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Water Adsorption at a Sodium Smectite Clay Surface: an Ab Initio Study of the First Stage Pascal Clausen,†,‡ Wanda Andreoni,*,§,| Alessandro Curioni,§ Eric Hughes,‡ and Christopher J. G. Plummer† Laboratoire de Technologie des Composites et Polyme`res (LTC), Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), 1015 Lausanne, Switzerland, Nestle´ Research Center, Vers-Chez-Les-Blanc, 1000 Lausanne 26, Switzerland, IBM Research GmbH, Zurich Research Laboratory, 8803 Ru¨schlikon, Switzerland, and Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland ReceiVed: February 8, 2009; ReVised Manuscript ReceiVed: May 31, 2009
Using calculations based on density-functional theory, we explore the configurations that water molecules (2,3,4;6) assume on the surface a sodium 2:1 smectite clay with isomorphic substitutions both on octahedral and tetrahedral sheets. The hydrophilicity of the surface is inhomogeneous, depending on the specific location of the counterions and of the cation replacements in the siloxane rings. The counterion does not complete the first hydration shell. Adsorption may occur in the form of coexisting monomers, dimers, and trimers, but at the level of six molecules, a water ring bound to two sodium ions becomes the most stable configuration. This structural transition observed for the adsorbate can be seen as marking the onset of the formation of water networks on the clay surface. I. Introduction Natural and synthetic clays are crucial in diverse areas of science, from geophysics to environmental chemistry and materials science, and in a wide range of applications, from construction to catalysis to nuclear waste disposal to petroleum extraction to drug and agrochemical delivery (see, e.g., refs 1-5). There is no doubt that understanding the physical chemistry of most clay materials implies understanding their interaction with water.6 Swelling of clays like smectites and vermiculites, for example, is a well-known phenomenon that strongly affects their behavior and is determined by the joint action of water and the charge-compensating counterions. In the attempt to master the physical chemistry of such complex systems and especially to characterize the structure and dynamics of water, counterions, and other guest atoms or molecules in the interlayer regions, computational physics and chemistry methods have recently started to play an important role (see, e.g., refs 7-11 and refs 12 and 13 for comprehensive reviews up to 2006). However to assess the accuracy of any simulation method, a substantial effort appears mandatory. Some progress has recently been reported, in particular for the validation of classical force fields (see, e.g., refs 14 and 15). A quantitative description is far from trivial because various interactions come into play in determining the adsorption (and desorption) of water: water-cation, water-clay substrate, cation-cation, water-water, and cation-substrate. In order to be able control their influence, one should first elucidate their relative role. As an initial step in this direction, in the present paper, we investigate the first stage of adsorption. It corresponds to a few water molecules interacting with the exposed surface of a dry smectite clay model. This includes sodium as chargecompensating cations and isomorphic substitutions in both * To whom correspondence should be addressed. † EPFL. ‡ Nestle´ Research Center. § IBM Research GmbH. | CECAM, Ecole Polytechnique Fédérale de Lausanne.
tetrahedral and octahedral layers, thus allowing us to identify and quantitatively distinguish the relevant interactions. The atomistic model we adopt here for the adsorbant was built up and tested in a precedent paper16 for the calculation of the structural properties of pyrophyllite, and used to study the adsorption of individual molecules of a few volatiles, including water. Specifically we use a slab, generated from a periodically repeated supercell of relatively large size (164 atoms), and apply density-functional theory (DFT)17 as implemented in the generalized gradient approximation (GGA) of the exchangecorrelation functional, in the frame of pseudopotentials and plane wave basis set. In section 2, we recall the basic features of the structural model and of the method (for more details, we refer the reader to ref 16). In section 3, after briefly summarizing our most relevant findings for the monomer adsorption, we will present and discuss the results we have obtained for two, three, four, and six molecules. Conclusions are drawn in section 4. II. Smectite Clay Model and Method As described in detail in ref 16, the reference smectite clay is Kunipia-F montmorillonite clay, which some of us have investigated experimentally in ref 18, with all Fe atoms replaced by Al. In the absence of crystallographic data for it, the initial model structure we built originated from pyrophyllite with substitution of silicon atoms by aluminum in the tetrahedral sheets and of aluminum atoms with magnesium in the octahedral sheet. The atoms to be replaced were chosen randomly with the only constraint that they were not located in neighboring positions. Our model thus corresponds to the chemical formula (Si3.875Al0.125)O10(OH)2Mg0.375Al1.625) and has sodium counterions. The net charge is -0.5e. To represent the clay surface, we considered a periodically repeated slab; the unit cell was derived from the 221 supercell of pyrophyllite (optimized within our scheme) with ion substitution and counterions (as mentioned above). The lattice param-
10.1021/jp901162s CCC: $40.75 2009 American Chemical Society Published on Web 08/05/2009
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Figure 1. Our clay model with Na counterions, with the substitutional atoms explicitly indicated. (a) Side and (b) top views of all types of hexagonal rings are shown from A to F; A, B, and C refer to the T-layer, D, E, and F to the O-layer; (c) and (d): detailed top view of the rings with a Na counterion. In the tetrahedral sheet, one of the Si atoms in the ring is substituted by Al (AlT); in the octahedral site three Al atoms are substituted by Mg. Oxygen, hydrogen, silicon, and aluminum atoms are represented by red, white, orange, and blue spheres, respectively. In (b) the white dashed lines delimit the unit cell considered in our calculations. From ref 16.
