Toward an Accurate Modeling of the Water−Zeolite Interaction

pubs.acs.org/JPCL

Toward an Accurate Modeling of the Water-Zeolite Interaction: Calibrating the DFT Approach Fr ed eric Labat, Alain H. Fuchs, and Carlo Adamo* Laboratoire d'Electrochimie, Chimie des Interfaces et Mod elisation pour l'Energie, CNRS UMR 7575, Chimie ParisTech (Ecole Nationale Superieure de Chimie de Paris), 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France

ABSTRACT The performances of nine selected exchange-correlation functionals for the description of the interaction of water with clusters modeling the silicalite-1 zeolite have been assessed. The chosen structural models cover different classes of interactions between water and a zeolite backbone, ranging from electrostatics to van der Waals types. Almost all of the considered functionals give qualitatively correct results for the considered systems with respect to the reference MP2 data. However, among all of the models, only two (M05-2X and B97-D) provide a quantitative agreement for all of the clusters taken into account. These functionals can thus be envisaged as affordable methods to study weakly interacting systems as well as to provide a database for the development of accurate and transferable intermolecular potentials for classical simulations. SECTION Molecular Structure, Quantum Chemistry, General Theory

attractive. “Hydrophobic” here does not mean water repelling but that the water-water interaction is much larger than the water-zeolite interaction.14 Beyond this specific problem of modeling the weak water-silicalite interaction, here, we address the very general and important problem of hydrophobic hydration, whose understanding is a key issue in biology.15 It is also well-known at the experimental level that filling of the micropores by organic molecules in silicalite-1 is characterized by enhancement of the adsorption energy due to an increase of dispersion forces,3,4 especially critical to describe at the theoretical level. Such large (macroscopic) systems, and the chemical processes that they involve, could be so complex that they have to be investigated using a wide panel of modeling and simulation tools. Indeed, as in other surface problems, local phenomena like reactivity can be studied using finite model (i.e., cluster) and quantum first-principles approaches. In contrast, collective properties such as diffusivities are accurately simulated only by considering large (and possibly periodic) structural models.16 In these cases, classical approaches like Monte Carlo (MC) or molecular dynamics (MD) are more suitable, while quantum methods are too time-consuming (if not unnecessary). Between these two classes of approaches, models combining the best of these two worlds (multiscale approaches) allow for micro-macro junctions. In all of the cases, a model calibration is necessary; an error bar to the searched properties can be defined at the quantum level, while accurate parameters are needed in classical models for meaningful simulation of experimental properties.

O

ften described as molecular sieve adsorbents”, zeolites are nanoporous crystalline materials built from TO4 units, where T generally refers to Al or Si atoms. Their finely tuned nanometer-sized pores, easily accessible from the outside and of dimensions comparable to that of molecules to be adsorbed, make them highly sought-after in industry, where they have been successfully applied to a number of processes including separation (due to the sizeand shape-selective environment that they provide to chemical reactions) or catalysis in their internal cages.1,2 One of the most-studied zeolites with both hydrophobic and organophilic selectivity, synthesized in relatively large crystal forms, combining mechanical, thermal, and chemical stabilities, is silicalite-1,3,4 which has been the material of choice to clean up water contaminated with organic compounds.5 With a large amount of reliable experimental data available, this material provides an adequate system to test and develop different computational techniques. From a computational viewpoint, zeolites are particularly challenging systems since chemical reactions occur inside of the material. Although molecular simulations have emerged as a powerful tool to shed light on some processes such as diffusion and adsorption taking place in zeolites, 6-8 available inter- and intramolecular interaction potentials are not always able to reproduce key differences in adsorption properties of similar compounds.9 Recently, the process of water adsorption (high-pressure intrusion) in hydrophobic silicalite-1 has raised some attention.10-13 It was shown that the use of different standard classical force fields could lead to rather different results, and it is not yet clear why certain force fields could reproduce the observed feature while others could not. This is an interesting problem from the theoretical point of view since the water-silicalite interaction is only slightly

r 2010 American Chemical Society

Received Date: January 5, 2010 Accepted Date: January 26, 2010 Published on Web Date: February 01, 2010

