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J. Phys. Chem. B 2002, 106, 1118-1123
Analysis of the Opposite Solvent Effects Caused by Different Solute Cavities on the Metal-Water Distance of Monoatomic Cation Hydrates Jose´ M. Martı´nez,†,‡ Rafael R. Pappalardo,† Enrique Sa´ nchez Marcos,*,† Benedetta Mennucci,‡ and Jacopo Tomasi‡ Departamento de Quı´mica Fı´sica, UniVersidad de SeVilla, 41012-SeVilla, Spain, and Dipartimento di Chimica e Chimica Industriale, UniVersita` di Pisa, Via Risorgimento 35, 56126 Pisa, Italy ReceiVed: June 25, 2001; In Final Form: October 29, 2001
Theoretical studies on metal cations in water have lead to a controversy regarding the distance between the cation and the oxygen nuclei of the first solvation shell. Apparently this is due to the differences in the description of solvent effects which can lead to opposite conclusions: a shortening or a lengthening of this distance in the bulk solution with respect to that found in the hydrated cation in a vacuum. This discrepancy has been attributed to the difference between discrete and continuum solvation models. Likewise, within the continuum model, two widely used methods, those of the multipole expansion (MPE), from the Nancy group (using a spherical cavity), and the polarized continuum model (PCM) from the Pisa group (using a molecularly shaped cavity), have given different results. This work reconsiders the solvent effects on the geometry of a set of hydrated cations ([M(H2O)m]n+, where M ) Be2+, Mg2+, Ca2+, Zn2+, and Al3+) by comparing results derived from a previous work [J. Phys. Chem. 1991, 95, 8928] using the MPE approach with new PCM calculations. It is shown that both methods lead to the same results when the same (spherical) cavity is used, but PCM results, with molecularly shaped cavities, are in better agreement with those obtained with discrete solvent models. A continuous change in the atomic parameters defining the cavity allows the transition from one cavity shape to another and to observe the reversal in the prediction of the change in the M-O distances. The present study shows the substantial equivalence of the two methods (never accurately checked in precedence) and reveals that the M-O distance in the first hydration shell is an appropriate parameter to monitor finer aspects of the solute-solvent interactions, related to the discreteness of the solvent interactions in the second shell. These effects can be reproduced at a very good extent by continuum models with molecularly shaped cavities.
1. Introduction The ionic radius of metal cations in solution is a primary concept, amply used in the literature belonging to the fields of chemistry, physics, biology, and chemical engineering to get a rationale of many physicochemical properties of electrolytes solutions. It has long been accepted that this property depends on the nature of the solvent, because of the strong cationsolvent interactions exerting an influence going beyond the first solvation shell. This fact has been recognized by the operational definition of “hydrated ions”, a new species formed in solution by the ion and a reduced number of water molecules.1 Actually “hydrated cations” limited to the first solvation shell still feel the effect of the surrounding medium and of its macroscopic parameters (temperature, salt concentration, etc.); for this reason the ionic radius cannot be considered a fixed observable quantity independent of the external conditions. As a consequence different sources of experimental information lead to different estimates of it. Excellent compilations can be found in the reviews of Marcus2 and Ohtaki and Radnai,3 and the book of Magini et al.4 A general idea rising from these global comparisons is that there is no an unique value, but rather a certain dispersion of values. * Author to whom correspondence should be addressed. E-mail: sanchez@ simulux.us.es. † Universidad de Sevilla. ‡ Universita ` di Pisa.
