Microhydration of the Selenite Dianion: A Theoretical Study of

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Microhydration of the Selenite Dianion: A Theoretical Study of Structures, Hydration Energies, and Electronic Stabilities of SeO32-(H2O)n (n ) 0-6, 9) Clusters Henryk Wicke* and Artur Meleshyn Institute of Radioecology and Radiation Protection, Leibniz UniVersita¨t HannoVer, Herrenha¨user Strasse 2, 30419 HannoVer, Germany ReceiVed: December 22, 2009; ReVised Manuscript ReceiVed: June 4, 2010

In extension of the ongoing investigations of oxyanion-water clusters, we studied energetically low-lying configurations of hydrated selenite dianion (and in select cases, SeO3-) clusters using density functional theory (B3LYP, M05-2X, PBE0) and second-order Møller-Plesset perturbation theory (MP2). Water molecules doubly hydrogen bond to the selenite oxygens for n e 3 and increasingly form singly hydrogen bonds with selenite oxygens upon an increase of the cluster size as water-water interactions gain relative importance as compared to the selenite-water interactions. The calculated average Se-O bond length of 1.69-1.71 Å and selenite tetrahedron height of 0.64-0.73 Å are in accordance with recent experimental results for selenite in aqueous solution or adsorbed on calcite. Structural perturbations due to the hydration are accompanied by a considerable charge transfer (up to 0.55|e|) from the selenite substructure to the water molecules. Furthermore, the calculated electron binding energies evidence that selenite-water clusters are electronically stable only for n g 4 (according to M05-2X) or n g 5 (according to B3LYP and PBE0). The hitherto unknown hydration free energy of selenite was calculated using a cluster/continuum approach to fall into the range from -224.6 to -245.5 kcal/mol depending on the applied continuum solvation model. 1. Introduction The element selenium plays the dual role of an essential trace element and toxin in the nutrition of humans and animals,1,2 with potentially fatal consequences in the case of deficiency or oversupply.3 Because of the radioactive isotope 79Se, which is a long-lived fission product4 with a half-life of ∼2.9 × 105 a,5 it is also of elevated radiological importance for nuclear waste disposal. Long-term radiation dose modellings predict 79Se to be the second most important contributor after 129I to the exposure of the general population due to releases into the biosphere from potential nuclear waste disposal sites.6,7 Therefore, it is important to develop an understanding of the behavior of the relevant selenium species in such fundamental chemical processes as hydration or adsorption. In this context, two strongly soluble and weakly adsorbed selenium species, the selenite (SeO32-) and selenate (SeO42-) dianions, deserve special attention.8–10 The oxyanion SeO32- is the dominating species under conditions typical for clays,9,11 which are considered as potential geo-engineered barriers in nuclear waste repositories.12 Consequentially, the interaction of selenite with mineral surfaces is an active field of experimental research.13–18 Differently from clay minerals, Fe(II)- and Fe(III)bearing minerals have been shown to adsorb selenite, followed by its (slow) reduction depending on the pH.19–23 However, even in this case, the reduced selenium species may be transported in a colloid-facilitated way within aquifers and reoxygenated.20 Moreover, because some nuclear waste disposal sites such as Yucca Mountain are characterized by oxidizing geochemical environments,24 further research on selenite remains essential. There are numerous investigations of other oxyanions and their aqueous clusters available in the literature, including those on the microhydration of oxyanions employing quantum chemical calculations. These latter studies have been focused mainly * Corresponding author. E-mail: [email protected].

