2275[29] C Mellot-Draznieks J Dutour G Feacuterey Angew Chem Int Ed 43 (2004)

6290ndash6296[30] DW Lewis AR Ruiz-Salvador A Goacutemez LM Rodriguez-Albelo F-X Coud-

ert B Slater AK Cheetham C Mellot-Draznieks CrystEngComm 11 (2009)2272

[31] NW Ockwig O Delgado-Friedrichs M OrsquoKeeffe OM Yaghi Acc Chem Res38 (2005) 176ndash182

[32] M OrsquoKeeffe OM Yaghi Chem Rev 112 (2012) 675ndash702[33] MD Foster O Delgado Friedrichs RG Bell FA Almeida Paz J Klinowski

Angew Chem Int Ed 42 (2003) 3896ndash3899[34] Database of Zeolite Structures Structure Commission of the International

Zeolite Association httpwwwiza-structureorgdatabases[35] Reticular Chemistry Structure Resource httprcsrnet[36] M OrsquoKeeffe MA Peskov SJ Ramsden OM Yaghi Acc Chem Res 41 (2008)

1782ndash1789[37] G Feacuterey C Serre C Mellot-Draznieks F Millange S Surbleacute J Dutour I

Margiolaki Angew Chem Int Ed 43 (2004) 6296ndash6301[38] G Ferey Science 309 (2005) 2040ndash2042[39] IA Baburin S Leoni G Seifert J Phys Chem B 112 (2008) 9437ndash9443[40] F Trousselet A Boutin F-X Coudert Chem Mater 27 (2015) 4422ndash4430[41] S Bureekaew R Schmid CrystEngComm 15 (2013) 1551[42] M Eddaoudi J Kim N Rosi D Vodak J Wachter M OrsquoKeeffe OM Yaghi

Science 295 (2002) 469ndash472[43] OM Yaghi H Li M Eddaoudi M OrsquoKeeffe Nature 402 (1999) 276ndash279[44] S Surbleacute C Serre C Mellot-Draznieks F Millange G Feacuterey Chem Commun

(2006) 284ndash286[45] RL Martin L-C Lin K Jariwala B Smit M Haranczyk J Phys Chem C 117

(2013) 12159ndash12167[46] OK Farha A Oumlzguumlr Yazaydın I Eryazici CD Malliakas BG Hauser

MG Kanatzidis ST Nguyen RQ Snurr JT Hupp Nat Chem 2 (2010)944ndash948

[47] DA Gomez-Gualdron OV Gutov V Krungleviciute B Borah JE Mond-loch JT Hupp T Yildirim OK Farha RQ Snurr Chem Mater 26 (2014)5632ndash5639

[48] A Jain SP Ong G Hautier W Chen WD Richards S Dacek S Cholia DGunter D Skinner G Ceder KA Persson APL Mater 1 (2013) 011002

[49] Materials Genome Initiative A Renaissance of American ManufacturingTom Kalil and Cyrus Wadia httpswwwwhitehousegovblog20110624materials-genome-initiative-renaissance-american-manufacturing

[50] CE Wilmer KC Kim RQ Snurr J Phys Chem Lett 3 (2012) 2506ndash2511[51] A Simperler MD Foster O Delgado Friedrichs RG Bell FA Almeida Paz J

Klinowski Acta Crystallogr B Struct Sci 61 (2005) 263ndash279[52] M D Foster and M M J Treacy A Database of Hypothetical Zeolite Structures

httpwwwhypotheticalzeolitesnet[53] I Rivin Nat Mater 5 (2006) 931ndash932[54] DJ Earl MW Deem Ind Eng Chem Res 45 (2006) 5449ndash5454[55] MW Deem R Pophale PA Cheeseman DJ Earl J Phys Chem C 113 (2009)

21353ndash21360


[56] R Pophale PA Cheeseman MW Deem Phys Chem Chem Phys 13 (2011)12407

[57] L-C Lin AH Berger RL Martin J Kim JA Swisher K Jariwala CH RycroftAS Bhown MW Deem M Haranczyk B Smit Nat Mater 11 (2012)633ndash641

[58] J Goldsmith AG Wong-Foy MJ Cafarella DJ Siegel Chem Mater 25 (2013)3373ndash3382

[59] FH Allen Acta Cryst Sect A Found Cryst 58 (2002) 380ndash388[60] CSD (Cambridge Structural Database) httpwwwccdccamacukSolutions

CSDSystemPagesCSDaspx[61] YG Chung J Camp M Haranczyk BJ Sikora W Bury V Krungleviciute T

Yildirim OK Farha DS Sholl RQ Snurr Chem Mater 26 (2014) 6185ndash6192[62] The Materials Project httpsmaterialsprojectorg[63] BJ Sikora CE Wilmer ML Greenfield RQ Snurr Chem Sci 3 (2012) 2217[64] CM Simon R Mercado SK Schnell B Smit M Haranczyk Chem Mater 27

(2015) 4459ndash4475[65] CM Simon J Kim DA Gomez-Gualdron JS Camp YG Chung RL Martin

R Mercado MW Deem D Gunter M Haranczyk DS Sholl RQ Snurr BSmit Energy Environ Sci 8 (2015) 1190ndash1199

[66] YJ Coloacuten D Fairen-Jimenez CE Wilmer RQ Snurr J Phys Chem C 118(2014) 5383ndash5389

[67] DA Gomez J Toda G Sastre Phys Chem Chem Phys 16 (2014) 19001[68] RL Martin CM Simon B Smit M Haranczyk J Am Chem Soc 136 (2014)

5006ndash5022[69] T Duumlren F Millange G Feacuterey KS Walton RQ Snurr J Phys Chem C 111

(2007) 15350ndash15356[70] RB Bird WE Stewart EN Lightfoot Transport Phenomena 2nd ed Wiley

2002[71] F Rouquerol J Rouquerol K Sing Adsorption by Powders and Porous Solids

Academic Press 1999[72] A Shrake J Rupley J Mol Biol 79 (1973) 351ndash371[73] H Kuumlppers F Liebau AL Spek J Appl Crystallogr 39 (2006) 338ndash346[74] M Phillips I Georgiev AK Dehof S Nickels L Marsalek H-P Lenhof A