A relevant structural parameter among all the data that can be obtained through various techniques is the distance between the metal cation and oxygen atoms of the first-shell water molecules (M-OI) when this cluster is immersed in solution. This distance can be imagined as the result of the coupling of solvent effects to the intrinsic distance of the isolated cluster, i.e., [M(H2O)m]n+. This observed structural parameter is coming from condensed media, either from X-ray diffraction data of crystals containing the hydrated cation or from X-ray, neutron diffraction, or EXAFS spectroscopies of aqueous solutions.1-5 Quantum and statistical mechanics theoretical computations represent alternative, complementary, and independent sources of information for understanding ion solvation, in general, and to give an estimate of the ionic radius, as a particular case.2 This means that the simultaneous consideration of an intrinsic and a surrounding component can be done by means of the quantum-mechanical methods that incorporate the solvent effects in the computations of the hydrated cluster distance. The typical approaches used to incorporate these effects have been the discrete model, where solvent molecules are explicitly considered,6,7 and the continuum model, where the solvent is described by a structureless dielectric polarizable continuum.8-11 The first approach is limited to a small number of solvent molecules, so that statistical contributions are not well represented. The second approach includes statistical factors of the bulk solvent through parameters characterizing the electric polarization of the con-
10.1021/jp012404z CCC: $22.00 © 2002 American Chemical Society Published on Web 01/09/2002
Opposite Solvent Effects in Monoatomic Cation Hydrates tinuum, but the solvent model is a rough representation of it as well as the cavity surface introduces an artificial discontinuity in the description of the solution.12 When water is considered as solvent, quantum-chemical computations using the discrete approach predict a shortening of the dM-OI distance when the cation hydrate [M(H2O)n]m+ is solvated by an explicit second hydration shell.13-18 The first geometry optimizations of [M(H2O)n]m+ clusters embedded in a dielectric continuum were carried out by means of the multipole expansion (MPE) method of the Nancy group,19 employing in these cases a monocentric expansion of the charge distribution and a spherical cavity.20 Contrary to what is found with discrete models, a lengthening of the cation-oxygen distance was found. A similar behavior was obtained by Tun˜on et al. studying the hydration of the proton21 and the hydroxide22 ions. A step beyond concerns the quantum-chemical combination of the discrete and continuum models that may be performed by including within a cavity surrounded by a dielectric continuum the hydrated cluster solvated by a second shell of water molecules, i.e., a [M(H2O)m]n+(H2O)y. The semicontinuum approach has been applied, within the framework of the MPE continuum model, to the solvation of silver23 ions and it has been shown that a mutual cancellation of effects appears, leading to an ion-oxygen distance remarkably closer to the gas-phase value. A semicontinuum study on the hydration of hydroxide ion with the same methodology led to the same conclusions.22 Recent EXAFS results of aqueous Ag+ and Sr2+ solutions at high temperature have shown that the contraction of the first shell of water molecules around these cations with increasing temperature can be considered as a fundamental property in aqueous solutions.24,25 These findings may be understood on the basis of the decrease of the bulk dielectric permittivity associated with a temperature increase.23,25 An independent source of information is provided by statistical computations based on simulations. By adding water molecules to a small ion cluster, [M(H2O)m]n+ + y(H2O), and determining the expected ion-water distance one should achieve information on the effects of successive hydration shells and bulk on the geometrical parameters. Marx et al.26,27 have studied the hydration of Be2+ by means of ab initio molecular dynamics. They found that Be-O distance in the tetrahydrate is reduced by the inclusion of a second and third hydration shells,27 whereas the application of periodic boundary conditions, including an uniformly charged background to the tetrahydrate, increases the distance. Cluster minimizations and classical MD simulations dealing with the Cr3+ hydration also shows a similar behavior. The addition of a second hydration shell to the [Cr(H2O)6]3+ unit leads to a shortening of the dCr-OI distance, whereas the average distance for a simulation with 512 water molecules slightly increases this value.28 This seems again to confirm the two opposite trends revealed by the quantum chemical computations. Recent studies on the hydration of lanthanides hydrates29 and the interaction of acetate anion with Al3+ in water30 have used the polarizable continuum model (PCM) of the Pisa group31 with a cavity fitting the molecular shape. They find a shortening of the cation-water distance. These recent results indicate that the continuum solvation models do not present an unique trend. The opposite behaviors found with two different continuum approaches (the MPE and the PCM) deserve a detailed examination in order to get insight into the possible sources of the discrepancy. The aim of this work is thus to re-compute the solvent effects on the geometry of a set of metal cation hydrates [M(H2O)m]n+ (for M ) Be2+, Mg2+,Ca2+, Zn2+, and
J. Phys. Chem. B, Vol. 106, No. 5, 2002 1119
Figure 1. Cavity shape used in the PCM model (a) and the Nancy’s MPE model (b) for the Be2+ tetrahydrate.
