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J. Phys. Chem. B 2004, 108, 5930-5936
Ab Initio Molecular Dynamics Study of a Monomolecular Water Layer on Octahedral and Tetrahedral Kaolinite Surfaces Daniel Tunega,*,†,‡ Martin H. Gerzabek,† and Hans Lischka‡ Institute of Soil Research, UniVersity of Agricultural Sciences Vienna, Gregor-Mendel-Strasse 33, A-1180 Vienna, Austria, and Institute for Theoretical Chemistry and Structural Biology, UniVersity of Vienna, Wa¨hringerstrasse 17, A-1090 Vienna, Austria ReceiVed: October 15, 2003; In Final Form: February 3, 2004
The structure and dynamics of a monomolecular water layer on the octahedral and tetrahedral surfaces of the kaolinite layer have been investigated using short-time ab initio molecular dynamics. The arrangement and the structure of the water layer differ significantly on both surfaces. On the octahedral side the water layer forms relatively strong hydrogen bonds with the surface hydroxyl groups. This interaction significantly influences the layout of the water molecules in this case. On the other hand, the water molecules on the tetrahedral surface have the tendency to aggregate, forming hydrogen bonds among themselves. Only weak hydrogen bonds with the basal oxygen atoms of the tetrahedral surface are formed. Thus, the octahedral and tetrahedral surfaces of the kaolinite layer are of different chemical nature and can be considered as hydrophilic and hydrophobic, respectively.
Introduction Water-clay systems play a central role both in natural environments and for industrial production processes. Clays, as natural inorganic component of soils, significantly affect transport, distribution, and stability of dissolved organic/ inorganic species occurring in soil solutions. Among these species special attention is paid to toxically active compounds, such as radionuclides, heavy metals, or pesticides, because of their potential adverse effects on the ecosystem.1,2 Clays also found a lot of industrial applications. They are considered as effective storage materials for nuclear waste or as potential catalysts for refining processes used in the oil industry. Clays are also applied in the preparation of pigment dispersions used for paper coatings. All these applications are directly related to the physicochemical properties of clays such as swelling, wetting, adsorption, ion exchange, surface activity, etc. A unique feature is their capability to accommodate various molecular species in their interlayer spaces. This can lead to the preparation of new materials with specific properties. In many of the justmentioned processes, water plays a crucial role as a natural solvent and as a transport medium for chemical species. Thus, the understanding of the structure and chemistry of the waterclay interface is of the high importance. Computer simulation techniques offer detailed insight into interactions between water molecules and clay mineral surfaces at the molecular level. Because proper molecular models of water-clay systems require the consideration of a large number of particles, so far mainly classical molecular mechanics (MM), molecular dynamics (MD), and Monte Carlo (MC) methods based on empirical interatomic potentials have been performed on various water-clay models.3-17 In these studies, various types of empirical potentials have been used. The most critical * To whom correspondence should be addressed. E-mail: Daniel.Tunega@ univie.ac.at. † University of Agricultural Sciences Vienna. ‡ University of Vienna.
point is the determination of well-balanced parameter sets for the interactions between clay layer atoms and water molecules. These interactions are mainly of hydrogen bond nature and a considerable perturbation of the electronic structure of both subsystems (water and clay) at the interface is expected. Additionally, in the studies cited above,3-17 a rigid body approximation for either the water molecules or the layers has been used. Simulations with empirical parameters have at least two advantages. Because of the simplicity of the potential, long MD runs (several tenths or hundreds of picoseconds) can be performed, permitting the evaluation of, e.g., diffusion coefficients. Moreover, a supercell approach with several hundreds or thousands of atoms can be used what can diminish artificial effects of periodic boundaries. The simulations with empirical potentials require critical validation, especially from the point of view of the accuracy of the interatomic potential energy function or force field.18 An ab initio approach can be followed as alternative to conventional MD methods. This type of calculation is much more reliable and does not suffer from parameter-fitting problems. However, calculations are much more time-consuming. Thus, there are significantly more severe limits to the simulation time and model size in ab initio MD simulations. Nevertheless, periodic ab initio pseudopotential calculations have been used successfully in static simulations of talc-water and pyrophyllite-water systems.19 First principles MD simulations were applied in the study of water adsorption at the surface of muscovite mica20 and in the description of the interaction of a single water molecule with different surfaces of a kaolinite layer.21 Special cases in the clay mineral family are minerals with neutral layers such as talc, pyrophyllite, or kaolinite. Talc and pyrophyllite are minerals of the 2:1 class. This means that both layer surfaces are identical and formed from basal surface atoms. Unlike talc and pyrophyllite, kaolinite belongs to the 1:1 class having a dioctahedral layer structure and a chemical composition of Si2Al2O5(OH)4.22 Kaolinite layers are composed of two sheets connected via a common plane of oxygen atomssa tetrahedral
10.1021/jp037121g CCC: $27.50 © 2004 American Chemical Society Published on Web 04/21/2004
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Figure 1. Structure of a single kaolinite layer.