Hildebrandt P Slusallek 2010 IEEE International Symposium on Parallel ampDistributed Processing Workshops and Phd Forum (IPDPSW) IEEE 2010 pp1ndash7

[75] J Weiser PS Shenkin WC Still J Comput Chem 20 (1999) 217ndash230[76] KV Klenin F Tristram T Strunk W Wenzel J Comput Chem 32 (2011)

2647ndash2653[77] J Getzschmann I Senkovska D Wallacher M Tovar D Fairen-Jimenez T

Duumlren JM van Baten R Krishna S Kaskel Microporous Mesoporous Mater136 (2010) 50ndash58

[78] G Horvaacuteth K Kawazoe J Chem Eng Jpn JCEJ 16 (1983) 470ndash475[79] J Landers GY Gor AV Neimark Colloids Surf A Physicochem Eng Asp 437

(2013) 3ndash32[80] LD Gelb KE Gubbins Langmuir 15 (1999) 305ndash308[81] S Bhattacharya KE Gubbins Langmuir 22 (2006) 7726ndash7731[82] Y-S Bae D Dubbeldam A Nelson KS Walton JT Hupp RQ Snurr Chem

Mater 21 (2009) 4768ndash4777[83] L Sarkisov A Harrison Mol Simul 37 (2011) 1248ndash1257[84] R Krishna JM van Baten Langmuir 26 (2010) 2975ndash2978[85] D Farrusseng C Daniel C Gaudillegravere U Ravon Y Schuurman C Mirodatos

D Dubbeldam H Frost RQ Snurr Langmuir 25 (2009) 7383ndash7388[86] TF Willems CH Rycroft M Kazi JC Meza M Haranczyk Microporous

Mesoporous Mater 149 (2012) 134ndash141[87] E Haldoupis S Nair DS Sholl J Am Chem Soc 132 (2010) 7528ndash7539[88] E Haldoupis S Nair DS Sholl Phys Chem Chem Phys 13 (2011) 5053[89] M Haranczyk JA Sethian J Chem Theory Comput 6 (2010) 3472ndash3480[90] J Hoshen R Kopelman Phys Rev B 14 (1976) 3438ndash3445[91] VA Blatov AP Shevchenko Acta Crystallogr A Found Crystallogr 59 (2003)

34ndash44[92] VA Blatov Crystallogr Rev 10 (2007) 249ndash318[93] M Foster I Rivin M Treacy O Delgado Friedrichs Microporous Mesoporous

Mater 90 (2006) 32ndash38[94] I Matito-Martos A Martin-Calvo JJ Gutieacuterrez-Sevillano M Haranczyk M

Doblare JB Parra CO Ania S Calero Phys Chem Chem Phys 16 (2014)19884

[95] Zeo++ an open source (but registration-required) software package for analy-sis of crystalline porous materials httpwwwmaciejharanczykinfoZeopp

[96] RL Martin B Smit M Haranczyk J Chem Inf Model 52 (2012) 308ndash318[97] EL First CE Gounaris J Wei CA Floudas Phys Chem Chem Phys 13 (2011)

17339[98] EL First CA Floudas Microporous Mesoporous Mater 165 (2013) 32ndash39[99] ZEOMICS Zeolites and Microporous Structures Characterization an auto-

mated computational method for characterizing the three-dimensionalporous networks of microporous materials such as zeolites httpheliosprincetoneduzeomics

[100] MOFomics Metal-Organic Frameworks Characterization an automated com-putational method for characterizing the three-dimensional porous networksof metal-organic frameworks httpheliosprincetonedumofomics

[101] IA Ibarra S Yang X Lin AJ Blake PJ Rizkallah H Nowell DR AllanNR Champness P Hubberstey M Schroumlder Chem Commun 47 (2011)8304

[102] KS Park Z Ni AP Cocircteacute JY Choi R Huang FJ Uribe-Romo HK Chae MOrsquoKeeffe OM Yaghi P Natl Acad Sci 103 (2006) 10186ndash10191

2 on Che


[103] F Nouar J Eckert JF Eubank P Forster M Eddaoudi J Am Chem Soc 131(2009) 2864ndash2870

[104] J Johnson X Zhang X Zhang J Zhang Curr Org Chem 18 (2014) 1973ndash2001[105] M Eddaoudi DF Sava JF Eubank K Adil V Guillerm Chem Soc Rev 44

(2015) 228ndash249[106] Y Liu VC Kravtsov R Larsen M Eddaoudi Chem Commun (2006) 1488[107] S Yang X Lin AJ Blake GS Walker P Hubberstey NR Champness M

Schroumlder Nat Chem 1 (2009) 487ndash493[108] D Banerjee SJ Kim H Wu W Xu LA Borkowski J Li JB Parise Inorg Chem

50 (2011) 208ndash212[109] M De Toni F-X Coudert S Paranthaman P Pullumbi A Boutin AH Fuchs

J Phys Chem C 116 (2012) 2952ndash2959[110] X-D Chen C-Q Wan HH-Y Sung ID Williams TCW Mak Chem Eur J

15 (2009) 6518ndash6528[111] MC Bernini D Fairen-Jimenez M Pasinetti AJ Ramirez-Pastor RQ Snurr

J Mater Chem B 2 (2014) 766ndash774[112] Y-X Tan Y-P He J Zhang Chem Commun 47 (2011) 10647[113] H Fei DL Rogow SRJ Oliver J Am Chem Soc 132 (2010) 7202ndash7209[114] H Fei L Paw U DL Rogow MR Bresler YA Abdollahian SRJ Oliver Chem

Mater 22 (2010) 2027ndash2032[115] Z Zhang L Zhang L Wojtas P Nugent M Eddaoudi MJ Zaworotko J Am

Chem Soc 134 (2012) 924ndash927[116] E Jaramillo CP Grey SM Auerbach J Phys Chem B 105 (2001)

12319ndash12329[117] G Maurin RG Bell S Devautour F Henn JC Giuntini J Phys Chem B 108

(2004) 3739ndash3745[118] M Jeffroy A Boutin AH Fuchs J Phys Chem B 115 (2011) 15059ndash15066[119] G Maurin P Senet S Devautour P Gaveau F Henn VE Van Doren JC

Giuntini J Phys Chem B 105 (2001) 9157ndash9161[120] C Beauvais X Guerrault F-X Coudert A Boutin AH Fuchs J Phys Chem B

