J. Phys. Chem. 1996, 100, 9689-9693
9689
Speciation in Aqueous Zinc Chloride. An ab Initio Hybrid Microsolvation/Continuum Approach Oswald G. Parchment,† Mark A. Vincent, and Ian H. Hillier* Department of Chemistry, The UniVersity of Manchester, Manchester M13 9PL, U.K. ReceiVed: January 10, 1996; In Final Form: March 20, 1996X
The structure and energetics of zinc chlorides (ZnCln2-n, n ) 0-4) in aqueous solution are studied by ab initio molecular orbital methods. The first solvation shell is included explicitly, the remainder of the solvent being modeled by the polarizable continuum method. The species Zn(H2O)62+, ZnCl2(H2O)2, ZnCl3(H2O)-, and ZnCl42- are predicted to occur in an aqueous environment. The predictions are consistent with the limited structural and energetic data available. A comparison with the predictions of the continuum model alone shows the necessity of including the first solvation shell explicitly to model solvation energies, although the continuum model is successful in predicting structural changes of ZnCl+ and ZnCl2 upon hydration.
Introduction Ab initio electronic structure methods are increasingly capable of yielding results which rival experiment in the insight that they give to understanding molecular properties and in their accurate prediction. However, this accuracy is still mainly limited to gas phase properties. Most of chemistry and all of biochemistry occurs in the condensed phase, particularly in solution where both the geometric and electronic structure of the solute may be modified by the solvent. One such area of particular interest is the formation of transition metal complexes in solution. The calculation of molecular properties in solution is complicated, especially for transition metals, by the possibility of complexation with solvent molecules. If such complexation occurs it is necessary to include the solvent ligands explicitly in a quantum mechanical calculation. Such a microsolvation approach has been shown to produce excellent results in studies on structural and energetic properties of metals in aqueous solution, most recently by Watanabe et al.1 and Woon and Dunning.2 However, this type of approach is computationally demanding, so that normally only the first solvation shell is considered, and quantities calculated from this approach are therefore considered to be approximations to their true values in bulk solvent. The explicit inclusion of the bulk solvent is traditionally treated Via Monte Carlo or molecular dynamics simulations using effective force fields. An alternative approach is to use a continuum description of the solvent which can readily be incorporated into standard quantum chemistry codes. Much work has been published using such reaction field theories as approximations to the bulk solvent,3-7 notably perhaps, the selfconsistent reaction field model (SCRF),8 which considers the interaction of the solute dipole or higher multipoles with the solvent dielectric. An alternative method, the polarizable continuum method (PCM), developed by Miertus et al.9 involves the generation of virtual point charges on the cavity surface, which is constructed from spheres centered on each atom of the molecule. Both approaches have been used with considerable success to study the solvation of a range of species, particularly organic molecules.10-13 However, relatively few studies have applied these methods to transition metal species in solution. A possible approach is to combine the microsol† Present address: School of Chemistry, University of Bath, Bath BA2 7AY, U.K. X Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(96)00123-2 CCC: $12.00
vation and continuum models, so that the first shell of solvent molecules is modeled explicity and the remainder of the bulk solvent is treated as a dielectric continuum. Recent work by Sanchez Marcos et al.14 on the hydration of metal cations in solution employed such a combined approach and yielded encouraging results. The work described herein applies such a combined microsolvation and continuum approach to a study of the structure and energetics of zinc chlorides in aqueous solution. Zinc is a transition metal which forms large hydrothermal ore deposits with anionic species such as S2-, HS-, and Cl-.15 The high solubility of such species in aqueous solution has greatly facilitated the experimental study of their physicochemical