sheet consisting of SiO4 tetrahedra sharing corners and an octahedral sheet consisting of AlO6 octahedra sharing edges. Hydroxyl groups are an important structural feature of the kaolinite layersone-fourth of them are inner hydroxyl groups whereas the rest groups form one surface on the octahedral side of the layer. The second plane on the tetrahedral side is formed from basal oxygen atoms. These surface hydroxyl groups form hydrogen bonds with the basal oxygen atoms from the adjacent layer. Figure 1 shows the structure of a single kaolinite layer. Previous studies12,14,15 on the kaolinite-water systems used empirical potentials on models with water slabs of varying thickness confined between mineral layers. The dynamics of the interlayer water molecules in structures with 8.5 and 10 Å clay layer spacings was described in the work of Smirnov and Bougeard.12 Their models corresponded to halloysite, a natural hydrated polymorph of kaolinite. In the two other studies,14,15 extended interlayer spacings of several tens of Angstroms were used. Thus, these models actually represented external clay surfaces. The present work follows our recent investigations of adsorption sites on (001) surfaces of kaolin group minerals,21,23 where structural, energetic, and dynamic characteristics of the adsorbed isolated molecules (water, acetic acid, and acetate anion) on the (001) tetrahedral and octahedral surfaces of the kaolinite layer were presented. The formation of multiple hydrogen bonds between the investigated molecules and the octahedral surface was found whereas in the case of the tetrahedral side only very weak hydrogen bonds were observed. Corresponding interaction energies differ significantly for both surfaces as well. These previous investigations represent modeling of the gas-phase adsorption on the kaolinite mineral surfaces. In this work we want to present studies of models, which come closer to the liquid water phase-solid system. An ab initio molecular dynamics study is performed on models of monomolecular water layers adsorbed on both kaolinite surfaces (octahedral and tetrahedral) with the aim to determine their structure and to describe the short-time dynamics of the adsorbed water layers. Structural and Computational Details Kaolinite and dickite are typical representatives of the kaolinite group minerals. The only difference occurs in the layer stacking. The structure of an individual kaolinite layer (Figure 1) was briefly described in the Introduction. Two basal layer surfaces (octahedral and tetrahedral) are parallel to the crystallographic (001) surface and form the major part of the surface of crystal particles.24 The interlayer space in kaolinite and dickite is empty and the total charge of the layers is zero. As was found in our previous investigations,21,23 octahedral and tetrahedral holes in both basal surfaces are favorable interaction sites for adsorption of small polar molecules. In this study we used the same model for the kaolinite layer as previously,21 which is derived from the structure of the mineral dickite.25 The computational unit cell parameters were
a ) 10.376 Å, b ) 8.818 Å, c ) 26.400 Å, and β ) 96.7°, which leads to about 21 Å vacuum above the layer surface. Using the room temperature density of liquid water, one finds that nine water molecules are necessary to form a monomolecular thin film on the a × b surface of the kaolinite layer. These nine molecules were randomly distributed above the surface in both the octahedral and tetrahedral cases at an approximate distance from the surface, as obtained in our previous simulations.21 In the case of the tetrahedral surface, we expected stronger interference of the periodic boundary conditions on the redistribution of water molecules because of the stronger interaction among themselves in comparison to the weaker interaction with the periodic surface. Thus, additional MD simulations were performed using a supercell, where a and b unit cell parameters were doubled resulting in 36 molecules in the water layer. The calculations with the basic computational cell and nine water molecules are denominated KL(o)-WL for the kaolinite octahedral surface-water layer, KL(t)-WL for the kaolinite tetrahedral surface-water layer, and KLSC(t)-WL for the extended model of the tetrahedral surface with 36 water molecules. Fixed-volume ab initio molecular