on the nitrate anion (NO3-)25–27 as well as the sulfate dianion (SO42-),28–35 while for other oxyanions as sulfite,36–38 tellurite,38,39 selenite,37,38 as well as other selenium40 and selenium-oxygen compounds,38,41–43 no hydration shell has been included in theoretical considerations as of yet. The aspect of electronic stability has been investigated with the help of electrospray and photodetachment photoelectron spectroscopy and theoretically for several oxyanions such as sulfate,29,44,45 selenate,44 or nitrate.25 These studies have revealed that only nitrate can exist in isolated form, while bare sulfate and selenate are unstable with respect to the removal of an electron, with sulfate requiring at least three water molecules to be electronically stable. The electron binding energies for selenite and selenite-water clusters remain hitherto unknown, thus precluding a conclusion concerning its electronic stability. Similarly, free energies of hydration have been determined experimentally for sulfate, sulfite, and selenate46 and have been supplemented by water molecule binding energies calculated by means of quantum chemical methods for sulfate-water clusters and nitrate-water clusters.25,29 However, to the authors’ knowledge, neither experimental nor theoretical determinations of the hydration free energy or water molecule binding energies are available for selenite. Therefore, the investigation of selenite and selenite-water clusters was deemed necessary to enable the derivation of water molecule and electron binding energies permitting assertions concerning the hydration free energy and electronic stability. While the incremental increase of the cluster size, beginning with the bare selenite dianion and concluding with the cluster containing six water molecules, allowed for a thorough analysis of the electronic stability, the hydration free energy was estimated by means of cluster/continuum calculations including up to nine explicit water molecules in the hydration shell of selenite. The calculated structures also enable the discussion of

10.1021/jp9120904  2010 American Chemical Society Published on Web 08/06/2010

Microhydration of the Selenite Dianion characteristics of the selenite hydration shell and a comparison to other oxyanion-water clusters. By including three different density functionals as well as a Post-Hartree-Fock method as discussed in more detail in the next section, an ample amount of theoretical methods was included to ensure the yield of reliable data. The unavailability of published experimental or theoretical results with a similar scope rendered the comparison of the results presented in this study to existing previous data difficult. However, this comparison is beneficial by taking into account the mentioned studies on other oxyanions as well as experimental results for selenite in solution or adsorbed on mineral surfaces.13,16,47

J. Phys. Chem. A, Vol. 114, No. 34, 2010 8949 298.15 K and 1 atm of pressure). Empirical scaling factors to account for anharmonicity effects were not applied to these data due to unavailability for the employed theory levels. Because of the sizable basis set, hypothetical ZPE scaling factors relatively close to unity may be assumed for the purpose of this study.69,70 To calculate the hydration energies, a scheme by Tuma et al. was used.71 The water molecule binding energy of the SeO32-(H2O)n cluster is

-∆Ee(n) ) n · Ee(H2O, Bw, Gw) + Ee(SeO23 , B0, G0) Ee(SeO23 (H2O)n, Bn, Gn)

(1)

2. Theoretical Methods The electronic structure calculations in this study were performed using the GAMESS-US program48,49 as well as two different revisions of the Gaussian 03 package.50,51 The results are based on calculations using Gaussian 03, revision E.01,51 while employing the 6-311+G(3df) basis set for SeO32- and the 6-311++G(3df,2pd) basis set for SeO32-(H2O)n.52–55 Both density functional theory (DFT) in the form of the hybrid functional B3LYP,56–62 the hybrid meta-GGA functional M052X,63 and the parameter-free hybrid functional PBE064–66 (also known as PBE1PBE51) and, for structures with up to three water molecules, second-order Møller-Plesset perturbation theory (MP2)67 in the frozen core approximation (FC-MP2) were used. Here, all terms identifying theory levels are referred to as defined in Gaussian 03. The UltraFine grid was used for all DFT calculations with Gaussian 03, while symmetry constraints were not imposed for any calculation. Self-consistent field cycles were done with tight convergence criteria; the same holds for almost all geometry optimizations, unless convergence could only be achieved in a reasonable time with default geometry convergence criteria. The computationally expensive decision to employ a relatively large basis set, more than just one density functional along with high-quality grids, as well as the Post-Hartree-Fock method FC-MP2, was made due to the uncertainty founded in the limited published experimental or theoretical data available for the validation of the results. For the microhydrated selenite clusters SeO32-(H2O)n with n ) 3, 4, 5, 6, a sizable amount of structures was considered initially (86, 393, 408, and 1101 geometries, respectively) to sufficiently cover the complicated potential energy surfaces of the larger systems by a somewhat systematic search. The initial guess configurations for SeO32-(H2O)n clusters were derived from the local minimum structures found for SeO32-(H2O)n-1 clusters by adding one water molecule in arbitrary ways. These initial structures were first optimized using GAMESS-US at the B3LYP/6-31++G(2d,2p) level68 as implemented in that program. (For SeO32-(H2O)6, the B3LYP/6-31G(d,p) level was used to save computation time.) The resulting minimum structures were then reoptimized at the B3LYP/6-311++G(2d,2p) level with GAMESS-US. The structures selected for further consideration using the Gaussian 03 program as described in the preceding paragraph were energetically low-lying local minima, including in all cases the lowest energy structure found, from the reoptimization. Vibrational frequencies of these structures were calculated to ensure that they indeed represent local minima on the potential energy surfaces, that is, that no imaginary frequencies are present. The thermochemical analyses of these calculations yielded the harmonic approximation of the zero-point energies (ZPE) as well as the enthalpies and Gibbs free energies (at