properties. It is clear that many different species may be present in solution, some with more than one possible conformation. Experimental evidence16-20 suggests the existence of the species ZnCl+, ZnCl2, ZnCl3-, and ZnCl42- with varying numbers of closely associated water molecules in various geometric arrangements. However, more precise details of the solvent structure close to the metal center is often difficult to define experimentally and is naturally dependent upon solute concentration. Suggested species include ZnCl2(H2O)4, having a linear ZnCl2 structure, tetrahedral ZnCl2(H2O)2, planar ZnCl3-, and tetrahedral ZnCl42-, or octahedral trans-ZnCl4(H2O)22-. The stability constants of the ZnCln2-n species have been evaluated experimentally, but there appears to be no consensus as to their magnitude.21-24 The aims of this study are to apply ab initio quantum mechanical methods to a study of zinc chlorides in aqueous solution to identify the species present and to assess their stability. It is not the purpose of this work to carry out state of the art calculations, but to employ an acceptable basis set and explore the correlation between theory and experiment at the Hartree-Fock level, in order to aid the interpretation of experimental data. Computational Details Unconstrained geometry optimization of the gas phase (ZnCln2-n) and hydrated (ZnCln(H2O)m2-n) species were performed, using a zinc basis set of Gianolio et al.25 This was modified with an extra set of d functions as suggested by Tossel,26 an s function of exponent 0.4, and three sets of p functions of exponents 0.26, 0.09, and 0.03. Split valence 6-31G*27 basis sets were used on the other atoms. The nature of the predicted stationary points was fully characterized by © 1996 American Chemical Society
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analytical calculation of the harmonic force constants. The effects of basis set superposition error (BSSE) on the energetics of the microsolvation model, which may be an important factor, were calculated using the counterpoise method.28 No attempt was made to correct the geometries for BSSE effects. The effect of the bulk solvent was estimated using the PCM approach of Miertus et al.9 Atomic radii were evaluated using the parameters developed by Aguilar and Olivares del Valle.29 However, for the Zn2+ cation no such parameters were available. Thus, the Pauling ionic radius of 0.75 Å was employed throughout this study.30 The dispersion contributions to the solvation energy were estimated within the PCM approximation, as developed by Floris and Tomasi.31 The cavitation energies were obtained following the procedure of Claverie et al.32 The statistical thermodynamic corrections to the SCF energies were calculated within the rigid rotor, harmonic oscillator approximation and employed to calculate the following quantities: (1) The first solvation shell hydration energy, ∆Esup
∆Esup ) E(M(H2O)n) - E(M) - nE(H2O) where E is the appropriate SCF energy. (2) The first solvation shell hydration enthalpy, ∆Hsup
∆Hsup ) ∆Esup + ∆ZPE + ∆H298K where ∆ZPE is the differential zero-point energy and ∆H298K is the enthalpy correction upon increasing the temperature from 0 to 298 K, both of these quantities being calculated in a similar manner to ∆Esup. (3) The first solvation shell hydration free energy, ∆Gsup
∆Gsup ) ∆Hsup - 298.15∆S where ∆S is calculated in a similar manner to ∆Esup. (4) The total free energy of solvation, ∆Gtot
∆Gtot ) ∆Gsup + ∆Gcont + ∆Gdisp + ∆Gcav + ∆Gvap Here ∆Gcont is the electrostatic contribution to the solvation free energy of the cluster calculated using the PCM as implemented33 within the GAMESS-UK ab initio code.34 ∆Gdisp and ∆Gcav are the dispersion and cavitation energies calculated as previously described. ∆Gvap is the free energy associated with the transfer of the appropriate number of water molecules involved in formation of the cluster, from the bulk to the vapor phase, taken to be 3.7 kcal mol-1 per water molecule.14 Values of this quantity in the range 3.4-5.5 kcal mol-1 have been suggested by Furuki et al.35 Finally, to assess the effect of bulk water on the structure of the zinc halide species, we have optimized the structures of ZnCl+ and ZnCl2 with the SCIPCM model as implemented within Gaussian94.36
Figure 1. Predicted structures of ZnCln(H2O)m2-n species; bond lengths in angstroms.