dynamics simulations were performed using the Vienna ab initio simulation package (VASP).26,27 In this approach an iterative solution of the KohnSham equations of density functional theory28 is performed on the basis of the minimization of the norm of the residual vector for each eigenstate and an efficient charge density mixing. For the exchange-correlation functional the localized density approximation (LDA) and the generalized gradient approximation (GGA) have been used. The LDA is parametrized according to Perdew-Zunger29 and the GGA according to Perdew-Wang.30 The calculations are performed in a plane-wave basis set using the projector-augmented wave (PAW) method31,32 and ultrasoft pseudo-potentials.33,34 The PAW method combines the advantage of the plane-wave basis set with the accuracy of the allelectron schemes. The Brillouin-zone sampling was restricted to the Γ point because the computational unit cell is sufficiently large. All simulations were performed using the plane-wave cutoff energy of 200 eV. Because the studied models are relatively complex, some preequilibration period of 10 ps was performed using a simulated annealing technique. The actual molecular dynamics simulations were run at 300 K. The canonical ensemble with the Nose´ thermostat procedure35 was used. The Verlet velocity algorithm36 with time step ∆t of 1 fs was chosen and a simulation time of 4 ps was used. The CPU time of the 4 ps MD was about 4 days using the parallel version of the VASP program on 8 processors of a Linux cluster equipped with AMD AthlonXP 1700+ processors. Results and Discussion A first insight into the microscopic structures can be gained by simply looking at snapshots obtained from the MD simulations. Figures 2-4 represent such snapshots of the three studied
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Figure 2. Representative snapshot of a MD simulation of the water layer on the octahedral kaolinite surface (KL(o)-WL model): (a) side view; (b) top view; (c) the same as (b) but just the water network and the surface hydroxyl groups are shown. The unit cell parameters (a, b) are also drawn.
models (KL(o)-WL, Figure 2; KL(t)-WL, Figure 3; KLSC(t)WL, Figure 4). Three different views of the models are given in each picture. Octahedral Surface. This kaolinite surface is formed from hydroxyl groups. These hydroxyl groups are very flexible, as has been found in the MD studies of the kaolinite and dickite minerals.37-39 This flexibility allows effective formation of hydrogen bonds with the polar molecules.21,23 It was also shown that these hydroxyl groups have amphoteric character. They are able to act as proton donors and/or acceptors, respectively. Moreover, the arrangement of these hydroxyl groups around octahedral holes allows the formation of multiple hydrogen bonds with polar functional groups of the adsorbed molecules. An adsorption energy of -14.7 kcal/mol was calculated for the single water molecule using a full static relaxation of all atomic positions and the same DFT approach (with an energy cutoff
Tunega et al.
Figure 3. Representative snapshot of a MD simulation of the water layer on the tetrahedral kaolinite surface (KL(t)-WL model): (a) side view; (b) top view; (c) the same as (b) but just the water network and the basal oxygen atoms are shown. The unit cell parameters (a, b) are also drawn.
350 eV). Three hydrogen bonds between one water molecule and the surface hydroxyl groups were observed. One of them (the strongest one with an average bond length of 1.621 Å) was formed between the water proton and the oxygen atom of one surface OH, whereas two others were formed between the water oxygen atom and the surface protons having bond lengths of more than 1.8 Å Figure 2 shows the arrangement of the monomolecular water layer above the octahedral surface. Two basic types of hydrogen bonds are formedsbetween the water molecules and the surface hydroxyl groups and mutual hydrogen bonds among water molecules only. The structural ordering of the water molecules in the layer results mainly from the effect of the hydrogen bonds formed between the water layer and the periodic surface. Similar to the case of adsorption of a single H2O molecule, two types
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Figure 5. Distribution of hydrogen bonds formed during the MD simulation of the KL(o)-WL model.