763

DOI: 10.1021/jz100011p |J. Phys. Chem. Lett. 2010, 1, 763–768

pubs.acs.org/JPCL

Of course, a calibrated quantum model could provide parameters to be injected into the classical model, thus providing fully theoretical consistent multiscale approaches. This calibration procedure could be particularly tedious in systems like zeolites, where a large variety of bonds and interactions (covalent, H-bond, van der Waals) take place. Indeed, an accurate description of both covalent (i.e., strong) and noncovalent (i.e., weak) bonds with only one model can still be a challenge for quantum chemical approaches. While the popularity of density functional theory (DFT) certainly originates from its optimal balance between the required computational effort and the quality of the obtained results (with similar accuracy compared to other correlated electronic structure methods), drawbacks of current functionals are well-known. In particular, common local and semilocal exchange-correlation functionals fail to describe London dispersion interactions, which are known to be a purely correlation effect.17 Different strategies have therefore been proposed to capture these medium- or longrange correlation effects (see ref 18 for instance and references therein), leading to the development of a number of promising functionals of varying complexity over the years. In this Letter, we seek to provide a comparison of both standard and newly developed DFT methods for the modeling of weak interactions using moderate and practical basis sets, considering the interaction of water with model zeolite clusters in view of application to much larger systems. In particular, from these calculations, we hope to provide highly accurate and transferable intermolecular potentials to describe confined polar molecules such as water in molecular simulations of such systems. Among the large panoply of functionals available in the literature, nine exchange-correlation functionals have been selected in the present work. Three are popular global hybrids (GH), PBE0,19,20 B3LYP,21,22 and mPW1PW91.23,24 Two highly parametrized hybrid meta-GGA functionals have also been considered, BMK,25 developed for reaction kinetics with 42% of the HF exchange, and M05-2X,26 aimed at an accurate description of both thermochemistry and nonbonded interactions, with 56% of the HF exchange. In addition, two rangeseparated hybrids (RSH), better accounting for long-range effects by using a fraction of HF exchange increasing with the interelectronic distance, have also been tested, namely, the LC-PBE27 and the LC-ωPBE28 functionals. The screened HSE hybrid functional,29 which includes HF exchange at shortrange only, has also been used. Finally, a dispersion-corrected GGA functional (B97-D),30 based on a reparametrized Becke's B97 functional31 and including a damped atom-pairwise dispersion correction, has been taken into account. These nine functionals have not been chosen at random; B3LYP is the most common GH functional and has been already used for validating the MC approach on water interacting with silica,32 M05-2X and PBE0 are respectively the best-performing functional and GH functional for hydrocarbon-zeolite interactions,33 and RSH hybrids have never been tested on this class of interactions. Finally, the mPW1PW model was developed to deliver accurate results both for covalent and noncovalent interactions.23

r 2010 American Chemical Society

Figure 1. From the silicalite-1 bulk structure to model clusters. Si, O, and H atoms are blue, red, and white balls, respectively. The center of gravity (CG), used to perform rigid scans along the H-CG distances, is represented as a black ball.

An orthorhombic Bravais lattice (space group Pnma), with 96 SiO2 formula units per unit cell, has been taken into account to model silicalite-1 (see Figure 1). Here, a typical structure of a MFI-type zeolite unit cell can be observed: two straight channels along b with an elliptical cross section and two zigzag channels in the bc plane with a nearly circular cross section of smaller dimensions, forming four cavities at their intersections.8 Starting from the experimental crystallographic structure (a = 20.090 Å; b = 19.738 Å; c = 13.142 Å34), four clusters have been obtained from the nanopores exposed to adsorbate molecules along the b direction (see Figure 1) since this is the direction of straight channels in which the diffusion of molecules is expected to be faster than in the zigzag channels. By naming these clusters after the number of their tetrahedral sites (T), they will be indicated as follows: T5a, T5b, T6, and T10 (see Figure 1). All of the energy profiles have been evaluated by performing rigid scans along the distance between one of the hydrogen atoms of water and the center of gravity (CG) of the cluster, without geometry optimization in order to avoid spurious effects due to the limited cluster size. Please note that, due to the limited size of the model, a total (or even partial) structural optimization could lead to spurious error. In Figure 2 are reported the computed potential energy profiles as a function of the distance between one H atom of the water molecule and the center of gravity of the zeolite cages, for all clusters and methods investigated. From these profiles, in all of the considered cases, interaction energies are weak but attractive, thus suggesting a favorable adsorption of H2O on the zeolite clusters. Furthermore, these values are in the physisorption energy range, as expected from a hydrophobic material such as silicalite-1 (explained above). The typical shape of the potential energy curve of interacting fragments is obtained; it is a repulsive component at shortrange, followed by an attractive component at larger distances, with more or fewer deep wells depending on the method and the cluster considered. Although all DFT functionals qualitatively reproduce the MP2 reference curve in all