TABLE 1: Calculated and Experimental Bond Lengths for the Hydrated ZnCln2-n Species bond lengths (Å) species
bond
calculated
experiment
Zn(H2O)62+ ZnCl+ ZnCl(H2O)5+
Zn-O Zn-Cl Zn-O Zn-Cl Zn-Cl Zn-O Zn-Cl Zn-O Zn-Cl Zn-Cl Zn-O Zn-Cl Zn-O Zn-Cl Zn-Cl
2.14 2.08 2.16, 2.19, 2.20, 2.21 2.27 2.13 2.22 2.35 2.14 2.22 2.26 2.37 2.32, 2.39 2.28 2.26, 2.32 2.39
2.08-2.09a
ZnCl2 ZnCl2(H2O)4 ZnCl2(H2O)2 ZnCl3ZnCl3(H2O)2ZnCl3(H2O)-
Results and Discussion Structural and Vibrational Properties. The calculated Zn-O and Zn-Cl distances for the various zinc species, shown in Figure 1, are given in Table 1. A great deal of experimental data are available for the hexaaqua zinc cation. Certainly the Zn2+ cation is known to exist bound to six water molecules in aqueous solution.37,38 Monte Carlo calculations by Yongyai et al.24 and Clementi et al.39 have also predicted the overall octahedral coordination of the zinc cation. Sufficient experimental data exist on the Zn(H2O)62+ species from which a meaningful comparison of theoretical and experimental results can be made. The geometry of Zn(H2O)62+ has been fully optimized to the symmetry point group Th (Figure 1). Earlier
ZnCl42a
b
c
2.07b 2.24b 2.07c
2.28d d
References 37, 40. Reference 18. Reference 41. Reference 16.
calculations on this complex have shown this nuclear configuration to be the most favored.26 Indeed, our own calculations show this configuration to be a minimum on the potential energy surface. The Zn-O distance is calculated as 2.14 Å, slightly larger than the observed value. The predicted harmonic ν(ZnO) stretching frequency (Table 2) is somewhat smaller than the experimental value by about 10%, consistent with the predicted longer bond length. Solution X-ray diffraction studies by Paschina et al.18 have yielded a value of 2.24 Å for the Zn-Cl bond length for zinc
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TABLE 2: Calculated Harmonic Raman Vibrational Frequencies for the Hydrated ZnCln2-n Species stretching frequency (cm-1) calculated
e
Zn(H2O)62+ ZnCl+ ZnCl(H2O)5+ ZnCl2
339 475 344 355
ZnCl2(H2O)4 ZnCl2(H2O)2 ZnCl3ZnCl3(H2O)2ZnCl3(H2O)ZnCl42-
294 320 294 274 284 238
experimental 380-400a 352 (Kr matrix)b 361 (gas)c 305 (ZnCl2(aq))d 286 (ZnCl2(aq))d 275-280 (ZnCl2(aq))e 288 (M2ZnCl4)e
a Reference 42. b Reference 45. c Reference 43. d Reference 17. Reference 44.
chloride in aqueous solution, for a species they have postulated to be ZnCl(H2O)5+. This length is considerably greater than predicted for bare ZnCl+ (2.08 Å) (Table 1) and indicates that ZnCl+ is strongly hydrated in aqueous solution. However, the experimental Zn-Cl length is in good agreement with our predicted value of 2.27 Å in ZnCl(H2O)5+, which provides further evidence for the existence of such a species in aqueous solution. The effect of hydration upon ν(Zn-Cl) is as dramatic, decreasing this stretching frequency from 475 cm-1 in ZnCl+ to 344 cm-1 in the hydrated species (Table 2). However, in ZnCl(H2O)5+, the calculated Zn-Cl stretching mode is strongly coupled to Zn-O modes. The identification of a mean Zn-O distance within the first coordination shell, by Paschina et al.,18 is compared to our own results, which predicts several distinct Zn-O distances, although they are within 0.06 Å of each other. In our calculated structure of ZnCl(H2O)5+ (Figure 1), intramolecular hydrogen bonding is apparent between the chlorine and the hydrogen atoms. These interactions cause the water molecules to orientate themselves so as to maximize the OH2‚‚‚ Cl interactions. The Zn-O distances therefore become nonequivalent. The axial water molecule (Zn-O ) 2.16 Å) is least affected, while the greater Cl‚‚‚H interactions involving the equatorial water molecules lead to increased Zn-O bond lengths (2.19, 2.20, 2.21 Å). This tendency in the hydrated chloro complexes for the water hydrogens to maximize the OH2‚‚‚Cl interactions has already been noted by Butterworth et al.46 and by Woon and Dunning.2 However, this effect is expected to have little importance in aqueous solution, where the competition between intra- and intermolecular interactions is likely to result in Zn-O lengths that are closer than in the isolated ZnCl(H2O)5+ cluster. It is of interest to record that the SCIPCM study of ZnCl+ yielded a bond length of 2.24 Å, a value very close to that predicted for the pentaaquo complex (Table 1). Turning now to the