Al3+), which were already calculated in ref 20 using the MPE model, now using the PCM continuum approach. To get insight into the origin of the discrepancy, the PCM model will be applied not only with its standard solute cavity options to fit the molecular shape, but also with modified cavity criteria to mimic previous spherical cavities. Here we recall that MPE and PCM models are two popular representatives of the continuum models, but other alternative approaches are also possible as large is the range of continuum solvation models developed so far.10,11 Applications of this type of continuum methods to ionic hydrates, what is effectively the use of a semicontinuum approach (supermolecule + cavity), have been undertaken by several authors when they study different ionic solution properties.32-35 2. Computational Methods Solvent effects have been introduced by means of the polarizable continuum model.31 Because the results obtained using this methodology will be compared with the previous ones obtained from the application of the MPE continuum model, a short outline of both methods will be given. Polarizable Continuum Model of Solvation (PCM). The bulk solvent effects have been represented by PCM using its recent re-formulation, known as integral equation formalism36,37 (IEF). The solvent is represented by a homogeneous dielectric continuum, which is polarized by the charge distribution of the solute, and on turn it polarizes the solute in a self-consistent way. In the standard PCM the solute is placed within a cavity in the dielectric, defined in terms of interlocking spheres centered on the solute’s nuclear positions (see Figure 1a). During geometry optimizations, as those here performed on the [M(H2O)m]n+ species, the cavity boundaries follow the changes in the nuclear positions.38,39 It is also possible to use PCM with a fixed cavity of a given shape, e.g., a sphere. In both cases the solute-solvent interactions are described in terms of a solvent reaction potential, which is defined by a set of surface charges located on the cavity surface. The problem is then shifted to the definition of the proper apparent surface charge. In practice, a partition of the cavity surface is made into small regions of known area called “tesserae”. In this scheme, the reaction potential introduced in the effective Hamiltonian is reduced to one-electron operators depending on the surface charges. The approach is carefully described elsewhere.8 Reaction Field Multipole Expansion Method. The solute’s charge distribution is defined by means of a multipole expansion centered on a representative point of the cavity19 (monocentric expansion). The use of a constant coordinate cavity (like a sphere or an ellipsoid, see Figure 1b), allows an analytical expression of the multipole moments which makes easy the quantum chemical implementation of the method. The solvent reaction
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TABLE 1: Optimized Geometrical Parameters for [M(H2O)m]n+ Complexes in the Gas Phase and in Aqueous Solutiona dM-OI gas phase i.s.b [M(H2O)m]
n+
[Be(H2O)4]2+ [Be(H2O)6]2+ [Mg(H2O)6]2+ [Ca(H2O)6]2+ [Zn(H2O)6]2+ [Al(H2O)6]3+
1.645 1.829 2.050 2.369 2.050 1.907
∠HOH
dO-H
solution
gas phase
s.c.c
PCM
PCM
MPE
1.628 1.812 2.032 2.347 2.033 1.875
1.681 1.842 2.072 2.433 2.079 1.928
1.665 1.847 2.082 2.414 2.074 1.925
solution i.s.b
0.975 0.968 0.969 0.969 0.968 0.978
gas phase
s.c.c
PCM
PCM
MPE
0.973 0.967 0.968 0.970 0.968 0.974
0.981 0.969 0.970 0.973 0.971 0.981
0.978 0.970 0.971 0.972 0.970 0.981
volume
solution i.s.b
110.6 111.4 110.2 109.0 109.8 109.6
s.c.c
PCM
PCM
MPE
111.5 111.8 110.3 109.0 109.9 111.1
107.3 110.4 109.0 106.8 108.0 107.7
108.4 110.1 108.6 107.2 108.2 107.8
i.s.b
s.c.c
95.2 132.2 147.4 169.0 147.2 135.7
186.0 213.0 252.9 319.3 252.3 229.8
a All computations are performed with 3-21G and 3-21G* sets for the atoms of the first and second period, respectively. Angles in degrees, distances in Å, and volumes in Å3. b Interlocked spheres. c Spherical cavity with volume equal to that used in ref 20.