where Ee refers to the total electronic energy, with its three arguments identifying the species, the species’ basis set (B), and the species’ geometry (G). Bw, for example, is used to indicate the basis set belonging to a single water molecule, while Gn means the geometry of the SeO32-(H2O)n cluster. The counterpoise corrected binding energy -∆Eecpc(n) can be derived by correcting the total energies for the basis set superposition error (BSSE), where the different water molecules, denoted {H2O}i, are considered separately:72 22Ecpc e (SeO3 (H2O)n) ) Ee(SeO3 (H2O)n, Bn, Gn) 2Ee(SeO23 , Bn, Gn) + Ee(SeO3 , B0, Gn)

-

n

n

i)1

i)1

∑ Ee({H2O}i, Bn, Gn) + ∑ Ee({H2O}i, Bw(i), Gn)

While the BSSE can be expected to be rather small at least with the (mean-field) DFT methods because of the relatively large basis set chosen,73 the employed counterpoise correction method may still overestimate the BSSE,74 and thus binding energies may be (slightly) underestimated with the counterpoise correction or (slightly) overestimated without.75–79 For these reasons, both corrected and uncorrected values are given later in this work. By inclusion of the ZPE difference ∆ZPE(n) ) ZPE(H2O) + ZPE(SeO32-(H2O)n-1) - ZPE(SeO32-(H2O)n), the ZPE corrected total binding energy -∆E0(n) ) -∆Ee(n) + ∆ZPE, which is also the negative heat of formation of the SeO32-(H2O)n cluster at 0 K,71 was calculated. Likewise, temperature and entropy corrections were applied to calculate enthalpy (-∆H) and Gibbs free energy changes (-∆G) for the clusters. Along with the dianionic systems, the anionic open-shell systems SeO3-(H2O)n were considered by means of unrestricted calculations (the spin contamination due to the unrestricted formalism is negligible in all cases as the expectation value of the total spin differs from s(s + 1), with 2s ) 1 being the number of unpaired electrons, only by 3.1% or less in all calculations) to probe the electronic stability of the dianionic clusters and to elucidate the effect of the additional negative charge of the dianion on the hydration shell structure. Geometry optimizations of the anionic clusters were only conducted with the lowest energy structures of the dianionic clusters as input geometries. On the basis of these calculations, electron binding energies in the form of adiabatic (ADE) and vertical (VDE) detachment energies were determined. The ADE is defined as the difference between the total energies of the optimized anion and dianion complexes, whereas the VDE refers to the difference between the total energies of the anion at the optimized dianion’s geometry and of the optimized dianion complex.29