hydration of ZnCl2, it has been suggested on the basis of Raman spectra that in aqueous solution ZnCl2 is linear and exists predominantly as the octahedral tetrahydrate.17 We have obtained minimum energy structures for two species (Table 1). As expected, successive hydration results in a corresponding increase in the Zn-Cl bond lengths, with a concomitant increase in the Zn-O length. However, in ZnCl2(H2O)2 the Cl-Zn-Cl angle is far from tetrahedral, being 145°. Thus it is far from clear if such a structure is excluded on experimental grounds. The SCIPCM study of hydrated ZnCl2 yielded a C2V structure with a Zn-Cl length of 2.20 Å and a bond angle of 162°, quite close to values predicted for the bisaquo complex. We find that, as in the case of ZnCl(H2O)5+, there is a tendency to maximize OH2‚‚‚Cl interactions (Figure 1). The
TABLE 3: Calculated First Solvation Shell Hydration Energies (kcal mol-1) for the ZnCln2-n Species in Aqueous Solution species 2+
Zn(H2O)6 ZnCl(H2O)5+ ZnCl2(H2O)4 ZnCl2(H2O)2 ZnCl3(H2O)2ZnCl3(H2O)-
∆Esup
∆Esup/H2O
-334.4 -157.5 -50.0 -32.1 -11.9 -7.5
-55.7 -31.5 -12.5 -16.1 -5.9 -7.5
Zn-Cl stretching frequency in both ZnCl2(H2O)4 and ZnCl2(H2O)2 are smaller than the value in ZnCl2, in line with the longer bond lengths in the hydrated complexes. We see that the experimental value of ν(Zn-Cl) for the hydrated ZnCl2 lies between the calculated values for the tetrahydrate and the dihydrate (Table 2). Thus we cannot say with confidence which species is prevalent in solution. The optimized structures for hydrated ZnCl3- are shown in Table 1 and Figure 1. Both the ZnCl3(H2O)- and ZnCl3(H2O)2structures were characterized as true minima, but no octahedral structure, ZnCl3(H2O)3-, corresponding to an energy minimum could be located. This suggests that such a structure is not favored in aqueous solution, but more extensive calculations may be needed to confirm this conclusion. In these species the variation in the Zn-Cl bond length upon hydration is more difficult to rationalize since the bond lengths depend upon the degree of intramolecular OH2‚‚‚Cl interaction. Thus, for example, in ZnCl3(H2O)-, two Cl atoms which are involved in H-bonding to the water molecule correspond to Zn-Cl distances (2.32 Å) which are 0.06 Å longer than the remaining Zn-Cl bond (2.26 Å), a value essentially unchanged from the length in ZnCl3- itself. A similar effect is found in the dihydrate where the Zn-Cl bond involved with two hydrogen bonds is 0.07 Å longer than the other two Zn-Cl bonds involved in just one hydrogen bond. An estimate of the strength of the OH2‚‚‚Cl interaction has been obtained by reorientating the water molecule in ZnCl3(H2O)- such that the H atoms are now directed away from the chlorine atoms and reoptimizing the structure. The resultant estimate of the H‚‚‚Cl interaction energy, ∼3 kcal mol-1, is less than the expected intermolecular hydrogen bonding in the bulk aqueous environment, so that distortion of the ZnCln2-n entity due to interaction with the first solvation shell is expected to be overestimated by the bare cluster calculations. The calculated Zn-Cl stretching frequencies are little changed upon hydration of ZnCl3-, in line with the fairly small geometry perturbations induced by the solvent. For the final species studied, ZnCl42-, an attempt was made to optimize the structure of the octahedral dihydrate, ZnCl4(H2O)22-. However, no minimum energy structure could be located. For the ZnCl42- species itself, the calculated value of ν(Zn-Cl), 238 cm-1, is somewhat less than the experimental value in solution, in line with this species being present, with no associated solvation shell. Hydration Energies. We first consider the predicted hydration energies of the complexes as calculated from the microsolvation model, given in Tables 3-5. For Zn2+, the calculated hydration free energy (∆Gsup, -271 kcal mol-1) is considerably less than the experimental value (close to -485 kcal mol-1),47,48 suggesting a large contribution from the bulk solvent beyond the first hydration shell. A continuum contribution of 92 kcal mol-1 has been suggested by Clementi et al.39 Upon increasing the number of coordinated chlorine atoms, the binding energies of the water molecules progressively decrease (Table 3). Thus, the binding energy per water molecule decreases from ∼56 kcal mol-1 in Zn(H2O)62+ to ∼7 kcal mol-1 in ZnCl3(H2O)-.