108 (2004) 399ndash404[121] DJ Earl MW Deem Phys Chem Chem Phys 7 (2005) 3910[122] R Babarao J Jiang J Am Chem Soc 131 (2009) 11417ndash11425[123] J Jiang AIChE J 55 (2009) 2422ndash2432[124] R Babarao J Jiang SI Sandler Langmuir 25 (2009) 5239ndash5247[125] R Babarao JW Jiang Ind Eng Chem Res 50 (2011) 62ndash68[126] H Wu YS Chua V Krungleviciute M Tyagi P Chen T Yildirim W Zhou J

Am Chem Soc 135 (2013) 10525ndash10532[127] M Fuentes-Cabrera DM Nicholson BG Sumpter M Widom J Chem Phys

123 (2005) 124713[128] F Birch J Geophys Res 57 (1952) 227ndash286[129] M Mattesini JM Soler F Ynduraacutein Phys Rev B 73 (2006)[130] A Samanta T Furuta J Li J Chem Phys 125 (2006) 084714[131] W Zhou T Yildirim Phys Rev B 74 (2006)[132] DF Bahr JA Reid WM Mook CA Bauer R Stumpf AJ Skulan NR Moody

BA Simmons MM Shindel MD Allendorf Phys Rev B 77 (2008)[133] A Kuc A Enyashin G Seifert J Phys Chem B 111 (2007) 8179ndash8186[134] J-C Tan B Civalleri C-C Lin L Valenzano R Galvelis P-F Chen T Bennett

C Mellot-Draznieks C Zicovich-Wilson A Cheetham Phys Rev Lett 108(2012) 095502

[135] SS Han WA Goddard J Phys Chem C 111 (2007) 15185ndash15191[136] M Tafipolsky S Amirjalayer R Schmid J Phys Chem C 114 (2010)

14402ndash14409[137] JC Tan TD Bennett AK Cheetham Proc Natl Acad Sci 107 (2010)

9938ndash9943[138] TD Bennett AL Goodwin MT Dove DA Keen MG Tucker ER Barney

AK Soper EG Bithell J-C Tan AK Cheetham Phys Rev Lett 104 (2010)[139] JC Tan AK Cheetham Chem Soc Rev 40 (2011) 1059[140] R Dovesi R Orlando B Civalleri C Roetti VR Saunders CM Zicovich-

Wilson Z Kristallogr 220 (2005) 571ndash573[141] W Perger J Criswell B Civalleri R Dovesi Comput Phys Commun 180

(2009) 1753ndash1759[142] A Marmier ZAD Lethbridge RI Walton CW Smith SC Parker KE Evans

Comput Phys Commun 181 (2010) 2102ndash2115[143] ELATE Elastic tensor analysis online tool for analysis of elastic tensors http

progscoudertnameelate[144] F-X Coudert A Boutin AH Fuchs AV Neimark J Phys Chem Lett 4 (2013)

3198ndash3205[145] AU Ortiz A Boutin AH Fuchs F-X Coudert Phys Rev Lett 109 (2012)

195502[146] AU Ortiz A Boutin AH Fuchs F-X Coudert J Chem Phys 138 (2013)

174703[147] S Horike S Shimomura S Kitagawa Nat Chem 1 (2009) 695[148] F-X Coudert Chem Mater 27 (2015) 1905ndash1916[149] AU Ortiz A Boutin F-X Coudert Chem Commun 50 (2014) 5867[150] F Niekiel J Lannoeye H Reinsch AS Munn A Heerwig I Zizak S Kaskel

RI Walton D de Vos P Llewellyn A Lieb G Maurin N Stock Inorg Chem53 (2014) 4610ndash4620

[151] AB Cairns AL Goodwin Phys Chem Chem Phys (2015)[152] W Miller KE Evans A Marmier Appl Phys Lett 106 (2015) 231903[153] AL Goodwin DA Keen MG Tucker Proc Natl Acad Sci 105 (2008)

18708ndash18713[154] AD Fortes E Suard KS Knight Science 331 (2011) 742ndash746[155] AB Cairns J Catafesta C Levelut J Rouquette A van der Lee L Peters

AL Thompson V Dmitriev J Haines AL Goodwin Nat Mater 12 (2013)212ndash216


[156] R Gatt R Caruana-Gauci JN Grima Nat Mater 12 (2013) 182ndash183[157] W Li MR Probert M Kosa TD Bennett A Thirumurugan RP Burwood

M Parinello JAK Howard AK Cheetham J Am Chem Soc 134 (2012)11940ndash11943

[158] P Serra-Crespo A Dikhtiarenko E Stavitski J Juan-Alca niz F Kapteijn F-XCoudert J Gascon CrystEngComm 17 (2015) 276ndash280

[159] W Cai A Katrusiak Nat Commun 5 (2014)[160] AU Ortiz A Boutin KJ Gagnon A Clearfield F-X Coudert J Am Chem Soc

136 (2014) 11540ndash11545[161] F Niekiel M Ackermann P Guerrier A Rothkirch N Stock Inorg Chem 52

(2013) 8699ndash8705[162] KJ Gagnon CM Beavers A Clearfield J Am Chem Soc 135 (2013)

1252ndash1255[163] AU Ortiz A Boutin AH Fuchs F-X Coudert J Phys Chem Lett 4 (2013)

1861ndash1865[164] M Parrinello J Chem Phys 76 (1982) 2662[165] F Mouhat F-X Coudert Phys Rev B 90 (2014)[166] L Boueumlssel du Bourg AU Ortiz A Boutin F-X Coudert APL Mater 2 (2014)

124110[167] JN Grima V Zammit R Gatt Xjenza J Malta Chamber Sci 11 (2006) 17ndash29[168] Y Wu A Kobayashi GJ Halder VK Peterson KW Chapman N Lock PD

Southon CJ Kepert Angew Chem Int Ed 47 (2008) 8929ndash8932[169] W Zhou H Wu T Yildirim JR Simpson ARH Walker Phys Rev B 78 (2008)[170] D Dubbeldam KS Walton DE Ellis RQ Snurr Angew Chem Int Ed 46

(2007) 4496ndash4499[171] VK Peterson GJ Kearley Y Wu AJ Ramirez-Cuesta E Kemner CJ Kepert