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The selenite hydration free energy ∆G*solv(SeO32-) was calculated by means of the cluster/continuum approach, where water molecule binding energies calculated with explicit hydration shell water molecules are combined with the results of continuum solvation calculations.80–83 For this purpose and as outlined by Bryantsev et al.,82 two thermodynamic cycles were employed, that is, the monomer cycle, where a selenite dianion is reckoned to react with n single water molecules to form a SeO32-(H2O)n cluster, as well as the cluster cycle of a selenite dianion reacting with a water cluster of n molecules to form a SeO32-(H2O)n cluster. In the former case, ∆G*solv(SeO32-) is calculated by80,82 ∆G*solv(SeO32-) ) ∆G°(M) + ∆G*solv(SeO32-(H2O)n) n · ∆G*solv(H2O) - n · (RT · ln[H2O] + ∆G◦f*)

whereas in the latter case and for n g 2 (the monomer and cluster cycles are identical for n ) 1, while ∆G*solv(SeO32-) is calculated directly by the continuum solvation method for n ) 0), ∆G*solv(SeO32-) ) ∆G°(C) + ∆G*solv(SeO32-(H2O)n) ∆G*solv((H2O)n) - RT · ln([H2O]/n) - ∆G◦f*

has to be used.82 ∆G°(M) and ∆G°(C) are the gas-phase water molecule binding free energies for the monomer and cluster cycle. ∆G°(M) values are derived from eq 1 by application of a temperature and entropy correction as described above (noncounterpoise corrected values were chosen), while for the cluster cycle ∆G°(C) ) G(SeO32-(H2O)n) - G(SeO32-) G((H2O)n) holds. Following convention,82,83 the hydration free energies are associated with the 1 mol/L (gas) f 1 mol/L (solution) process, and thus a standard state correction has to be applied. For both cycles, it includes ∆G°f* ) 1.89 kcal/ mol, the free energy change of 1 mol of an ideal gas from a pressure of 1 atm to 1 mol/L.82 Furthermore, the free energy change -RT · ln[H2O] ) -RT · ln(55.34) ) -2.38 kcal/mol from the 55.34 mol/L liquid state of H2O to 1 mol/L (monomer cycle) or the free energy change -RT · ln(55.34/n) from the 55.34/n mol/L liquid state of (H2O)n to 1 mol/L (cluster cycle) have to be included in the standard state correction.82 The standard free energies of hydration for the water molecule as well as the water and selenite-water clusters, ∆G*solv(H2O), ∆G*solv((H2O)n), and ∆G*solv(SeO32-(H2O)n), were evaluated by single-point continuum solvation calculations of the optimized gas-phase geometries. Here, the conductor-like polarizable continuum model (CPCM),84,85 which is the implementation of the conductor-like screening model (COSMO)86 in the polarizable continuum model (PCM) framework,87–91 and the static isodensity surface polarized continuum model (IPCM)92 as implemented in Gaussian 03 were used as continuum solvation methods. (The IPCM method was applied only to clusters with n e 6 due to computing time constraints.) For the CPCM calculations, the cavity was built by using the United Atom Topological Model applied on two types of atomic radii, namely radii optimized for the PBE0/6-31G(d) level of theory51 (dubbed UAKS in Gaussian 03) as well as radii optimized for COSMO-RS93 (dubbed Klamt in Gaussian 03). The nonelectrostatic component ∆Gnonel of the free energy of hydration was estimated for the IPCM calculations by inserting the solvent accessible surface area A (in Å2) as calculated by Gaussian 03 into the empirical formula ∆Gnonel ) 1.09 + 0.005 · A according to Tannor et al.,94

Wicke and Meleshyn TABLE 1: Calculated Bond Lengths (Å) and Angles (deg) of SeO32method

dSe-Oa

RO-Se-Ob

B3LYP/6-311+G(3df)c M05-2X/6-311+G(3df)c PBE0/6-311+G(3df)c FC-MP2/6-311+G(3df)c HF/ECP38 d FC-MP2/ECP38 d CISD+Q/ECP38 d HF/all-electron37 e