TABLE 2: Optimized Geometrical Parameters for [Al(H2O)6]3+ Complexes in the Gas Phase and in Aqueous Solution Using the 3-21G*/3-21G and the 6-311+G(2d,2p) Basis Sets and Different Cavity Sizes Using the PCM Methoda dM-OI gas phase 3-21G*/3-21G 3-21G*/3-21G 3-21G*/3-21G 6-311+G(2d,2p) b
solution i.s.b
basis sets 1.907 1.907 1.907 1.919
1.875 1.880 1.887
∠HOH
dO-H gas phase
s.c.c 1.928(1.925) 1.966 1.946
solution i.s.b
0.978 0.978 0.978 0.954
0.974 0.976 0.950
gas phase
s.c.c 0.981(0.981) 0.988 0.957
solution i.s.b
109.6 109.6 109.6 107.7
volume
111.1 110.8 109.3
s.c.c 107.7(107.8) 105.3 105.7
i.s.b 135.7 229.8 135.6
s.c.c 229.8 195.4 229.8
a Angles in degrees, distances in Å and volumes in Å3. Values in parentheses correspond to results obtained in ref 20 using the MPE method. Interlocked spheres. c Spherical cavity.
field is defined as the linear response of the dielectric medium to the multipole expansion of the solute charge distribution, weighted by a function of the dielectric permittivity and the cavity properties, called “reaction field factor”. The solutesolvent interaction is defined as the generalized product of the solvent reaction field and molecular multipole moments. Geometry optimization of the metal cation hydrates in ref 20 was performed using a constant-volume spherical cavity for each system. The cavity radius was chosen by adding the van der Waals radius of hydrogen (1.2 Å) to the M-H distance of the hydrate in gas phase. Multipole expansion was truncated at the order l ) 6, a good convergence of the series was observed. It is worth mentioning that these computations were obtained using the SCRF formalism based on the multipole expansion approach, as implemented by Rinaldi and Pappalardo in extra-links of the Gaussian-92 program package.40 Further developments allowed the optimization procedure for a variable cavity.41 A detailed description of the method can be found elsewhere.9 For the sake of comparison, the basic computational level used in this work has been the same as that used in the previous work.20 Then, computations have been carried out at the HF level with the standard 3-21G* basis sets. To check that the behavior of geometrical parameters are not basis dependent, additional computations with the 6-311+G(2d,2p) basis sets have been performed for the Al3+ hexahydrate. Standard radii have been used for the oxygen and hydrogen atoms when building the solute cavity42 whereas for metal cations Marcus’ ionic radii2 have been employed. All computations have been performed with the Gaussian99 package.43 3. Results Table 1 reports the optimized geometrical parameters for the [M(H2O)m]n+ clusters in a vacuum and in solution considering solvent effects by the PCM method. In the latter case, two different cavities were considered: (a) interlocked spheres (i.s. PCM column) which mimic the molecular shape using the aforementioned atomic radii and (b) the spherical cavities (s.c.