Angew Chem Int Ed 49 (2010) 585ndash588[172] LHN Rimmer MT Dove AL Goodwin DC Palmer Phys Chem Chem Phys

16 (2014) 21144ndash21152[173] B Mu KS Walton J Phys Chem C 115 (2011) 22748ndash22754[174] JK Bristow D Tiana A Walsh J Chem Theory Comput 10 (2014) 4644ndash4652[175] KT Butler CH Hendon A Walsh J Am Chem Soc 136 (2014) 2703ndash2706[176] MD Allendorf CA Bauer RK Bhakta RJT Houk Chem Soc Rev 38 (2009)

1330[177] Y Cui Y Yue G Qian B Chen Chem Rev 112 (2012) 1126ndash1162[178] CG Silva A Corma H Garcamprsquoiacute J Mater Chem 20 (2010) 3141[179] MD Allendorf A Schwartzberg V Stavila AA Talin Chem Eur J 17 (2011)

11372ndash11388[180] C Wang Z Xie KE deKrafft W Lin J Am Chem Soc 133 (2011)

13445ndash13454[181] L-M Yang G-Y Fang J Ma E Ganz SS Han Cryst Growth Des 14 (2014)

2532ndash2541[182] E Flage-Larsen A Roslashyset JH Cavka K Thorshaug J Phys Chem C 117 (2013)

20610ndash20616[183] B Civalleri F Napoli Y Noeumll C Roetti R Dovesi CrystEngComm 8 (2006)

364[184] CH Hendon KE Wittering T-H Chen W Kaveevivitchai I Popov KT But-

ler CC Wilson DL Cruickshank OS Miljanic A Walsh Nano Lett 15 (2015)2149ndash2154

[185] M Dan-Hardi C Serre T Frot L Rozes G Maurin C Sanchez G Feacuterey J AmChem Soc 131 (2009) 10857ndash10859

[186] KT Butler CH Hendon A Walsh ACS Appl Mater Interfaces 6 (2014)22044ndash22050

[187] S Ling B Slater J Phys Chem C 119 (2015) 16667ndash16677[188] Z Hu BJ Deibert J Li Chem Soc Rev 43 (2014) 5815ndash5840[189] MA Marques CA Ullrich F Nogueira A Rubio K Burke EKU Gross Time-

Dependent Density Functional Theory Springer BerlinHeidelberg 2006[190] C Adamo D Jacquemin Chem Soc Rev 42 (2013) 845ndash856[191] H Zhang L Zhou J Wei Z Li P Lin S Du J Mater Chem 22 (2012) 21210[192] M Ji C Hao D Wang H Li J Qiu Dalton Trans 42 (2013) 3464ndash3470[193] M Ji X Lan Z Han C Hao J Qiu Inorg Chem 51 (2012) 12389ndash12394[194] J-R Li RJ Kuppler H-C Zhou Chem Soc Rev 38 (2009) 1477[195] J-R Li Y Ma MC McCarthy J Sculley J Yu H-K Jeong PB Balbuena H-C

Zhou Coord Chem Rev 255 (2011) 1791ndash1823[196] J-R Li J Sculley H-C Zhou Chem Rev 112 (2012) 869ndash932[197] J Liu PK Thallapally BP McGrail DR Brown J Liu Chem Soc Rev 41 (2012)

2308ndash2322[198] K Sumida DL Rogow JA Mason TM McDonald ED Bloch ZR Herm T-H

Bae JR Long Chem Rev 112 (2012) 724ndash781[199] S Brunauer PH Emmett E Teller J Am Chem Soc 60 (1938) 309ndash319[200] J Rouquerol D Avnir CW Fairbridge DH Everett JM Haynes N Pernicone

JDF Ramsay KSW Sing KK Unger Pure Appl Chem 66 (1994)[201] LJ Murray M Dinca JR Long Chem Soc Rev 38 (2009) 1294[202] MP Suh HJ Park TK Prasad D-W Lim Chem Rev 112 (2012) 782ndash835[203] Y Yan S Yang AJ Blake M Schroumlder Acc Chem Res 47 (2014) 296ndash307[204] J Canivet A Fateeva Y Guo B Coasne D Farrusseng Chem Soc Rev 43

(2014) 5594ndash5617[205] NC Burtch H Jasuja KS Walton Chem Rev 114 (2014) 10575ndash10612[206] H Wu Q Gong DH Olson J Li Chem Rev 112 (2012) 836ndash868[207] N Lamia M Jorge MA Granato FA Almeida Paz H Chevreau AE Rodrigues

Chem Eng Sci 64 (2009) 3246ndash3259

[208] AH Fuchs AK Cheetham J Phys Chem B 105 (2001) 7375ndash7383[209] B Smit TLM Maesen Chem Rev 108 (2008) 4125ndash4184[210] P Ungerer B Tavitian A Boutin Applications of Molecular Simulation in the

Oil and Gas Industry Editions Technip 2005[211] AL Myers PA Monson Langmuir 18 (2002) 10261ndash10273

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212] MG Martin JI Siepmann J Phys Chem B 102 (1998) 2569ndash2577213] P Ungerer C Beauvais J Delhommelle A Boutin B Rousseau AH Fuchs J

Chem Phys 112 (2000) 5499214] AK Rappe CJ Casewit KS Colwell WA Goddard WM Skiff J Am Chem

Soc 114 (1992) 10024ndash10035215] SL Mayo BD Olafson WA Goddard J Phys Chem 94 (1990) 8897ndash8909216] D Fairen-Jimenez P Lozano-Casal T Duumlren S Kaskel P Llewellyn F

Rodriguez-Reinoso NA Seaton Proceedings of the 8th International Sym-posium on the Characterisation of Porous Solids Royal Society of Chemistry2009 pp 80ndash87

217] MA Addicoat N Vankova IF Akter T Heine J Chem Theory Comput 10(2014) 880ndash891

218] RS Mulliken J Chem Phys 23 (1955) 1833219] FL Hirshfeld Theoret Chim Acta 44 (1977) 129ndash138220] RF Bader Atoms in Molecules Wiley Online Library 1990221] CM Breneman KB Wiberg J Comput Chem 11 (1990) 361ndash373222] P Cieplak WD Cornell C Bayly PA Kollman J Comput Chem 16 (1995)

1357ndash1377223] C Campa naacute B Mussard TK Woo J Chem Theory Comput 5 (2009)