1.706 1.687 1.689 1.695 1.662 1.708 1.699 1.664

106.9 106.5 106.8 106.8 106.8 107.3 107.1 106.4

a Se-O bond length in the bare selenite dianion. b O-Se-O angle in the bare selenite dianion. c This work. d Relativistic effective core potentials for selenium and oxygen have been used.38 e For selenium a (13s11p6d/6s6p4d) basis set and for oxygen a (9s6p1d/4s3p1d) basis set have been used.37

while it was calculated directly by Gaussian 03 for the CPCM solvation model. For the cluster cycle calculations, the necessary water cluster geometries ((H2O)n with n ) 2-6, 9) were taken from Su et al.95 For n ) 2-5, 9, the respective global minimum structure was chosen,95 while for n ) 6, a cyclic structure that has the lowest Gibbs free energy at 50 K according to Su et al.95 was used. Prior to the continuum solvation treatment for the calculation of ∆G*solv((H2O)n), all gas-phase water clusters were fully geometry optimized at the different theory levels (B3LYP, M05-2X, PBE0, and FC-MP2 with the 6-311++G(3df,2pd) basis set). In this study, a geometrical definition was used for the hydrogen bonds (H-bonds).96 According to this definition, two molecules are considered as H-bonded if dO · · · O e 3.5 Å and dO · · · H e 2.6 Å hold for the distances and RH-O · · · O e 30° for the H-bond angle. The molecular visualizations were produced with the help of the ORTEP-3 for Windows97 and ECCE98 programs. 3. Results and Discussion 3.1. Description of Structures. SeO32-. To our knowledge, the SeO32- species is the only system studied in this work, for which a direct comparison to another computational study is possible (Table 1). Unlike the neutral species SeO3 or the nitrate oxyanion NO3-, which are trigonal planar in their ground states,25,42 the selenite dianion with its electron lone-pair has C3V symmetry according to the theoretical as well as Raman spectroscopy results of selenite in aqueous solution.47,99 Expectedly, the deviation from the planar structure is more pronounced for the dianion than for the anion as discussed in more detail below. B3LYP gives slightly higher and M05-2X as well as PBE0 slightly shorter Se-O bond lengths than FCMP2. This relative behavior of the employed methods was also observed for the SeO32-(H2O)n clusters. The HF method likely underestimates the Se-O bond length as these calculations have yielded significantly lower values than the other methods.37,38 The additional d and f polarization functions in the 6-311+G(3df) basis set lead to a reduction of the bond length by ∼0.01 Å as compared to the 6-311+G(2d) basis set, which therefore may overestimate it. SeO32-(H2O)1-3. The selenite-water clusters with one to three water molecules were studied at the B3LYP, M05-2X, PBE0, and FC-MP2 levels. The B3LYP-optimized structures are depicted in Figure 1, whereas the binding energies, enthalpies, and Gibbs free energies for the different structures are given in Tables 2 and 3. The appearance of the geometries

Microhydration of the Selenite Dianion

Figure 1. Optimized structures of SeO32-(H2O)1-3 at the B3LYP/6311++G(3df,2pd) level. H-bonds are indicated by dotted double lines.

according to the different theory levels is in all cases very similar, yet with the used density functionals marginally disagreeing on a few of the H-bonds with their geometry parameters being borderline relative to the used H-bond definition. The two structures shown in Figure 1 for the SeO32-(H2O)1 system are both in very good approximation Cs symmetric. Structure 1-A, exhibiting symmetric double H-bonding, unlike, for example, the minimum energy structure of NO3-(H2O)1,25,27 is lower in energy (i.e., shows a higher binding energy) than the species 1-B with a single H-bond, according to all four methods used. The B3LYP functional gives the smallest energy difference between 1-A and 1-B (3.6 kcal/mol), and FC-MP2 gives the highest (4.4 kcal/mol). The agreement between the three density functionals B3LYP, PBE0, and M05-2X in terms of energy differences between 1-A and 1-B is decent, especially when the ZPE corrected binding energies or enthalpies are considered (2.1-2.4 kcal/mol and 2.5-2.7 kcal/mol, respectively, depending on the functional). In the case of the SeO32-(H2O)2 system, all three structures depicted in Figure 1 build on structure 1-A in that they maintain at least one doubly H-bonded water molecule. Structure 2-A,