eters then are a ) 10.32 Å, b ) 17.932 Å, whereas c ) 25 Å was chosen to minimize the interaction between periodically repeated images. The geometrical characteristics of the model were optimized in ref 16, where we also studied the case of unimolecular adsorption of a few volatiles, including water. In particular, the sodium counterions were initially positioned by taking into account the location of the basal oxygen atoms with higher negative Mulliken charges and according to homogeneity considerations. Then we performed ultrashort Car-Parrinello molecular dynamics runs of the adsorbent system, and a few structures corresponding to energy minima in the trajectory were selected for geometry optimization. For the initial configuration of the dry adsorbent for the study of adsorption, we chose the one with lowest energy. The clay surface is shown in Figure 1, which is borrowed from ref 16 and in particular gives the nomenclature of the local domains A through F that will henceforth be used. The C and D rings do not contain a counterion. Note that about one in thirty surface silicon atoms is replaced by an aluminum atom. As a result, less than one-fifth of the surface hexagonal rings (types A and B) are affected by the aluminum replacement. Therefore, domains E and F can be considered as better representatives of the real clay surface. To simplify the notation, also the corresponding sodium sites are denoted by A to F. Note further that the ratio of the substituent atoms AlT:Mg is 1:3, so
that an octahedral sheet is more negatively charged than a tetrahedral one. The method we adopted is DFT in the pseudopotential-plane wave approach as implemented in the CPMD software,19 with the Perdew-Burke-Ernzerhof20 approximation for the exchangecorrelation functional, norm-conserving pseudopotentials21 and a 100 Ry cutoff for the plane wave expansion of the k ) 0 electron Bloch wave functions. Convergence tests were reported in ref 16. The accuracy of our computational scheme was confirmed there by comparing the calculated values for structural properties of the reference pyrophyllite and structural/electronic characteristics of relevant molecular systems with experimental results. In Appendix A of the present paper, we also report the results obtained for those gas-phase Na-water clusters for which experimental data were available. We also note that the PBE approximation has been demonstrated to describe rather accurately the physical properties of water22 and other hydrogenbonded systems.23 The calculations we present in this paper refer to the adsorption of two to six molecules of water. Most of them are from geometry optimization runs starting from a number of initial configurations of the water molecules that have at least one water molecule bound to a sodium counterion and without keeping any of the atomic positions fixed. The threshold for the largest off-diagonal component of the energy gradient was
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TABLE 1: Single Water Molecule Adsorptiona Na-Ob position
configuration
B.E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Na-T plane (Å)
EL (kJ/mol)
CN(1)
CN(2)
A
a b c d a b c a b a b
54 53 51 46 60 52 49 46 45 45 44
2.30 2.27 2.29 2.26 2.27 2.275 2.30 2.28 2.30 2.28 2.30
2.12 2.495 2.44 2.01 1.90 >3 2.42 >3 2.47 >3 2.53
1.58 [0.29] 1.52 [0.23] 1.56 [0.26] 1.54 [0.24] 1.57 [0.28] 1.50 [0.21] 1.63 [0.34] 1.17 [0.24] 1.24 [0.32] 1.14 [0.21] 1.185[0.26]
6 3 4 6 7 3 6 3 5 3 4
3 3 3 3 3 3 3 3 3 3 3
2 2 2 3 2 1 1 3 3 3 3
B E F
a Binding energies (B.E.), “deformation” energy EL, and distances: sodium to water, closest water to basal oxygen Ob, and sodium to the silicon plane (with the deviation from the corresponding value on the dry surface, given in square brackets) (from ref 16). CN(i) denotes the Na-Ob coordination numbers in the ith shell (see text).