764

DOI: 10.1021/jz100011p |J. Phys. Chem. Lett. 2010, 1, 763–768

pubs.acs.org/JPCL

of the cases, quantitative reproduction in both the optimal vertical distance and interaction energy is highly sensitive to the chosen DFT method. In more detail, for the T5a model system, all of the results are contained between the MP2, B97-D, and M05-2X profiles (which are practically indistinguishable at the scale of the plot) and the BMK curve. On the other hand, three different groups appear for the T5b and T6 clusters, where the MP2, B97-D, and M05-2X (lowest) and the BMK (highest) plots bracket the results obtained with the other functionals. A similar trend also holds for the T10 model, but this time, the M05-2X results are grouped with the other functionals, so that, in this case, only B97-D provides a correct description of the interaction. It must be also stressed that the BMK functional does not exhibit a stable behavior providing a double-well shape for T5b and T6. More details can be obtained from the computed errors of all of the functionals for the equilibrium H-CG distances and interaction energies, collected in Table 1. From these values, two functionals, namely, B97-D and M05-2X, clearly outperform the others, providing the smallest errors for both distances and energies. In more detail, B97-D gives the same MP2 distances in three cases out of four (T5a, T5b, T10) and a small error in the last one (0.2 Å for T6). The mean unsigned error (MUE) on the interaction energies is very low (0.8 kJ/mol), accounting for around 3% of the average MP2 interaction energy (-24.3 kJ/mol). The M052X model has similar performances for distances (except in the T6 case, where an error of 0.6 Å is computed) but a significantly larger error for energies (MUE = 2.6 kJ/mol). This last result well illustrates how such systems represent a challenging playground even for the most recent and sophisticated DFT approaches. Furthermore, it must be pointed out that the dispersion contribution in the B97-D functional has been parametrized on molecular systems, like rare gas dimers, benzene VdW complexes, and aromatic VdW dimers, so that even better results can be expected upon an ad-hoc reparameterization. Behind these two functionals, RSH approaches (LC-PBE, LC-ωPBE, and HSE) are practically equivalent to the GHs containing 25% of the HF exchange (mPW1PW and PBE0), while the popular B3LYP is slightly less accurate than the others. When considering data computed for each cluster, the largest discrepancies between the different functionals and the MP2 reference data arise for the T10 cluster, which appears as a particularly challenging system. Moreover, upon going from the T5a and T5b clusters to the larger T6 and T10 ones, errors on de significantly increase, being maximal for this latter cluster (except for B97-D). This could be related to a subtle balance between electrostatic interactions and dispersive forces taking place in all clusters. Indeed, the interaction in the smaller clusters (T5a and T5b) can be considered as mainly governed by electrostatic interactions that are accurately described by all DFT methods since equilibrium structures of these noncovalent complexes are mainly dominated by medium-range exchange and correlation energies (see ref 35 and references therein). In contrast, larger clusters such as T10 could have a dominant dispersion contribution, for which DFT methods performances differ greatly. The T6 cluster would therefore appear as an intermediate case between

Figure 2. Potential energy profiles of the (a) T5a, (b) T5b, (c) T6, and (d) T10 adsorption models, computed performing a rigid scan along the d(H-CG) distance. A zoom around the curve minima is also given, when relevant.

r 2010 American Chemical Society

765

DOI: 10.1021/jz100011p |J. Phys. Chem. Lett. 2010, 1, 763–768

pubs.acs.org/JPCL

Table 1. Relative Errors on the Equilibrium H-CG Distance (de, Å) and Interaction Energies (Eint, kJ/mol) for All of the Considered Functionals and Clusters, Computed with Respect to the Reference MP2 Values (second column)a MP2