PCM column) of the previous work20 using just the cavity centered on the metal ion with the radius used in that study. For comparative reasons, values obtained in ref 20, are also included in the s.c. MPE column. The main geometrical parameter of a hydrated metal cation is the metal-oxygen distance (dM-OI). Taking the gas-phase value as reference, opposite trends are observed when using the molecular-shape cavity and the spherical one. For the latter case, results derived from PCM and MPE formalisms are equivalent, bulk solvent effects induce a lengthening of the distance of several hundredths of angstroms (0.013-0.064 Å). On the contrary, a cavity fitting the molecular shape induces a shortening of that parameter of ca. 0.02 Å. Concerning the intramolecular water parameters, opposite tendencies are also identified when both types of cavities are used, although the changes induced are much smaller than in the case of dM-OI. Table 2 shows additional results in order to test some methodological aspects, using the Al3+ hydrate case. First, basis sets dependence has been examined by using the more extended 6-311+G(2d,2p). Although the optimized gas-phase geometry for the hydrate is different, the shifts observed in the geometrical parameters with both types of cavities are similar to those obtained with the smaller 3-21G* basis sets. The two cavity definitions (s.c. and i.c.) used in this work imply very different final volumes as shown in the last column of Table 1, with the molecularly shaped volume always smaller than the spherical one. With the aim of elucidating the possible influence of this factor on the final geometries, two additional optimizations were performed for the Al3+ hydrate using the PCM method; the following results are included in Table 2. In the first optimization, the interlocked sphere cavity was built by applying a scaling factor (1.33) to the standard atomic radii so to obtain a cavity volume corresponding to the spherical case (namely, 229.8 Å3), but retaining the molecular shape. Such increase of the cavity size reduces the solvent effects but still maintains the previous results (i.e., a shortening of the M-OI distance, dAl-OI ) 1.880 Å when an i.s. cavity is used). A
Opposite Solvent Effects in Monoatomic Cation Hydrates
J. Phys. Chem. B, Vol. 106, No. 5, 2002 1121 spherical and a transition in the metal-oxygen distance is observed toward values larger than the gas-phase value. Further computations with larger metal radii, lead back to a dM-OI distance very close to its value in the gas phase, as a consequence of the decreasing of the continuum solvent effects when the cavity volume increases. A similar study can be done changing the radii of the oxygen and hydrogen atoms of the water molecule. Figures 2b and 2c show the variation of the dM-OI parameter as a function of the atomic radius used for oxygen (RO) and hydrogen (RH) atoms. Figures 3b and 3c plot the change of the cavity shape by increasing these atomic radii. In these cases the behavior is different since the gas-phase value is never reached and an asymptotic limit is inferred. It is worth pointing out that the observed behavior appears even for cavities whose volumes are much larger than that obtained in the spherical cavity computation (186.0 Å3). Such volume is approximately reached when RO is 2.5 Å and when RH is 2.0 Å and becomes 280.0 Å3 and 357.0 Å3, respectively, for the largest radii employed. 4. Discussions
Figure 2. Change of the optimized metal-oxygen distance (dM-OI) for the Be2+ tetrahydrate when the atomic radius (a) RBe, (b) RO, (c) RH used to build the cavity is varied. (Horizontal dashed lines correspond to the gas phase dM-OI value.)
parallel reasoning line would be to compute the solvent effects using a spherical cavity of the same volume as that obtained for the interlocking spheres with standard atomic radii (namely, 135.7 Å3). However, the cavity one would obtain in this way is too small to accommodate the solute. For this reason, a computation exploiting a spherical cavity with an intermediate volume (195.4 Å3) has been carried out. In this case, the decrease of the original spherical volume emphasizes the solvent effects, but it still presents the original trend of a lengthening of the distance (dAl-OI ) 1.966 Å). Also this second set of computations using the two cavities (the molecularly shaped and the spherical one) show opposite tendencies on the metal-oxygen distance, with the gas-phase distance as an intermediate value. It is then of interest to investigate the possibility of finding a continuous path connecting both limit behaviors by modifying the shape cavity. Such a study has been carried out performing a set of geometrical optimizations of the Be2+ tetrahydrate in which the radius of the metal ion (RBe) was systematically increased from its initial value (0.336 Å) to a final one, large enough to enclose the spheres corresponding to the water atoms and then reaching the spherical shape (see Figure 3a). Figure 2a shows the evolution of the dM-OI parameter as a function of the beryllium radius. For RBe values smaller than ca. 2.5 Å the contribution of the beryllium sphere to the molecular surface is negligible. For larger values, the effect of the solvent is dominated by the increase of the cavity volume which leads the dM-OI distance close to the gas-phase value (represented by the dashed line). When the RBe is close to 3.5 Å, the cavity shape becomes nearly