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(2015) 3829ndash3843227] ES Kadantsev PG Boyd TD Daff TK Woo J Phys Chem Lett 4 (2013)

3056ndash3061228] T Watanabe TA Manz DS Sholl J Phys Chem C 115 (2011) 4824ndash4836229] S Bureekaew S Amirjalayer M Tafipolsky C Spickermann TK Roy R

Schmid Phys Status Solidi B 250 (2013) 1128ndash1141230] L Vanduyfhuys T Verstraelen M Vandichel M Waroquier V Van Spey-

broeck J Chem Theory Comput 8 (2012) 3217ndash3231231] L Vanduyfhuys S Vandenbrande T Verstraelen R Schmid M Waroquier V

Van Speybroeck J Comput Chem 36 (2015) 1015ndash1027232] SS Han D Kim DH Jung S Cho S-H Choi Y Jung J Phys Chem C 116

(2012) 20254ndash20261233] JR Schmidt K Yu JG McDaniel Acc Chem Res 48 (2015) 548ndash556234] JG McDaniel S Li E Tylianakis RQ Snurr JR Schmidt J Phys Chem C 119

(2015) 3143ndash3152235] M Tafipolsky R Schmid J Phys Chem B 113 (2009) 1341ndash1352236] Y Gurdal S Keskin Ind Eng Chem Res 51 (2012) 7373ndash7382237] AL Myers JM Prausnitz AIChE J 11 (1965) 121ndash127238] E Costa JL Sotelo G Calleja C Marroacuten AIChE J 27 (1981) 5ndash12239] L Hamon N Heymans PL Llewellyn V Guillerm A Ghoufi S Vaesen G

Maurin C Serre G De Weireld GD Pirngruber Dalton Trans 41 (2012) 4052240] S Suwanayuen RP Danner AIChE J 26 (1980) 76ndash83241] AD Wiersum J-S Chang C Serre PL Llewellyn Langmuir 29 (2013)

3301ndash3309242] AN Dickey AO Yazaydın RR Willis RQ Snurr Can J Chem Eng 90 (2012)

825ndash832243] Q Yang C Xue C Zhong J-F Chen AIChE J 53 (2007) 2832ndash2840244] Y-S Bae KL Mulfort H Frost P Ryan S Punnathanam LJ Broadbelt JT

Hupp RQ Snurr Langmuir 24 (2008) 8592ndash8598245] NF Cessford NA Seaton T Duumlren Ind Eng Chem Res 51 (2012) 4911ndash4921246] M Fischer B Kuchta L Firlej F Hoffmann M Froumlba J Phys Chem C 114

(2010) 19116ndash19126247] L Chen L Grajciar P Nachtigall T Duumlren J Phys Chem C 115 (2011)

23074ndash23080248] AO Yazaydın RQ Snurr T-H Park K Koh J Liu MD LeVan AI Benin P

Jakubczak M Lanuza DB Galloway JJ Low RR Willis J Am Chem Soc 131(2009) 18198ndash18199

249] L Chen CA Morrison T Duumlren J Phys Chem C 116 (2012) 18899ndash18909250] M Fischer JRB Gomes M Froumlba M Jorge Langmuir 28 (2012)

8537ndash8549251] D Yu AO Yazaydin JR Lane PDC Dietzel RQ Snurr Chem Sci 4 (2013)

3544252] L Grajciar P Nachtigall O Bludsky M Rubes J Chem Theory Comput 11

(2015) 230ndash238253] MK Rana HS Koh J Hwang DJ Siegel J Phys Chem C 116 (2012)

16957ndash16968254] H Ji J Park M Cho Y Jung ChemPhysChem 15 (2014) 3157ndash3165255] J Zang S Nair DS Sholl J Phys Chem C 117 (2013) 7519ndash7525256] AL Dzubak L-C Lin J Kim JA Swisher R Poloni SN Maximoff B Smit L

Gagliardi Nat Chem 4 (2012) 810ndash816257] L-C Lin K Lee L Gagliardi JB Neaton B Smit J Chem Theory Comput 10

(2014) 1477ndash1488258] J Borycz L-C Lin ED Bloch J Kim AL Dzubak R Maurice D Semrouni K

Lee B Smit L Gagliardi J Phys Chem C 118 (2014) 12230ndash12240259] S Grimme J Chem Phys 124 (2006) 034108260] S Grimme J Comput Chem 27 (2006) 1787261] K Deb A Sinha Evolutionary Multi-Criterion Optimization Springer 2009

pp 110ndash124

262] Z-J Lin J Luuml M Hong R Cao Chem Soc Rev 43 (2014) 5867ndash5895263] A Schneemann V Bon I Schwedler I Senkovska S Kaskel RA Fischer

Chem Soc Rev 43 (2014) 6062ndash6096264] D Fairen-Jimenez SA Moggach MT Wharmby PA Wright S Parsons T

Duumlren J Am Chem Soc 133 (2011) 8900ndash8902


[265] CO Ania E Garciacutea-Peacuterez M Haro JJ Gutieacuterrez-Sevillano T Valdeacutes-Soliacutes JBParra S Calero J Phys Chem Lett 3 (2012) 1159ndash1164

[266] F-X Coudert M Jeffroy AH Fuchs A Boutin C Mellot-Draznieks J AmChem Soc 130 (2008) 14294ndash14302

[267] S Duane A Kennedy BJ Pendleton D Roweth Phys Lett B 195 (1987)216ndash222

[268] S Chempath LA Clark RQ Snurr J Chem Phys 118 (2003) 7635[269] D Dubbeldam S Calero DE Ellis RQ Snurr Mol Simul (2015) 1ndash21[270] A Ghoufi G Maurin J Phys Chem C 114 (2010) 6496ndash6502[271] A Ghoufi A Subercaze Q Ma P Yot Y Ke I Puente-Orench T Devic V

Guillerm C Zhong C Serre G Feacuterey G Maurin J Phys Chem C 116 (2012)13289ndash13295

[272] S Watanabe H Sugiyama M Miyahara Adsorption 14 (2008) 165ndash170[273] H Sugiyama S Watanabe H Tanaka MT Miyahara Langmuir 28 (2012)

5093ndash5100[274] D Bousquet F-X Coudert A Boutin J Chem Phys 137 (2012) 044118[275] D Bousquet F-X Coudert AGJ Fossati AV Neimark AH Fuchs A Boutin