B3LYP

PBE0

mPW1PW91

LC-PBE

LC-ωPBE

BMK

M05-2X

HSE

B97-D

de T5a T5b

2.8 2.8

0.20 0.40

0.20 0.20

0.20 0.40

0.00 0.00

0.20 0.20

0.20 1.00

0.00 0.00

0.20 0.20

0.00 0.00

T6

1.8

0.80

0.60

0.80

0.40

0.60

1.40

0.00

0.60

0.20

T10

1.0

1.80

1.20

1.40

1.60

1.60

2.20

0.60

1.00

0.00

0.80

0.55

0.70

0.50

0.65

1.20

0.15

0.50

0.05

MUEb

Eint T5a

-26.8

-8.1

-4.6

-6.9

-2.9

-6.2

-10.7

0.5

-4.2

0.7

T5b

-26.0

-11.0

-7.6

-9.7

-7.8

-9.2

-16.0

-1.7

-7.2

-1.3

T6 T10

-27.4 -17.1

-9.2 -7.9

-8.2 -6.4

-10.1 -5.4

-8.1 -7.2

-10.0 -7.2

-17.4 -8.9

-2.2 -5.9

-7.8 -6.2

-0.2 -0.8

9.1

6.7

8.0

6.5

8.2

13.3

2.6

6.4

0.8

MUEb a

Bold values correspond to the lowest errors. b Mean unsigned error.

Table 2. Computed Interaction Energies (kJ/mol) With (EintC) and Without (Eint) BSSE Correction at the Equilibrium H-CG Distance (de, Å) for All Clusters and the B97-D, M05-2X, and MP2 Methods T5a B97-D

M05-2X

T5b MP2

B97-D

T6

M05-2X

MP2

B97-D

M05-2X

T10 MP2

B97-D

M05-2X

MP2

2.8

2.8

2.8

2.8

2.8

2.8

2.0

1.8

1.8

1.0

1.6

1.0

Eint

-27.4

-27.2

-26.8

-24.7

-24.3

-26.0

-27.2

-25.2

-27.4

-16.3

-11.2

-17.1

EintC

-23.2

-21.9

-17.2

-19.4

-18.0

-14.0

-17.2

-17.1

-7.9

-12.3

-7.3

-8.1

de

electrostatics-dominated (T5a and T5b) and dispersion-dominated systems (T10). This is confirmed by the shapes of the wells of all of the potential energy curves computed, which get shallower upon increasing the cluster sizes. As already pointed out,18,36 the two best-performing functionals (M05-2X and B97-D) give similar results for both electrostatics-dominated and mixed clusters (T5a, T5b, and T6), while B97-D significantly outperforms M05-2X for dispersion-dominated systems at large distances (T10). This can probably be related to the medium- and long-range correlation effects since dispersion interactions are long-range correlation effects. While the M05-2X functional is claimed to capture the former,35 it lacks the latter, as opposed to B97-D, which is supposed to capture both.18 In addition, it is interesting to note that all DFT functionals accurately reproduce the shape of the MP2 curve, particularly in the well region, for all electrostatics-dominated clusters (T5a and T5b), except for the BMK data. In contrast, the behavior of the two best-performing functionals (B97-D and M05-2X) for the dispersion-dominated cluster (T10) can be clearly separated for the short (d(H-CG) below 1.6 Å) and long-range parts (d(H-CG) above 1.6 Å) of the potential energy curve. The B97-D curve accurately reproduces the MP2 data at long-range, while it rises too steeply at shortrange. The M05-2X functional has, instead, the opposite behavior. The separation distance of 1.6 Å corresponds to a minimal H(water)-O(silicalite) distance of about 5 Å, which is the value defined by Zhao and Truhlar to separate mediumand long-range parts of correlation.35

r 2010 American Chemical Society

Finally, it can be noticed that both the LC-PBE and LC-ωPBE functionals fail to accurately describe the dispersion-dominated complex, clearly outlining that dispersion interactions are long-range correlation effects. Table 2 presents computed interaction energies, at the equilibrium H-CG distances, for the B97-D, M05-2X, and MP2 methods. They are in line with typical values obtained for weakly interacting systems, such as a dispersion-dominated system like C6H6-CH4 for instance. For a given complex, BSSE corrections computed are similar for all DFT methods, contributing up to 35% to the total interaction energy. On the other hand, corrections obtained at the MP2 level are much larger, accounting for nearly 70% of the interaction energy in the worst case. This is however expected since MP2 BSSE-free interaction energies of noncovalently bound systems do require much larger basis sets, of at least aug-cc-pVTZ quality.33 Nevertheless, we recall that the goal of the present paper is to assess the performances of both common and newly developed DFT methods for the modeling of weak interactions using moderate basis sets, in view of application to much larger systems, and not to provide benchmark interaction energies of H2O with zeolites. Conclusions drawn above are therefore still valid, especially when dealing with a qualitative comparison of the performances of the different methods. In summary, the obtained results reveal that, upon increasing cluster size, the dominant interaction character goes from electrostatics to dispersion. Consequently, although all functionals give qualitatively correct results with respect to the reference MP2 data for all electrostatics-dominated systems,