Figure 4. Representative snapshot of MD simulation of the water layer on the tetrahedral kaolinite surfacesthe extended model, KLSC(t)WL: (a) side view; (b) top view; (c) the same as (b) but just the water network and the basal oxygen atoms are shown. The unit cell parameters (a, b) are also drawn.
of hydrogen bonds are distinguished between the water layer and the octahedral surfacesin the first case the water molecules act as proton donors to the surface OH groups whereas in the second case some surface OH groups are proton donors to the water oxygen atoms. Figure 5 shows the total distribution curve for all hydrogen bonds formed and its decomposition into the three components representing three types of hydrogen bonds. In contrast to the single water case, the difference between the two types of the hydrogen bonds formed between the water layer and the octahedral surface is not so pronounced. The main reason is found in the mutual interactions among water molecules themselves. The peak maximum for the Osurf‚‚‚Hw curve is about 1.9 Å whereas for the Ow‚‚‚Hsurf curve it is about 2.0 Å. The peak maximum for hydrogen bonds formed within the water layer is somewhere located between these two values.
The averaged number of hydrogen bonds per water molecule is 2.5. All surface hydroxyl groups are involved in the hydrogen bond formation either as proton donors or acceptors. The hydrogen bonds among water molecules cause an additional reorientation. Although the water layer forms relatively strong hydrogen bonds with the octahedral surface, water molecules are not firmly sticking to the surface at one fixed place. Mutual interactions and the thermal energy affect motions of water molecules above the surface. Analysis of the MD simulation showed that hydrogen bonds are breaking and re-forming and some molecules are able to diffuse within the layer. Figure 6 presents for each type of the hydrogen bond the time evolution of selected intermolecular O‚‚‚H distances belonging to two different oxygen-hydrogen pairs. These oxygen-hydrogen pairs are different for each type of hydrogen bonding. These particular examples have been chosen to demonstrate different situations in the dynamics of the system. One can see the formation and the breaking of hydrogen bonds (dotted lines) in the middle and in the bottom graphs (Figure 6b,c) due to translational and large-amplitude rotational motions. Relatively large fluctuations for the strongest type of the hydrogen bonds between surface oxygen and water hydrogen atoms (Figure 6a) are noted as well. The structural ordering of the water layer on the octahedral surface is illustrated in Figures 7 and 8. Figure 7a shows the one-dimensional densities of the z coordinates of all oxygen and hydrogen atoms in the KL(o)-WL system from the 4 ps MD simulation (the averaged plane of Si atoms is placed in the xy plane having z ) 0). A distinct and relatively narrow peak around 6.5 Å of the water oxygen atoms is observed, signifying a stable position of the water layer with respect to the octahedral surface. The shoulder observed above 7 Å represents one interesting phenomenon. One can see in the snapshot in Figure 2 that one water molecule is located above the water layer. During the thermal equilibration period one molecule was displaced from the first water layer. In the 4 ps MD run, this molecule was observed to diffuse back into the water layer and to replace another molecule, which diffuses above the water layer (the dotted line in Figure 6c includes such a process). The aforementioned shoulder in Figure 7 corresponds to such a displaced molecule. This molecule will be a member of the
5934 J. Phys. Chem. B, Vol. 108, No. 19, 2004
Figure 6. Time evolution of selected O‚‚‚H interatomic distances for the KL(o)-WL model. Solid and dotted lines correspond to two selected intermolecular O‚‚‚H distances belonging to two different oxygenhydrogen pairs.
Figure 7. One-dimensional profiles of z-coordinate distributions of oxygen and hydrogen atoms: (a) KL(o)-WL model; (b) single water molecule adsorbed on the octahedral surface.
second nearest water layer above the octahedral surface. From the fact that one water is leaving the first water layer, one can conclude that the density in the water layer closest to the surface is less than that in bulk water. The distribution curve of the
Tunega et al.