10-4 a.u.. To further explore probable molecular configurations on the complicated surface of the clay and their stability, in some cases we also ran ultrashort DFT (Car-Parrinello) molecular dynamics24 in the canonical ensemble. The duration of these simulations after equilibration was 1.5 and 0.67 ps for 4 and 6 molecules respectively. A time step of 0.073 fs was used throughout. III. Results and Discussion In ref 16 we determined the adsorption sites and binding energies of one water molecule on the dry surface of the same clay model as we consider here. In Table 1 we summarize the main results, which will be used as reference in the following. The C and D domains in Figure 1 do not contain a counterion and are not hydrophilic. Therefore they will not be considered further. The structural characteristics in Table 1 describe the various configurations (ordered according to their binding energy) at each site, in a rather exhaustive manner. The water monomer mainly interacts via oxygen with the sodium counterion on the surface that moves away from the clay surface; the Na-Ow distance (∼2.3 Å) is fairly independent of the specific orientation of the molecule. Hydrogen bonds can also form with the basal oxygen atoms (Hw-Ob distance 3 1.955 2.76 2.23 2.305
a The single molecule configurations refer to Table 1. Simple notation A or B corresponds to cases when the configuration of molecule [2] turned out to be different from those given in Table 1. Binding energy (B.E.), reference configuration of single-molecule adsorption, and binding energy (b.e.) of the additional molecule. Adsorbant “deformation” energy EL; closest distances between sodium and silicon (T) plane, sodium and water oxygen Ow, and hydrogen water Hw and basal oxygen Ob, and sodium-basal oxygen Ob coordination numbers. Note that in A-2b, an H-bond (1.934 Å) exists between the water molecules.
Figure 3. Three water molecules around one counterion. (a) A[B]-R1 and (b) E-β. Colors as in Figure 1. The yellow dashed lines denote hydrogen bonds.
water molecule is the one with binding to the basal oxygen atom linked to the (replacing) aluminum in the tetrahedral sheet. This is present in the B-2a configuration (Figure 2a), to which the highest binding energy for the two-molecule system pertains. In each of the six structures reported in Table 2B, one can still recognize at least one of the single-molecule adsorption configurations in Table 1 (see also Figure 2b). Therefore, taking this one as reference ([1] in Table 2B), we evaluated the incremental binding energy (b.e.), which in all cases turns out to be by about 10 kJ/mol lower than the single-molecule B.E. The structural characteristics and in particular the changes induced by water adsorption on the clay surface are given in Table 2C. When comparing with Table 1, the latter have become more significant, with Na progressively moving away from the surface, and thus involve much larger EL values.
B. Three Water Molecules at One Sodium Site. Here we position three molecules at each of the four sites of the counterion and let the coordinates relax to close energy minima. The results are reported in Table 3. Positions A and B continue to be more favorable than E and F by at least 10 kJ/mol. Two different types of configurations (R and β) were found. In R (Figure 3a), the three molecules are bound to the cation and form hydrogen bonds with three different basal oxygen atoms, of which two belong to the same hexagonal silicon-oxygen structure and the other to an adjacent one (belonging to the domain of a different ion position as indicated in square brackets). This type of configuration was observed for all four different cation positions A through F. A[B]-R1 has a higher binding energy than the others because one of the water molecules forms a hydrogen bond with a basal oxygen atom linked to the (replacing) aluminum atom (Figure 3a) (see B-a in Table 1). In β (Figure 3b), the adsorbate is a trimer in which one molecule forms an H-bond with a basal oxygen and one is farther from the counterion than the others (2.5-2.6 Å). The values of the binding energies show that the intermolecular interaction starts to be competitive with that with the surface. As expected, the energy loss EL due the structural changes of the substrate induced by water adsorption increases. Correspondingly, Na moves further away from the surface as measured by the distance from the T-plane or by that from Al in the case of the A and B rings. For the β-configurations, the sodium-to-silicon-plane distance is shorter than for the R-configurations, corresponding to the much weaker binding of the third molecule.