Although the MPE and PMC continuum models have been extensively used during the last twenty years, to our best knowledge, no previous direct comparisons between them have been carried out so far. In this work, the equivalence of both methods has been shown when the same cavity is employed, i.e., regardless of the way in which the solvent reaction field is computed, the changes induced on the geometrical parameters of the examined clusters are similar (cf. values in s.c. columns of Table 1). For the most interesting parameter, i.e., the metaloxygen distance, an increase is found when the spherical cavity is used. As previously reported,29,30 the standard application of the PCM method using the interlocked sphere procedure to define the solute cavity predicts a shortening of the metal-water distance in the metal cation hydrates compared to the gas-phase optimized geometry. On one hand, Tunega et al.30 have suggested that the behavior observed with the spherical cavity could be ascribed to the constancy of the volume, and on the other hand, Tun˜on et al.21 and Akesson et al.44 pointed out that the behavior could be due to an inappropriately large volume for the cavity. However, Table 2 shows that the optimization of the Al3+ hydrate, when the volume is reduced, leads only to an enhancement of the observed solvent effects for the larger cavity but maintaining the trend, that is, dAl-OI is larger for the smaller cavity. The trend in the opposite direction has also been examined as shown in Figure 2a where the behavior of dBe-OI for spherical cavities larger than that used in the original work,20 RBe g 3.5 Å, is plotted. It is observed that solvent effects still induce an increase in the meta-water distance, though this effect is damped by the larger cavity size. In addition to these new results, the use of nonconstant volume spherical cavity in a previous study on the Ag+ hydration,23 using the MPE approach of the Nancy group, reported the same trend for the metaloxygen distance. As a matter of fact, once a particular shape is selected, the modification of the cavity volume causes an effect proportional in the bond lengths within a defined trend. Let us consider the Al3+ hydrate optimization with the PCM method using interlocked spheres cavity, with the radii scaled to reproduce the spherical cavity volume. The effect is a shortening of dAl-OI though this effect is reduced because of the increase of the cavity size (see Table 2). Recent studies on the influence of a complete second hydration shell on the cations here considered have been carried
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Figure 3. Influence of the atomic radii in the cavity shape for the Be2+ tetrahydrate. (a) Radius of Be is changed from 0.4 to 4.2 Å. (b) Radius of O is changed from 1.8 to 3.8 Å. (c) Radius of H is changed from 1.2 to 2.7 Å. (Surface contributions from Be are displayed in magenta, O in red, and H in blue, non atomic ones are in gray.)
out by Pavlov et al. for the divalent cations,15 and by Rudolph et al. for Al3+, Mg2+, and Zn2+.16-18 HF, MP2, and B3LYP computational methods and different basis sets were applied to the hydrates. The average effect on the dM-OI parameter caused by the inclusion of the second hydration shell is a decreasing of 0.015-0.025 Å, that is close to the decreasing observed in this work when the PCM method is applied with cavity fitting the molecular shape. Results presented have shown that a selective change of the atomic radii corresponding to some of the atoms of the cluster represents a way of changing the shape of the cavity. Figure 3a illustrates the smooth change of the [Be(H2O)4]2+ cavity shape with the increase of the beryllium radius. Figure 2a shows that the influence of solvent effects on the hydrate geometry changes as a function of the cavity shape, proving that a continuous process of cavity modification is able to connect the opposite trends observed by using a molecularly shaped or a spherical cavity, respectively. This finding is confirmed by the trends found as a result of changing the atomic radii of the water molecule atoms, as presented in Figure 3b,c. In these two cases, the molecular shape remains quite different from a sphere and consequently the dBe-OI value remains smaller than the gasphase one, regardless of the volume of the cavity (Figure 2b,c). Bearing in mind the opposite phenomenological behavior observed for the metal-oxygen distance with the two different cavity shapes, an emerging conclusion is that the effect of using a continuum model employing the molecular-adapted shape cavities is similar to that resultant from a molecular (discrete) description of the solvent, managing at representing the specific interactions of an associated liquid. A picture that could be imagined to rationalize this behavior is raised from the consideration of the local regions outside of the cavity, but close
Figure 4. Superposition of the PCM model cavity surface and the spherical one for the Be2+ tetrahydrate.