Figure 8. Distribution of the angle between the intraatomic HH vector of water and the z-coordinate: (a) KL(o)-WL and KL(t)-WL models; (b) single water cases.
hydrogen atoms (dotted line in Figure 7a) gives additional information on the distribution of the adsorbed water molecules. One, clear and narrow peak at around 5.7 Å corresponds to hydrogen atoms of water involved in the strongest hydrogen bonds, as described above. The second, less regular and broader peak, which almost overlaps with the water oxygen atom peak, corresponds to the hydrogen atoms involved in weaker hydrogen bonds formed within the water layer. A similar shoulder as in the case of the water oxygen atoms is observed also for the hydrogen atoms corresponding to the displaced water molecule. The aforementioned overlap of the oxygen and hydrogen distribution functions means that the water-water interactions orient part of the molecules in such way that their H-O-H plane is almost parallel to the surface. This conclusion also supports Figure 8 where the distribution of the angle between the HH interatomic vector within a water molecule and the z axis is presented. The solid curve refers to the KL(o)-WL system. One can see three dominant peaks for the KL(o)-WL system. The central peak has a maximum at around 80° and corresponds to the water molecules having the HH vector parallel to the surface. Two other peaks (around 20° and 120°) can be assigned to two other types of the water molecules: to those involved in the strongest hydrogen bonds and/or to the one displaced from the water layer. For comparison, the distribution curves of water obtained from the simulation of the single molecule adsorption21 are also presented in Figures 7b and 8b. One observes narrow regular peaks indicating a strong fixation of the single water molecule to the octahedral surface as opposed to the much broader peaks derived from the water layer calculation. Tetrahedral Surface. From our previous MD simulation21 of a single water molecule on the tetrahedral surface we concluded that the water molecule only weakly interacted with this surface. The water molecule performed a slow rotational movement above the ditrigonal hole in the tetrahedral sheet accompanied with breaking and forming weak hydrogen bonds with the basal oxygen atoms surrounding the ditrigonal hole.
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Figure 9. Distribution of hydrogen bond distances formed during the MD simulation of the KL(t)-WL model.
Static relaxation showed that the plane of the water molecule is practically perpendicular to the layer surface and the water hydrogen atoms point toward the basal oxygen atoms of this surface at distances larger than 2.8 Å. The calculated interaction energy was -4.1 kcal/mol. The snapshots presented in Figures 3 and 4 show the distribution of the water layer on the tetrahedral surface after 4 ps MD for the KL(t)-WL and the extended KLSC(t)-WL models. The distribution of molecules differs significantly from what was observed on the octahedral surface. No noticeable ordering like in the previous case is found. The water molecules show the tendency to associate and form molecular water clusters because hydrogen bonds formed among water molecules prevail over the weak hydrogen bonds formed between the water layer and the tetrahedral surface. These latter hydrogen bonds are formed and broken during the rotational-translational movement of the water molecules within the water molecular layer. Figure 9 displays the distribution curves of all hydrogen bonds formed for the KL(t)-WL model and also its decomposition into the two components for the interactions within the water layer and between the water layer and the tetrahedral surface. The difference between both types is evident. The first type corresponds to “classical” hydrogen bonds such as in liquid water with a maximum at about 1.9 Å. The second type is characterized by a very broad peak with the maximum at about 2.2 Å and corresponds to the weak interactions of the water hydrogen atoms and the basal oxygen atoms of the tetrahedral surface. The total averaged number of hydrogen bonds per water molecule is nearly 2 but only about 10% of this value corresponds to the weak hydrogen bonds between the water layer and the tetrahedral surface. The structural ordering of the water layer on the tetrahedral surface is presented in Figure 10 by one-dimensional densities of z coordinates of all oxygen and hydrogen atoms. The upper graph (a) corresponds to the KL(o)-WL model and the bottom one (b) to the KLSC(t)-WL, respectively. As in the case of the octahedral layer, the averaged plane of Si atoms is chosen as the xy plane with z ) 0. The comparison of the distribution curves for the hydrogen and the oxygen atoms in both graphs in Figure 10 shows only minor differences. Thus, the periodic
Figure 10. One-dimensional profiles of z-coordinate of oxygen and hydrogen atoms: (a) KL(o)-WL model; (b) KLSC(t)-WL model.