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TABLE 4: Effects of Thermodynamic Corrections on the Estimates of the First Solvation Shell Hydration Energies (kcal mol-1) 2+
Zn(H2O)6 ZnCl(H2O)5+ ZnCl2(H2O)4 ZnCl2(H2O)2 ZnCl3(H2O)2ZnCl3(H2O)-
∆Esup
∆Hsup
∆Gsup
-334.4 -157.5 -50.0 -32.1 -11.9 -7.5
-324.5 -149.1 -43.2 -29.0 -8.1 -5.6
-270.9 -104.4 -7.4 -12.3 +10.1 +3.1
TABLE 5: Calculated Hydration Free Energies of the Aquo Complexes of Zinc Chloride (kcal mol-1) Zn(H2O)62+ ZnCl(H2O)5+ ZnCl2(H2O)4 ZnCl2(H2O)2 ZnCl3(H2O)2ZnCl3(H2O)-
∆Gsup
∆Gcont
∆Gtot
-270.9 -104.4 -7.4 -12.3 +10.1 +3.1
-194.6 -71.8 -21.8 -16.9 -41.5 -40.6
-433.1 -146.8 -2.5 -10.2 -10.8 -20.8
However, for the clusters involving each ZnCln2-n species the binding energy per added water molecule does not change by more than a few kcal mol-1, being close to 14 and 6 kcal mol-1 for ZnCl2 and ZnCl3-, respectively. The calculated values of the enthalpy of water complexation (Table 4) are less than the energies of Table 3, due mainly to the inclusion of zero point effects, which naturally depend on the number of coordinated water molecules. The inclusion of the entropic contribution leads to the estimates of the free energy of hydration, within the microsolvation model, shown in Table 4. These are, as expected, considerably smaller than the corresponding enthalpies. Indeed, at this level, explicitly solvated ZnCl3- is not favored thermodynamically. A more realistic prediction of the solvation free energies of the ZnCln2-n species may be obtained by considering the continuum contribution to the solvation energies of the hydrated complexes given in Table 5. These are largest for the charged species. An important result is that for all the structures arising from a particular ZnCln2-n species the contribution of the solvent beyond the first hydration shell is essentially the same, showing the overriding importance of the first shell of solvent in determining the structures present in solution. However, in contrast to the microsolvation model, the ZnCl3- species are now predicted to be thermodynamically stable in aqueous solution. With regard to which hydrated ZnCl2 and ZnCl3species is actually present, we predict that ZnCl2(H2O)2 is preferred over ZnCl2(H2O)4 and that in the absence of a minimum energy structure for ZnCl3(H2O)3-, ZnCl3(H2O)- is preferred over ZnCl3(H2O)2-. As far as quantitative comparison with experiment is concerned, the predicted solvation free energy of Zn2+ (-430 kcal mol-1) is reasonably close to the experimental value, near -485 kcal mol-1,47,48 when both the level of theory used and the model employed are considered. We note that Floris et al.49 have obtained similar values of -434.9 and of -432.3 kcal mol-1. It is of value to compare the predictions of the continuum model using fixed atomic radii, applied to the ZnCln2-n species alone, without explicitly coordinated water molecules, with those from the more detailed microsolvation plus continuum approach described here. The results of the former, simpler method are given in Table 6. For ZnCl3-, the two methods give similar predictions. This is expected since the explicitly included water molecules are quite weakly bound. For ZnCl+, where strong coordination of the first shell of water molecules is found, the two approaches give solvation free energies that differ significantly. For ZnCl2, the continuum model seriously underesti-
TABLE 6: Free Energies (kcal mol-1) of Solvation of the Zinc Chloride Species, As Calculated by the Continuum Model ∆Gtot +
ZnCl ZnCl2 ZnCl3ZnCl42a
-430.3a +6.9 -26.5 -133.2
This value is extremely sensitive to the radius used for zinc.