J Chem Phys 138 (2013) 174706[276] VK Shen DW Siderius J Chem Phys 140 (2014) 244106[277] Z Wang SM Cohen J Am Chem Soc 131 (2009) 16675ndash16677[278] JA Gee DS Sholl J Phys Chem C 117 (2013) 20636ndash20642[279] C Zhang JA Gee DS Sholl RP Lively J Phys Chem C 118 (2014)

20727ndash20733[280] R Numaguchi H Tanaka S Watanabe MT Miyahara J Chem Phys 140

(2014) 044707[281] A Ghysels L Vanduyfhuys M Vandichel M Waroquier V Van Speybroeck

B Smit J Phys Chem C 117 (2013) 11540ndash11554[282] F-X Coudert C Mellot-Draznieks AH Fuchs A Boutin J Am Chem Soc 131

(2009) 2442ndash2443[283] A Boutin M-A Springuel-Huet A Nossov A Gedeon T Loiseau C

Volkringer G Ferey F-X Coudert AH Fuchs Angew Chem Int Ed 48 (2009)8314ndash8317

[284] F-X Coudert C Mellot-Draznieks AH Fuchs A Boutin J Am Chem Soc 131(2009) 11329ndash11331

[285] F-X Coudert Phys Chem Chem Phys 12 (2010) 10904[286] AU Ortiz M-A Springuel-Huet F-X Coudert AH Fuchs A Boutin Langmuir

28 (2012) 494ndash498[287] P Chowdhury C Bikkina D Meister F Dreisbach S Gumma Microporous

Mesoporous Mater 117 (2009) 406ndash413[288] G Garberoglio AI Skoulidas JK Johnson J Phys Chem B 109 (2005)

13094ndash13103[289] K Sing F Rouquerol J Rouquerol Adsorption by Powders and Porous Solids

Academic Press San Diego 1999[290] J Silvestre-Albero A Sepuacutelveda-Escribano F Rodriacute guez-Reinoso V Kou-

velos G Pilatos NK Kanellopoulos M Krutyeva F Grinberg J Kaumlrger AISpjelkavik M Stoumlcker A Ferreira S Brouwer F Kapteijn J Weitkamp SDSklari VT Zaspalis DJ Jones LC de Menorval M Lindheimer P Caffarelli EBorsella AAG Tomlinson MJG Linders JL Tempelman EA Bal Proceed-ings of the 8th International Symposium on the Characterization of PorousSolids 318 2009

[291] Z Fang JP Duumlrholt M Kauer W Zhang C Lochenie B Jee B Albada NMetzler-Nolte A Poumlppl B Weber M Muhler Y Wang R Schmid RA FischerJ Am Chem Soc 136 (2014) 9627ndash9636

[292] G Barin V Krungleviciute O Gutov JT Hupp T Yildirim OK Farha InorgChem 53 (2014) 6914ndash6919

[293] P Ghosh YJ Coloacuten RQ Snurr Chem Commun 50 (2014) 11329[294] MJ Cliffe W Wan X Zou PA Chater AK Kleppe MG Tucker H Wilhelm

NP Funnell F-X Coudert AL Goodwin Nat Commun 5 (2014) 4176[295] KS Walton RQ Snurr J Am Chem Soc 129 (2007) 8552ndash8556[296] K Sillar J Sauer J Am Chem Soc 134 (2012) 18354ndash18365[297] JN Lalena DA Cleary Principles of Inorganic Materials Design John Wiley

amp Sons 2010[298] SM Auerbach KA Carrado PK Dutta Handbook of Zeolite Science and

Technology CRC Press 2003[299] S Oslashien D Wragg H Reinsch S Svelle S Bordiga C Lamberti KP Lillerud

Crystal Growth amp Design 14 (2014) 5370ndash5372[300] F Vermoortele B Bueken G Le Bars B Van de Voorde M Vandichel

K Houthoofd A Vimont M Daturi M Waroquier V Van Spey-broeck C Kirschhock DE De Vos J Am Chem Soc 135 (2013)11465ndash11468

[301] B Tu Q Pang D Wu Y Song L Weng Q Li J Am Chem Soc 136 (2014)14465ndash14471

[302] H Furukawa U Muumlller OM Yaghi Angew Chem Int Ed 54 (2015)3417ndash3430

[303] JM Taylor S Dekura R Ikeda H Kitagawa Chem Mater 27 (2015)2286ndash2289

[304] Z Fang B Bueken DE De Vos RA Fischer Angew Chem Int Ed 54 (2015)7234ndash7254

[305] C J Cramer (ChemProfCramer) 5 June 2015 tweet httpstwittercomChemProfCramerstatus606715379902214144

[306] C Chizallet S Lazare D Bazer-Bachi F Bonnier V Lecocq E Soyer A-A

Quoineaud N Bats J Am Chem Soc 132 (2010) 12365ndash12377

[307] MJ Cliffe JA Hill CA Murray F-X Coudert AL Goodwin Phys ChemChem Phys 17 (2015) 11586ndash11592

[308] O Karagiaridi W Bury AA Sarjeant CL Stern OK Farha JT Hupp ChemSci 3 (2012) 3256

2 on Che


[309] O Karagiaridi W Bury JE Mondloch JT Hupp OK Farha Angew ChemInt Ed 53 (2014) 4530ndash4540

[310] P Deria JE Mondloch O Karagiaridi W Bury JT Hupp OK Farha ChemSoc Rev 43 (2014) 5896ndash5912

[311] T Besara P Jain NS Dalal PL Kuhns AP Reyes HW Kroto AK CheethamProc Natl Acad Sci 108 (2011) 6828ndash6832

[312] TD Bennett AK Cheetham Acc Chem Res 47 (2014) 1555ndash1562[313] T D Bennett J-C Tan Y Z Yue C Ducati N Terril H H M Yeung Z Zhou

W Chen S Henke A K Cheetham G N Greaves (2014) ArXiv14093980(httparxivorgabs14093980)

[314] M Fernandez PG Boyd TD Daff MZ Aghaji TK Woo J Phys Chem Lett5 (2014) 3056ndash3060

[315] AW Thornton DA Winkler MS Liu M Haranczyk DF Kennedy RSC Adv5 (2015) 44361ndash44370