Figure 11. Mean square displacements of the center-of-mass of water molecules averaged over their number.
boundary conditions do not significantly affect the global picture of the water layer distribution on the tetrahedral surface. Both the peaks of the water oxygen and hydrogen atoms are broader than those peaks for the water atoms on the octahedral surface (Figure 7). This distribution corresponds to the formation of molecular aggregates on the surface, as was observed in Figures 3 and 4. The shape of both broad peaks does not indicate any significant preferential orientation of the water molecules with respect to the tetrahedral surface. This is also supported by the distribution curve of the angle between the HH water interatomic vector and the z axis in Figure 8a (dotted line). Information about the dynamics of the system can also be obtained from the self-diffusion coefficient D. It has been computed from the time-averaged mean square displacements of the center-of-mass (CoM) of all molecules also averaged over the number of molecules. Unfortunately, values of self-diffusion coefficients computed from relatively short MD runs are of substantial uncertainity.12,40 Thus, our computed values present
5936 J. Phys. Chem. B, Vol. 108, No. 19, 2004 only rough estimates. The mean square displacements for both surfaces as function of time and their fits by a linear regression are given in Figure 11. Calculated diffusion coefficients are (8.314 ( 0.003) × 10-11 m2 s-1 for the octahedral and (6.478 ( 0.005) × 10-11 m2 s-1 for the tetrahedral side, respectively. The regression coefficient R was 0.999 in both cases. These values are in quite good agreement with the value of 9.63 × 10-11 m2 s-1 obtained from the much longer classical MD simulation (100 ps) of the water slab confined between the kaolinite layers.14 The calculated averaged values for both surfaces are lower by about 2 orders of magnitude than the experimental41 (2.4 × 10-9 m2 s-1) or calculated40 (1.3 × 10-9 m2 s-1, BLYP functional) value of the bulk water. It reflects the markedly slower movement and certain ordering of the water molecules in the vicinity of both surfaces. It is certainly unexpected that the diffusion coefficient of water on the tetrahedral surface is of the same magnitude as the coefficient on the octahedral surface. Conclusions The structure and short-time dynamics of a monomolecular water slab on the octahedral and tetrahedral surfaces of a kaolinite layer were studied by means of ab initio molecular dynamics simulations. A significantly different behavior of the water molecules was observed for the two surface types. The water layer on the octahedral surface is well structured and has the tendency to form the maximum number of hydrogen bonds with the surface hydroxyl groups. The water molecules form also hydrogen bonds among themselves. These interactions competing with those to the surface lead to a certain disorder to the water coverage on the octahedral surface. On the other hand, the results obtained for the tetrahedral surface showed that in this case the water layer has only a weak contact with basal oxygen atoms of the tetrahedral surface and exhibits, therefore, the tendency to form water clusters with typical hydrogen bonds among water molecules. In both cases, the computed self-diffusion coefficients are significantly lower than in the bulk water. Our results are in contrast to conclusions of Smirnov and Bougeard.12 On the basis of classical MD simulations, they concluded that water molecules are only weakly interacting with the octahedral surface hydroxyl groups and strongly interacting with the basal oxygen atoms. These results were caused by the use of the same empirical potential parameters for the basal oxygen atoms and the oxygen atoms from the octahedral surface hydroxyl groups, neglecting the different chemical character of both types of oxygen atoms. This case clearly demonstrates that empirical force fields have to be applied with great care, especially when force field parameters are not refined for a particular case. The presented results confirmed our previous conclusions21,23 on the different chemical nature of both kaolinite surfaces labeled as hydrophilic (octahedral) and hydrophobic (tetrahedral), respectively.