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TABLE 3: Three Water Molecules Adsorption Part Aa
site
conf.
B.E. (kJ/mol)
A[B]
R1 R2 R1 R2 β R1 R2 β R1 R2
156 130 143 140 135 123 117 118 120 118
B[A] B E[F] E F[E]
Hw-Ob (Å)
Na-Ow (Å)
Hw-Ow (Å)
[1]
[2]
[3]
[1]
[2]
[3]
2.24 2.22 2.29 2.24 2.34 2.25 2.255 2.32 2.24 2.27
2.29 2.25 2.30 2.25 2.41 2.27 2.27 2.37 2.26 2.29
2.29 2.47 2.45 2.30 2.50 2.31 2.31 2.57 2.30 2.30
1.77 1.78 1.83 1.75 1.80 1.87 1.89 1.78 1.90 1.78
1.86 1.85 1.95 1.86 >3 1.86 1.92 >3 1.91 1.945
1.91 2.01 2.095 1.88 >3 1.91 1.97 >3 1.94 1.98
[1-2]
[2-3]
1.96
2.05
1.95
1.98
Part Bb Na-Ob site
conf.
EL (kJ/mol)
Na-T plane (Å)
A[B]
R1 R2 R1 R2 β R1 R2 β R1 R2
97 137 86 121 40 116 113 62 138 113
2.89 2.87 2.715 2.93 2.28 2.83 2.805 2.19 3.02 2.72
B[A] B E[F] E F[E]
Na-Al (Å) 3.33[0.10] 5.07[1.84] 3.09[0.01] 4.46[1.38] 3.03[-0.05]
CN(1) 2 2 2 2 2 1 1 2 2 1
CN(2) 0 0 0 0 1 1 1 1 0 0
a Binding energies, closest water to sodium, water to basal oxygen, and water to water distances. X[Y] indicates that one of the water molecule at X is H-bonded to an Ob of the Y ring. b “Deformation” energy EL, sodium distances to T-plane and aluminum, and sodium-basal oxygen coordination numbers. The changes with respect to the dry substrate are given in square brackets.
C. Four Water Molecules. Most of the findings in Table 4 correspond to geometry optimization started from a cluster of molecules located around one cation, except for the E&F configuration, which resulted from quenching from a trajectory obtained with Car-Parrinello molecular dynamics at 400 K. Although not exhaustive, our search for low-energy configurations has allowed us to identify the three most relevant types, depending on the number of molecules directly bound to the counterions, namely, four (Table 4A), three (Table 4B), and two (Table 4C). The presence of an aluminum replacement in the tetrahedral sheet continues to render A more hydrophilic than F. The competing role of the surface (counterions and basal oxygens) and the water-water interaction in attracting water molecules clearly emerges from inspection of Table 4 and Figure 4. The two water arrangements in A are clearly different but are degenerate within the accuracy of the calculations. Indeed in A[B] (Figure 4a), four monomers are adsorbed separately, with three of them being H-bonded to the basal oxygen atoms (two bound to Al), whereas in A (Figure 4b) the adsorbate can be described as three (distant) molecules bound to both the counterion and to an extra off-plane molecule. By contrast, the three configurations we calculated on the F domain differ significantly in the binding energy. In both F[E]a and F[E]b, one molecule is also relatively close to the E site (2.5 Å). However, the two structures are quite different: Water is adsorbed in the form of a dimer and two monomers in F[E]a (Figure 4c) and in the form of four monomers in F[E]b; the latter is similar to the case of A[B] but with weaker H-bonds to the surface as reflected in the large energy difference (∼30 kJ/mol). In F (Figure 4d), one can recognize a monomer and a trimer, with the latter having only one molecule connected to the surface and one acting as bridge between the molecules bound to the counterion. Interestingly, the case of two dimers
Figure 4. Four-molecule adsorbate configurations: (a) A[B], (b) A, (c) F[E]-a, (d) F[E]-b, (e) F, and (f) E&F. Colors as in Figure 1. The yellow dashed lines denote hydrogen bonds.
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TABLE 4: Four Water Molecules Adsorptiona: (A) Four Molecules Bound to One Counterion; (B) Three Molecules Bound to One Counterion; (C) Two-Site Adsorption; (D) Sodium to T-Plane Distance in Å and Na-Ob Coordination Numbers (CN(1); CN(2)) Part A site config.