766

DOI: 10.1021/jz100011p |J. Phys. Chem. Lett. 2010, 1, 763–768

pubs.acs.org/JPCL

dispersion-corrected GGA (B97-D) as well as hybrid meta-GGA functionals (M05-2X) significantly improve the DFT performances for dispersion-dominated systems. These latter two functionals therefore hold great promise as useful and affordable methods to study weakly interacting systems as well as to provide a database for the development of accurate and transferable intermolecular potentials for molecular dynamics and Monte Carlo simulations of confined polar molecules such as water in hydrophobic or hydrophilic zeolites. This would thus enable efficient computational prescreening to significantly reduce the huge array of candidate materials and guide the experimental investigation for the design of new and efficient nanoporous materials for catalysis and separation purposes. Work is in progress to develop such potentials.

(10)

(11)

(12)

(13)

(14)

SUPPORTING INFORMATION AVAILABLE Computational (15)

details. This material is available free of charge via the Internet at http://pubs.acs.org.

(16)

AUTHOR INFORMATION Corresponding Author:

(17)

*To whom correspondence should be addressed. E-mail: [email protected].

(18)

ACKNOWLEDGMENT The CINES (Montpellier) is acknowledged

for allocation of computer resources (Project 6064). This work was supported by the French “Agence Nationale de la Recherche”, under Contract BLAN06-3_144027.

(19)

REFERENCES

(20)

(1) (2) (3)

(4)

(5)

(6)

(7)

(8)

(9)

Handbook of Zeolite Science and Technology; Auerbach, S. M., Carrado, K. A., Dutta, P. K., Eds.; Marcel Dekker: New York, 2003. Patarin, J.; Gies, H. Crystalline and Organized Porous Solids (thematic issue). C. R. Chim. 2005, 8. Flanigen, E. M.; Bennett, J. M.; Grose, R. W.; Cohen, J. P.; Patton, R. L.; Kirchner, R. M.; Smith, J. V. Silicalite, A New Hydrophobic Crystalline Silica Molecular-Sieve. Nature 1978, 271, 512–516. Guth, J.-L.; Kessler, H.; Wey, R. Studies in Surface Science Catalysis; Proceedings of the 7th International Zeolite Conference, Tokyo, Japan, 1986; Murakami, Y., Iijima, A., Ward, J. W., Eds.; Elsevier: Amsterdam, The Netherlands, 1986; pp 121-128. Stelzer, J.; Paulus, M.; Hunger, M.; Weitkamp, J. Hydrophobic Properties of All-Silica Zeolite Beta. Microporous Mesoporous Mater. 1998, 22, 1–8. Auerbach, S. M. Theory and Simulation of Jump Dynamics, Diffusion and Phase Equilibrium in Nanopores. Int. Rev. Phys. Chem. 2000, 19, 155–198. Fuchs, A. H.; Cheetham, A. K. Adsorption of Guest Molecules in Zeolitic Materials: Computational Aspects. J. Phys. Chem. B 2001, 105, 7375–7383. Smit, B.; Maesen, T. M. L. Molecular Simulations of Zeolites: Adsorption, Diffusion, And Shape Selectivity. Chem. Rev. 2008, 108, 4125–4184. Sauer, J.; Sierka, M. Combining Quantum Mechanics and Interatomic Potential Functions in Ab Initio Studies of Extended Systems. J. Comput. Chem. 2000, 21, 1470–1493.