[316] Z Yıldız H Uzun Microporous Mesoporous Mater 208 (2015) 50ndash54[317] D Majda F Paz O Friedrichs M Foster A Simperler R Bell J Klinowski J

Phys Chem C 112 (2008) 1040ndash1047[318] VA Blatov GD Ilyushin DM Proserpio Chem Mater 25 (2013) 412ndash424

[319] Y Li J Yu R Xu Angew Chem Int Ed 52 (2013) 1673ndash1677[320] M Edgar R Mitchell AMZ Slawin P Lightfoot PA Wright Chem Eur J 7

(2001) 5168ndash5175[321] C-B Tian R-P Chen C He W-J Li Q Wei X-D Zhang S-W Du Chem

Commun 50 (2014) 1915


[322] WD Cornell P Cieplak CI Bayly IR Gould KM Merz DM Ferguson DCSpellmeyer T Fox JW Caldwell PA Kollman J Am Chem Soc 117 (1995)5179ndash5197

[323] B Zheng M Sant P Demontis GB Suffritti J Phys Chem C 116 (2012)933ndash938

[324] Z Hu L Zhang J Jiang J Chem Phys 136 (2012) 244703[325] X Wu J Huang W Cai M Jaroniec RSC Adv 4 (2014) 16503ndash16511[326] F Salles A Ghoufi G Maurin RG Bell C Mellot-Draznieks G Feacuterey Angew

Chem Int Ed 47 (2008) 8487ndash8491[327] DS Coombes F Cora C Mellot-Draznieks RG Bell J Phys Chem C 113

(2009) 544ndash552[328] L Zhang Z Hu J Jiang J Am Chem Soc 135 (2013) 3722ndash3728[329] DN Dybtsev H Chun K Kim Angew Chem Int Ed 43 (2004) 5033ndash5036[330] M Kondo S Furukawa K Hirai T Tsuruoka J Reboul H Uehara S Diring Y

Sakata O Sakata S Kitagawa J Am Chem Soc 136 (2014) 4938ndash4944[331] C Triguero F-X Coudert A Boutin AH Fuchs AV Neimark J Phys Chem

Lett 2 (2011) 2033ndash2037[332] C Triguero F-X Coudert A Boutin AH Fuchs AV Neimark J Chem Phys

137 (2012) 184702[333] M Yoneya S Tsuzuki M Aoyagi Phys Chem Chem Phys 17 (2015)

8649ndash8652[334] L Jin SM Auerbach PA Monson J Phys Chem C 114 (2010) 14393ndash14401[335] SM Auerbach W Fan PA Monson Int Rev Phys Chem 34 (2014) 35ndash70

Computational characterization and prediction of metalndashorganic framework properties

1 Introduction



22 Large-scale screening enumeration of hypothetical structures

23 Geometrical properties surface area pore volume and pore size distribution







4 Adsorption




44 Beyond classical force fields open metal sites and chemisorption



5 Perspectives




Acknowledgments

References


AASBU automated assembly of secondary building unitsANN artificial neural networkAUA anistropic united atomBET BrunauerndashEmmettndashTellerCC coupled clusterCHelpG charges from electrostatic potentials using a grid-

based methodCSD Cambridge structural databaseCOF covalent organic frameworkCoRE MOF computation-ready experimental MOFDFT density functional theoryGCMC grand canonical Monte CarloHMC hybrid Monte CarloHPC high-performance computingIAST ideal adsorbed solution theoryIRMOF iso-reticular metalndashorganic frameworkMC Monte CarloMD molecular dynamicsMMSV MorsendashMorsendashsplinendashvan der WaalsMOF metalndashorganic frameworkNLC negative linear compressibilityNTE negative thermal expansionOFAST osmotic framework adsorption solution theoryPSD pore size distributionQSPR quantitative structurendashproperty relationshipRAST real adsorbed solution theoryRCSR reticular chemistry structure resourceRESP restrained electrostatic potentialSBU secondary building unitSPC soft porous crystalTDDFT time-dependent density functional theoryUA united atomUFF universal force fieldVST vacancy solution theoryZAG zinc alkyl gateZIF zeolitic imidazolate frameworkZMOF zeolite-like metalndashorganic framework

1

aattmtapocwShcrnwCtca

Table 1List of reviews published on computational characterization of metalndashorganicframeworks

Year Topic Ref

2015 General modeling of MOFs (book) [1]2015 Quantum chemical characterization of MOFs

including catalysis[2]

2014 High-throughput computational screening [3]2014 First-principles force fields for guest molecules [4]2013 Gas separation [5]2012 Screening for adsorption and separation [6]2012 Methane hydrogen and acetylene storage [7]2011 Adsorption in flexible MOFs [8]2011 Energy environmental and pharmaceutical

applications[9]

2011 Screening for separation applications [10]2009 Hydrogen storage [11]2009 Adsorption [12]

These structures can then either be used to guide the synthesis ofnovel materials or to identify materials already synthesized but

Introduction

Since its emergence in the 1950s molecular simulation has seenn ever-growing use in research in the fields of physical chemicalnd materials sciences where it offers an additional dimension tohe characterization and understanding of systems complemen-ary to experimental techniques and pen-and-paper theoretical

odels The development of novel computational methodologiesogether with the exponential increase in computational powervailable to researchers have dramatically expanded the range ofroblems that can be addressed through modeling This is truef resource-intensive calculations performed on high-performanceomputing (HPC) supercomputers but it is also true of desktoporkstations and even now of laptops and mobile devices [1516]

everal of the simulation techniques of computational chemistryave now reached the status of being relatively ldquoroutinerdquo cal-ulations and are nowadays considered an integral part of theesearcherrsquos toolbox just like experimental characterization tech-iques like X-ray diffraction and NMR spectroscopy Among thosee can cite Density Functional Theory calculations and Grandanonical Monte Carlo simulations It is possible to become a user of

hese tools with relatively little training relying either on commer-ial or academic software with user-friendly interfaces Howevers with any technique one should always take great care in

2008 Adsorption and transport [13]2007 Adsorption of small molecules [14]

checking the validity of the tools for the system at hand as wellas in interpreting the results obtained