B.E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Hw-Ow (Å)
A[B] F[E]a F[E]b
184 171 153
2.235, 2.25, 2.32, 2.37 2.29, 2.28, 2.39, 2.42 2.245; 2.33; 2.35; 2.36
1.695, 1.78, 1.835 1.90, 1.93, 1.99, 2.15; (2.71) 1.83; 2.01; 2.105; 2.42; 2.44
1.97
Part B site
B.E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Hw-Ow (Å)
A F
180 164
2.33; 2.35; 2.44 2.27; 2.27; 2.33
1.895; 2.525 1.78; 1.89; (2.71)
1.82; 1.91; 2.02 1.725; 1.83
Part Cb site config.
B.E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Hw-Ow (Å)
159
2.32;2.27
>2.6
1.81 [E]; 1.83 [F]
E&F Part D A[B]
F[E]a
F[E]b
A
F
E&F
3.88 0;0
3.07 1;0
3.26 0;1
2.295 1;2
2.80 1;1
1.16 (E); 1.24 (F) 3; 3 (E); 3;3 (F)
a Binding energies (B.E.), closest sodium to water, water to basal oxygen, and water to water distances. X[Y] indicates that one of the water molecules on X is H-bonded to a basal oxygen atom of the Y ring. Na-Ow data refer to the Na on the X site. b Each dimer is bound to one separate site.
Figure 5. Six-water-molecules adsorbates. Correspondence to Table 5 is as follows: (a) A[B], (b) F[E], (c) F, (d) E&F. Details as in Figure 2.
separately adsorbed on the E and F domains (Figure 4e) (Ow-Ow distance of ∼3.6 Å) is also an energetically competitive configuration.
The structural changes induced by the four-molecule adsorption localized at a specific domain are significant. As expected, the
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TABLE 5: Six Water Molecules Adsorptiona: (A) Six Molecules Bound to One Counterion; (B) Three Molecules Bound to One Counterion; (C) Two-Site Adsorption (Water Hexamer); (D) Sodium to T-Plane Distance in Å and Na-Ob Coordination Numbers (CN(1); CN(2)) Part A site config. A[B] F[E]
B.E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Hw-Ow (Å)
289 244
2.31, 2.31, 2.32, 2.37, 2.48, 2.41(B), (2.53(B)) 2.315, 2.33, 2.35, 2.36, 2.47, (2.53(E))
1.645(B) 1.68, 1.83, 2.06 1.79, 1.85 1.82(E)
1.81, 1.885, 1.91 1.82, 1.91, 1.93, 1.98
Part B site
B.E.(kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Hw-Ow (Å)
F
249
2.26, 2.27, 2.34
1.77, 2.03, 2.59, 2.62, (2.72)
1.725, 1.78, 1.78, 1.81, 2.03
Part C site config. E&F
B.E. (kJ/mol)
Na-Ow (Å)
Hw-Ob (Å)
Hw-Ow (Å)
295
2.32; 2.24
2.68(E); 2.85(F)
1.64, 1.74, 1.74, 1.77, 1.855, 1.89, (2.085)
Part D A[B]
F[E]
F
E&F
4.01 0;0
4.02 0;0
2.80 1;1
1.37(E); 1.03(F); 3;3 (E); 3;3 (F)
a Binding energies (B.E.), closest sodium to water, water to basal oxygen, and water to water distances. X[Y] indicates that one of the water molecules at X is H-bonded to an Ob of the Y ring. Na-Ow distances refer to X, unless indicated otherwise.