Tunega et al. Acknowledgment. This work was supported by the Austrian Science Fund, project no. P15051-CHE. We are grateful for technical support and computer time at the Linux-PC cluster Schro¨dinger I of the computer center of the University of Vienna. References and Notes (1) Rae, J.; Parker, A. In EnViromental interactions of clays; Rae, J., Parker, A., Eds.; Springer-Verlag: Berlin, 1988. (2) Schachtschabel, P.; Blume, H. P.; Bru¨mmer, G.; Hartge, K.-H.; Schwertmann, U. Lehrbuch der Bodenkunde; Ferdinand Enke Verlag: Stuttgart, 1989. (3) Skipper, N. T.; Refson, K.; McConnell, J. D. C. J. Chem. Phys. 1991, 94, 7434. (4) Delville, A.; Sokolowski, S. J. Phys. Chem. 1993, 97, 6261. (5) Delville, A. J. Phys. Chem. 1995, 99, 2033. (6) Boek, E. S.; Coveney, P. V.; Skipper, N. T. Langmuir 1995, 11, 4629. (7) Bridgeman, C. H.; Skipper, N. T. J. Phys. Condens.-Mater. 1997, 9, 4081. (8) DeSiqueira, A. V. C.; Skipper, N. T.; Coveney, P. V. Mol. Phys. 1997, 92, 1. (9) DeSiqueira, A. V. C.; Skipper, N. T.; Coveney, P. V. Mol. Phys. 1998, 95, 123. (10) Skipper, N. T. Mineral. Magn. 1998, 62, 657. (11) Greathouse, J.; Sposito, G. J. Phys. Chem. B 1998, 102, 2406. (12) Smirnov, K. S.; Bougeard, D. J. Phys. Chem. B 1999, 103, 5266. (13) Shroll, R. M.; Smith, D. E. J. Chem. Phys. 1999, 111, 9025. (14) Warne, M. R.; Allan, N. L., Cosgrove, T. Phys. Chem. Chem. Phys. 2000, 2, 3663. (15) Hwang, S.; Blanco, M.; Demiralp, E.; Cagin, T.; Goddard, W. A., III. J. Phys. Chem. B 2001, 105, 4122. (16) Hensen, E. J. M.; Smit, B. J. Phys. Chem. B 2002, 106, 12664. (17) Marry, V.; Turq, P. J. Phys. Chem. B 2003, 107, 1832. (18) Van Gunsteren, W. F.; Mark, A. E. J. Chem. Phys. 1998, 108, 6109. (19) Bridgeman, C. H.; Buckingham, A. D.; Skipper, N. T.; Payne, M. C. Mol. Phys. 1996, 89, 879. (20) Odelius, M.; Bernasconi, M.; Parrinello, M. Phys. ReV. Lett. 2000, 78, 2855. (21) Tunega, D.; Benco, L.; Haberhauer, G.; Gerzabek, M. H.; Lischka, H. J. Phys. Chem. B 2002, 106, 11515. (22) Bailey, S. W. Structures of layered silicates. In Crystal structures of clay minerals and their X-ray identification; Brindley, G. W., Brown, G., Eds.; Mineralogical Society: London, 1980. (23) Tunega, D.; Haberhauer, G.; Gerzabek, M. H.; Lischka, H. Langmuir 2002, 18, 139. (24) Zbik, M.; Smart, R. St. C. Clays Clay Miner. 1998, 46, 153. (25) Joswig, W.; Drits, V. A. N. Jb. Miner. Mh. 1986, 19. (26) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. (27) Kresse, G.; Furthmu¨lleer, J. J. Comput. Mater. Sci. 1996, 6, 15. (28) Jones, R. O.; Gunnarsson, O. ReV. Mod. Phys. 1989, 61, 689. (29) Perdew, J. P.; Zunger, A. Phys. ReV. B 1981, 23, 548. (30) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (31) Blo¨chl, P.; Parrinello, M. Phys. ReV. B 1992, 45, 9413. (32) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (33) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (34) Kresse, G.; Hafner, J. J. Phys. Condens. Matter 1994, 6, 8245. (35) Nose´, S. J. Chem. Phys. 1984, 81, 511. (36) Ferrario, M.; Ryckaert, J. P. Mol. Phys. 1985, 54, 587. (37) Benco, L.; Tunega, D.; Hafner, J.; Lischka H. Chem. Phys. Lett. 2001, 333, 479. (38) Benco, L.; Tunega, D.; Hafner, J.; Lischka, H. J. Phys. Chem. B 2001, 105, 10812. (39) Benco, L.; Tunega, D.; Hafner, J.; Lischka, H. Am. Mineral. 2001, 86, 1057. (40) Sprik, M.; Hutter, J.; Parrinello, M. J. Chem. Phys. 1996, 105, 1142. (41) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926.