to it, which are filled by the dielectric continuum up to form a cavity of constant coordinates (Figure 4). In a certain degree, the assumption that these narrow regions are filled by the solvent implicitly recognizes the ability of the solvent molecules to fit regions close to the solute, that is, the possibility of some kind of molecular behavior of the dielectric. Figure 4 gives an illustration of this hypothesis by indicating the critical region
Opposite Solvent Effects in Monoatomic Cation Hydrates occupied by the continuum that seems to implicitly take into account the molecular nature of the solvent to generate dielectric screening in these zones. As already pointed out by Coulson et al.,45 hydrogen bonding itself is electrostatic to a large extent, and in general, the electrostatic component of specific interactions associated to protic solvents could be particularly well reproduced by a set of partial charges, if they may adopt an adequate spatial distribution.46 This idea has motivated further developments of implicit solvation model where corrections of the SCRF continuum dielectric are included to account specific solute-solvent interactions.11,47 Likewise, this type of reasoning line has been supported by a comparative study of the aqueous solvation of water by means of a continuum method and a Molecular Dynamics (MD) simulation, this study has in fact shown the success of scaled radius in defining the cavity to provide results in good agreement with MD results.48 In summary, methods such as the PCM which has classically been considered as a continuum model of solvation, seems to incorporate some specific features of the discrete models of solvation, as far as the cavity fitting the molecular shape allows a strong asymmetry of the solvation reaction field potential. The classical generalization of the Kirkwood model, based on a regular cavity form is not bad at predicting the solvation effect, but rather it is giving the symmetric response expected for a bulk, resulting in an incomplete description for some solvation phenomena and properties. When an associative solvent is considered, the representation given by this model is unable to deal with the highly asymmetric short-range solute-solvent interactions that for some properties, such as the metal-oxygen distance, may counterbalance the effects induced by the longrange ion-solvent interactions. Acknowledgment. J.M.M. thanks the Ministerio de Educacio´n y Cultura (MEC) of Spain for a postdoctoral fellowship. DGICYT of Spain is acknowledged by financial support (PB981153). References and Notes (1) Richens, D. T. The Chemistry of Aqua Ions; John Wiley: Chichester, 1997. (2) Marcus, Y. Chem. ReV. 1988, 88, 1475. (3) Ohtaki, H.; Radnai, T. Chem. ReV. 1993, 93, 1157. (4) Magini, M.; Licheri, G.; Paschina, G. G.; Piccaluga, G.; Pinna, G. X-ray Diffraction of Ions in Aqueous Solutions: Hydration and Complex Formation; CRC Press: Boca Raton, FL, 1988. (5) Enderby, J. E. Diffraction Techniques for Determining the Structure of Electrolyte in the Liquid Phase. In Techniques for Characterization of Electrodes and Electrochemical Processes; Varma, R., Selman, J. R., Eds.; John Wiley and Sons: New York, 1991; Chapter 7. (6) Pullman, A. In Quantum Theory of Chemical Reactions, Vol. II.; Daudel, R., Pullman, A., Salem, L., Veillard, A., Eds.; Reidel Publishing Co.: Dordrecht, 1981. (7) Claverie, P.; Daudey, J. P.; Langlet, J.; Pullman, B.; Piazzola, D.; Huron, M. J. J. Phys. Chem. 1978, 82, 405. (8) Tomasi, J.; Persico, M. Chem. ReV. 1994, 94, 2027. (9) Rivail, J. L.; Rinaldi, D. In Computational Chemistry, ReView of Current Trends, Vol. 1; Leszczynski, J., Ed.; World Scientific: New York, 1996; Chapter 4. (10) Tomasi, J.; Mennucci, B. In Encyclopedia of Computational Chemistry, Vol. 4; Wiley & Sons: New York, 1998. (11) Cramer, C. J.; Truhlar, D. G. Chem. ReV. 1999, 99, 2161. (12) Tapia, O. In Molecular Interactions, Vol. 3; Ratajczak, H., OrvilleThomas, W. J., Eds.; Wiley: New York, 1982.
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