r 2010 American Chemical Society

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

767

Desbiens, N.; Demachy, I.; Fuchs, A. H.; Kirsch-Rodeschini, H.; Soulard, M.; Patarin, J. Water Condensation in Hydrophobic Nanopores. Angew. Chem., Int. Ed. 2005, 44, 5310– 5313. Ramachandran, C. E.; Chempath, S.; Broadbelt, L. J.; Snurr, R. Q. Water Adsorption in Hydrophobic Nanopores: Monte Carlo Simulations of Water in Silicalite. Microporous Mesoporous Materials 2006, 90, 293–298. Bougeard, D.; Smirnov, K. S. Modelling Studies of Water in Crystalline Nanoporous Aluminosilicates. Phys. Chem. Chem. Phys. 2007, 9, 226–245. Puibasset, J.; Pellenq, R.J.-M. Grand Canonical Monte Carlo Simulation Study of Water Adsorption in Silicalite at 300 K. J. Phys. Chem. B 2008, 112, 6390–6397. Cailliez, F.; Tzrpit, M.; Soulard, M.; Demachy, I.; Boutin, A.; Patarin, J.; Fuchs, A. H. Thermodynamics of Water Intrusion in Nanoporous Hydrophobic Solids. Phys. Chem. Chem. Phys. 2008, 10, 4817–4826. Ball, P. Water As an Active Constituent in Cell Biology. Chem. Rev. 2008, 108, 74–108. Leroy, F.; Rousseau, B.; Fuchs, A. H. Self-Diffusion of n-Alkanes in Silicalite Using Molecular Dynamics Simulation: A Comparison between Rigid and Flexible Frameworks. Phys. Chem. Chem. Phys. 2004, 6, 775–783. Peverati, R.; Baldridge, K. K. Implementation and Performance of DFT-D with Respect to Basis Set and Functional for Study of Dispersion Interactions in Nanoscale Aromatic Hydrocarbons. J. Chem. Theory Comput. 2008, 4, 2030–2048. Hohenstein, E. G.; Chill, S. T.; Sherrill, C. D. Assessment of the Performance of the M05-2X and M06-2X Exchange-Correlation Functionals for Noncovalent Interactions in Biomolecules. J. Chem. Theory Comput. 2008, 4, 1996–2000. Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158–6170. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868. Becke, A. D. Density Functional Exchange Energy Approximation with Correct Asymptotic Behaviour. Phys. Rev. A 1998, 38, 3098–3100. Lee, C.; Yang, W.; Parr, R. G. Development of the ColleSalvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785–789. Adamo, C.; Barone, V. Exchange Functionals with Improved Long-Range Behavior and Adiabatic Connection Methods without Adjustable Parameters: The mPW and mPW1PW Models. J. Chem. Phys. 1998, 108, 664–675. Perdew, J. P.; Burke, K.; Wang, Y. Generalized Gradient Approximation for the Exchange-Correlation Hole of a Many-Electron System. Phys. Rev. B 1996, 54, 16533–16539. Boese, A. D.; Martin, J. M. L. Development of Density Functionals for Thermochemical Kinetics. J. Chem. Phys. 2004, 121, 3405–3416. Zhao, Y.; Schultz, N. E.; Truhlar, D. G. Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, And Noncovalent Interactions. J. Chem. Theory Comput. 2006, 2, 364–382. Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K. A Long-Range Correction Scheme for Generalized-Gradient-Approximation Exchange Functionals. J. Chem. Phys. 2001, 115, 3540–3544. Vydrov, O. A.; Heyd, J.; Krukau, A. V.; Scuseria, G. E. Importance of Short-Range versus Long-Range Hartree-Fock

DOI: 10.1021/jz100011p |J. Phys. Chem. Lett. 2010, 1, 763–768

pubs.acs.org/JPCL

(29)

(30)

(31)

(32)

(33)

(34)

(35)

(36)

Exchange for the Performance of Hybrid Density Functionals. J. Chem. Phys. 2006, 125, 74106. Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207–8215. Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787–1799. Becke, A. D. Density-Functional Thermochemistry. 5. Systematic Optimization of Exchange-Correlation Functionals. J. Chem. Phys. 1997, 107, 8554–8560. Shirono, K.; Daiguji, H. Molecular Simulation of the Phase Behavior of Water Confined in Silica Nanopores. J. Phys. Chem. C 2007, 111, 7938–7946. Zhao, Y.; Truhlar, D. G. Benchmark Data for Interactions in Zeolite Model Complexes and Their Use for Assessment and Validation of Electronic Structure Methods. J. Phys. Chem. C 2008, 112, 6860–6868. Olson, D. H.; Kokotailo, G. T.; Lawton, S. L.; Meier, W. M. Crystal-Structure and Structure-Related Properties of ZSM-5. J. Phys. Chem. 1981, 85, 2238–2243. Zhao, Y.; Truhlar, D. G. Density Functionals with Broad Applicability in Chemistry. Acc. Chem. Res. 2008, 41, 157– 167. Sato, T.; Tsuneda, T.; Hirao, K. Long-Range Corrected Density Functional Study on Weakly Bound Systems: Balanced Descriptions of Various Types of Molecular Interactions. J. Chem. Phys. 2007, 126, 234114.

r 2010 American Chemical Society

768

DOI: 10.1021/jz100011p |J. Phys. Chem. Lett. 2010, 1, 763–768