Given the formidable research effort focused on metalndashorganicframeworks (MOFs) in the past decade with more than 20000papers published (at a current rate of more than 5 MOF papers perday [17]) 15000 structures on record at the Cambridge Crystallo-graphic Data Centre and over 170 review articles dedicated to thistopic the published literature on computational studies of MOFs isin itself abundant Theoretical approaches are in many cases usedin combination with experimental characterization techniques tostudy newly synthesized materials and understand their proper-ties at the microscopic level In this introductory review we givean overview of the computational chemistry methods commonlyused in the field of MOFs to describe the structures themselves andcharacterize (or predict) their various properties It is by no meansa systematic review of existing computational work on MOFs ofwhich there simply is too much to systematically enumerate hereRather we will try to give the reader an idea of what is possiblein theoretical studies of MOFs both at the quantum chemical leveland through classical molecular simulations For more details onspecific areas of interest we refer to existing reviews of compu-tational MOF studies which are listed in Table 12 We finish thereview by pointing out some of the open questions and challengesin the field



In most cases the structure of a newly synthesizedmetalndashorganic framework is determined experimentally usingsingle-crystal X-ray diffraction data when possible or solving thestructure from powder diffraction data if single crystals of suffi-cient size or quality cannot be obtained In the latter case it oftenhappens that because of the molecular complexity of the materiala low symmetry or a large unit cell the structure solution is ardu-ous or impossible to solve Moreover in other cases there is a needfor methodologies of true (or ab initio) computational predictionof MOF crystal structures without any input of experimental data

2 In particular we do not address in this review the very specific topic of thecatalytic activity of MOFs on this we refer the reader to the very recent review byOdoh et al [2]

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miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


F een) a( o the

S

poatVeib5[

2

tnegafaCcnfmo2

atbc[ifitpotsos

ut



































SC

bmpCldquoettoipt

mamMiifaBirdmct




















F by quaY tio (

Uud

fsscdfsi

Tsbc

bull

bull

bull

bull

Ptw

fpeasfltF







ij =sum

kl

Cijklkl (1)













F inimiu

S istry)

cfescc

dtiiTaoo











2 on Che

sdirfpfttwZ[tashe

3

dtbtsarcpthhwt

puedc

˛

wefmwvvrtawp

vv(










V = 1V

(partV

partT

)N

˛ = 1

(part

partT

)N

(2)






kT

V

)Cminus1





ik = minus(

part log ωik

part log V

)(3)






gap





F pictins

S mical

Otuwgespo

optdeMtau









Society


4 Adsorption




F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References














SC

bmpCldquoettoipt

mamMiifaBirdmct




















F by quaY tio (

Uud

fsscdfsi

Tsbc

bull

bull

bull

bull

Ptw

fpeasfltF







ij =sum

kl

Cijklkl (1)













F inimiu

S istry)

cfescc

dtiiTaoo











2 on Che

sdirfpfttwZ[tashe

3

dtbtsarcpthhwt

puedc

˛

wefmwvvrtawp

vv(










V = 1V

(partV

partT

)N

˛ = 1

(part

partT

)N

(2)






kT

V

)Cminus1





ik = minus(

part log ωik

part log V

)(3)






gap





F pictins

S mical

Otuwgespo

optdeMtau









Society


4 Adsorption




F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


F by quaY tio (

Uud

fsscdfsi

Tsbc

bull

bull

bull

bull

Ptw

fpeasfltF







ij =sum

kl

Cijklkl (1)













F inimiu

S istry)

cfescc

dtiiTaoo











2 on Che

sdirfpfttwZ[tashe

3

dtbtsarcpthhwt

puedc

˛

wefmwvvrtawp

vv(










V = 1V

(partV

partT

)N

˛ = 1

(part

partT

)N

(2)






kT

V

)Cminus1





ik = minus(

part log ωik

part log V

)(3)






gap





F pictins

S mical

Otuwgespo

optdeMtau









Society


4 Adsorption




F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


F inimiu

S istry)

cfescc

dtiiTaoo











2 on Che

sdirfpfttwZ[tashe

3

dtbtsarcpthhwt

puedc

˛

wefmwvvrtawp

vv(










V = 1V

(partV

partT

)N

˛ = 1

(part

partT

)N

(2)






kT

V

)Cminus1





ik = minus(

part log ωik

part log V

)(3)






gap





F pictins

S mical

Otuwgespo

optdeMtau









Society


4 Adsorption




F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References

2 on Che

sdirfpfttwZ[tashe

3

dtbtsarcpthhwt

puedc

˛

wefmwvvrtawp

vv(










V = 1V

(partV

partT

)N

˛ = 1

(part

partT

)N

(2)






kT

V

)Cminus1





ik = minus(

part log ωik

part log V

)(3)






gap





F pictins

S mical

Otuwgespo

optdeMtau









Society


4 Adsorption




F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References




F pictins

S mical

Otuwgespo

optdeMtau









Society


4 Adsorption




F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


F s hoste

orew

ragBoCwimms

cialipooofCls

4

mMCuiT

















n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References

n Che

cwlostweTfmbroIta

4


fmamt(ispp

(at






















coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


coads

suo[o

4

cmoobfhs

ssttwmpimoi

Fsp

S


















iety


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


metalS ry

Tac

4c

MtdctcWmdmslgd

iucamasavrcs

admoMeaagslgwQe























Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References



Si

BabC

S














S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References



S Ameri

md

uipNi[ttmassCi

Casbsfslttt

eMtisf



















F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References


F xenont

S KGaA

ei

4

tctmdtdiritf

1

2

3

4















Weinheim



5 Perspectives





n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References

n Che

opnamiatgt[ai

ssmeppsfbe

miiDattUotcai

ibcairtbtMtrwuho[

5

fptrMa





















2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

[

[[[

[[

[
































pp 110ndash124










































2 on Che













Commun 50 (2014) 1915












1 Introduction











4 Adsorption







5 Perspectives




Acknowledgments

References

2 on Che

CttgdotsHtbtbaacapf

5

cimsspcdiflimgtdtao


















Acknowledgments


References




n Che



































21353ndash21360



































2 on Che




































































n Che

[[

[

[[

[

[[[[[

[

[[[

[

[[

[

[

[

[[

[[[[[

[[

[

[[

[[

[

[

[[

[

[

[

[[[

[

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Acknowledgments

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Acknowledgments

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Acknowledgments

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5 Perspectives




Acknowledgments

References

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