counterion is pulled further away from the surface with increasing number of water molecules bound to it (Table 4D); the formation of water-water bonds decreases this effect (compare, e.g., FE[a] with FE[b]). D. Six Water Molecules. Of the configurations we have determined with either geometry optimization or by quenching from molecular dynamics trajectories, we shall now consider the most interesting ones. We have distinguished them according to the number of molecules bound to one cation. There is apparently no possibility for six molecules to bind to a single counterion located at the surface. Five is the upper limit (see Table 5A) both for the A and F cations, however, with one being significantly farther (2.47-2.48 Å), but also not too distant from a closer cation (B or E) and H-bonded to a basal oxygen of its ring. In the A[B] arrangement (Figure 5a), the adsorbate can be described as composed of two monomers (one bound to the B-ring via a strong H-bond) and a chain of four (with intrachain Ow-Ow distances ranging from 2.75 to 2.84 Å), out of which three form H-bonds with basal oxygens. In F[E] (Figure 5b), a single monomer coexists with a complex of five (with Ow-Ow distances ranging from 2.74 to 2.82 Å), of which only two are H-bonded to the Ob. In the F case (Figure 5c), only three molecules are bound to the counterion: one is adsorbed as a monomer, also H-bonded to the surface, whereas the other two are part of a pentamer (with Ow-Ow distances ranging from 2.69 to 2.91 Å). Of these, one forms four H-bonds to the surface and acts as the (offplane) cap of a quasi-planar 4-fold ring. The most interesting configuration is the one designated as E&F (Table 5C) to clarify that each cation is directly bound to only one molecule. One can recognize (see Figure 5d) a water hexamer (two tetramers joined in the shape of a hut) with one relatively long H-bond (3 Å) and two molecules bound to an Ob with relatively weak H-bonds. This cluster has a higher B.E. than the other (dissociated) arrangements, thus showing that at this stage the intermolecular attraction starts to gain over that of the clay in determining the energetically favored structures for the adsorbates. In this way, the E and F domains start to offer a more favorable adsorption center than the A and B domains.
The sodium to T-plane distances (Table 5D) follow the trends already identified in the preceding sections. IV. Conclusions The study presented here has provided an interesting picture of the first stage of the adsorption of water on the smectite surface. As expected, the binding energies significantly depend on the location of the counterion, namely, on the local charge distribution at the underlying layer, and the basal oxygen ions play an important role via the formation of hydrogen bonds. However, especially by comparing a number of different adsorbate configurations for a given number of molecules, calculations have permitted a quantification of this site dependence as well as of the difference between the various contributions to the binding. Moreover, the comparison of systems with different water coverage allows us to make a few more observations: (i) At the surface, sodium does not complete the first hydration shell. Water-water H-bonds become gradually more effective than the sodium-water interaction, thus limiting the number of sodiumbound molecules to five. Moreover, the formation of sodium-water complexes corresponds to the progressive detachment of the cation from the surface: Already at the level of three molecules, is sodium ∼3 Å away from the surface. (ii) The cooperation of nonequivalent cation sites in stabilizing the adsorbate on the surface becomes important already for a threemolecule system. This finding by itself discourages modeling using small cells for the clay that include only one cation site. (iii) No tendency of the water molecules to dissociate was observed. (iv) Different configurations are found within 1-2 kcal/mol, corresponding also to different structural adjustments of the adsorbant that accompany the adsorption process. Accordingly, a rigid clay model would not be appropriate for its description. (v) The A and B sites provide stronger attraction centers for water molecules and thus tend to prevent the formation of a water network. In contrast, at the E and F sites, such a water network forms already at the level of six molecules and becomes their thermodynamically stable configuration, with two molecules trapped at the two different positions of the cations that remain at the surface.
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(vi) The six-molecule adsorbate structure can also be seen as the onset of a disorder-order transition. In conclusion, although not exhaustive, our DFT-based search for probable configurations of water on the smectite surface has allowed the characterization of salient and also unforeseen features of adsorption in the low-coverage regime. The study of adsorption at the internal surfaces and diffusion in the interlayer regions of the solid is the natural extension of these studies. The information obtained in this paper should turn out to be useful also for the further modeling of these and related systems.13 Acknowledgment. This study was supported financially by the Nestle´ Research Center (NESTEC, Switzerland). One of us (P.C.) acknowledges the kind hospitality of the IBM Zurich Research Laboratory, where all of the calculations presented here were performed. Appendix TABLE A1: Na(H2O)n in the Gas Phase: Binding Energy of the Additional Molecule (b.e.) and Hydration Radius (R). Note: b.e. ) E(n) - E(n-1) no. of molecules “n” 1 2 3 4 5 6
b.e. (kcal/mol) exp.
25
24.0 19.2 13.2
R (Å)
this work
ref 14
this work
ref 14
24.3 21.8 18.0 12.5 12.2 9.0
24.1 20.8
2.197 2.214 2.244 2.300 2.334 2.372
2.215 2.244
14.1
References and Notes (1) Murray, H. H. Appl. Clay Sci 2000, 17, 207.
2.368
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