mates the solvation free energy and cannot of course contribute to an understanding of the local water structure around the solute. The easily identified sources of error in the approach we have adopted have been previously discussed by Floris et al.49 Thus, geometry optimization within the continuum model does not lead to an improved agreement with experiment as far as Zn(H2O)62+ is concerned.14 It is worth noting that our attempts to optimize structures within the SCIPCM model of Gaussian94 were generally unsuccessful with the exception of the two cases described here. Finally, the use of the Hartree-Fock approximation leads to errors similar to those due to basis set truncation,49 and thus electron correlation has not been included in our studies. Conclusions The calculations described herein have shown the value of the hybrid explicit water/continuum approach for describing both the structure and energetics of ZnCln2-n species in aqueous solution. Thus, the local solvent structure in the immediate vicinity of the zinc halide is in agreement with experiment as judged by the actual bond lengths. The predicted structures also lead to vibrational spectra in line with the experimental observations. Finally, with regard to actual solvation free energies, there is acceptable agreement with the very limited experimental data. Thus, there are grounds for believing that calculations at the level described here are of real value in understanding the structure of quite complex metal species in aqueous solution. Acknowledgment. We thank SERC for financial support, Professor D. Vaughan for helpful discussions, and the reviewer for useful comments. References and Notes (1) Watanabe, H.; Iwata, S.; Hashimoto, K.; Misaizu, F.; Fuke, K. J. Am. Chem. Soc. 1995, 117, 755. (2) Woon, D. E.; Dunning, T. H., Jr. J. Am. Chem. Soc. 1995, 117, 1090. (3) Varnek, A. A.; Wipff, G.; Glebov, A. S.; Fiel, D. J. Comput. Chem. 1995, 16, 1. (4) Still, W. C.; Tempczyk, A.; Hawley, R. C.; Hendrickson, T. J. Am. Chem. Soc. 1990, 112, 6127. (5) Varnek, A. A.; Wipff, G. J. Phys. Chem. 1993, 97, 10840. (6) Lee, F. S.; Chu, Z. T.; Warshel, A. J. Comput. Chem. 1993, 14, 161. (7) Davies, M. E.; McCammon, J. A. Chem. ReV. 1990, 90, 509. (8) Tapia, O.; Goscinski, O. Mol. Phys. 1975, 29, 1653. (9) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (10) Rivail, J. L.; Terryn, B.; Rinaldi, D.; Ruiz-Lopez, M. F. J. Mol. Struct. (THEOCHEM) 1985, 120, 387. (11) Parchment, O. G.; Green, D. V. S.; Taylor, P. J.; Hillier, I. H. J. Am. Chem. Soc. 1993, 115, 2352. (12) Contreras, J. G.; Alderete, J. B. Chem. Phys. Lett. 1995, 232, 61. (13) Davidson, M. M.; Hillier, I. H.; Hall, R. J.; Burton, N. A. J. Am. Chem. Soc. 1994, 116, 9294. (14) Sanchez Marcos, E.; Pappalardo, R. R.; Rinaldi, D. J. Phys. Chem. 1991, 95, 8928. (15) Crerar, D.; Wood, S.; Brantley, S.; Bocarsly, A. Can. Mineral. 1983, 23, 333. (16) Kruh, R. F.; Standley, C. L. Inorg. Chem. 1962, 1, 941.
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