J. Phys. Chem. A, Vol. 114, No. 34, 2010 8951 which has two doubly H-bonded water molecules and Cs symmetry, is energetically most favorable according to all four methods used. 2-C (Cs symmetry) is the second most favorable structure (with the exception of B3LYP/∆G), ahead of 2-B (C1 symmetry), indicating that it is energetically more favorable if each selenite oxygen accepts an H-bond as compared to the configuration with one accepting two H-bonds and another remaining without any. Similar to the clusters with one water molecule, the binding energy, ZPE-corrected binding energy, and enthalpy differences between the three structures are within 0.3 kcal/mol for the different density functionals and thus in good agreement with each other. The lowest energy structure 2-A has a characteristic different from 1-A in that the doubly H-bonded water molecules each donate a stronger and a weaker H-bond. These differ in the O · · · H length by ∼0.06 Å according to the DFT methods and by ∼0.04 Å according to FC-MP2. Correspondingly, the bond length between selenium and the oxygens accepting two H-bonds is longer by ∼0.02 Å than the other two Se-O bonds for all methods. Structure 3-A is, according to all four methods used, the lowest energy structure studied for the SeO32-(H2O)3 cluster. It has C3V symmetry with three symmetrically doubly H-bonded water molecules. 3-B and 3-C, which are similar to the SeO32-(H2O)2 structure 2-B, with the third water molecule donating H-bonds to two selenite oxygens, are in most cases within 3 kcal/mol of 3-A. All other structures with one water molecule residing in the second hydration shell, including the structure 3-D, are generally energetically less favorable. Using the minimum energy structures of the SeO32-(H2O)1-3 clusters as initial structures for the optimization of the anionic SeO3-(H2O)1-3 clusters leads to qualitatively similar arrangements of the water molecules, albeit with a decreased strength of the H-bonding interaction between the SeO3 structure and the water molecules. SeO32-(H2O)4-6. Because of computing time constraints, structures with four to six water molecules were optimized using the DFT methods B3LYP, M05-2X, and PBE0 only. The B3LYP-optimized structures of the selenite-water clusters with four to five and six water molecules, respectively, are shown in Figures 2 and 3. As for the smaller clusters, the appearances of the geometries according to the M05-2X and PBE0 functionals are again very similar to the B3LYP results, with the different functionals marginally not agreeing on a few of the H-bonds due to their geometry parameters being borderline relative to the used H-bond definition. The SeO32-(H2O)4 cluster is the largest studied system, for which an unambiguous identification of the lowest energy structure was possible with the employed methods. Yet, even in this case, several structures are within 2 kcal/mol (Tables 2 and 3). The fact that the structure 4-C, a Cs symmetric structure with one water molecule residing in the second hydration shell, is energetically comparable to the lowest energy structure (especially in terms of ∆Ee and ∆Eecpc for B3LYP and PBE0) highlights that the selenite-water interaction becomes increasingly less important as compared to the water-water interactions. Structure 4-C with a doubly H-bonded second shell water molecule is, in terms of ∆Ee, ∆E0, and ∆H, energetically more favorable than 4-D with an only singly H-bonded second shell water molecule. It has to be noted that the three density functionals do not agree on the energetic hierarchy of the structures 4-B through 4-G. Albeit only relatively small differences exist between B3LYP and PBE0, M05-2X yields considerably different orders, except for the Gibbs free energies. Nevertheless, structure 4-A, which has C1 symmetry, is the

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TABLE 2: B3LYP and M05-2X Results (kcal/mol) for the Binding Energies (-∆Ee), ZPE-Corrected Binding Energies (-∆E0), Binding Enthalpies (-∆H), and Binding Gibbs Free Energies (-∆G) at 298.15 K and 1 atm for SeO32-(H2O)1-9a B3LYP/6-311++G(3df,2pd)

M05-2X/6-311++G(3df,2pd)

structure -∆Ee (-∆Eecpc) -∆E0 (-∆E0cpc) -∆H (-∆Hcpc) -∆G (-∆Gcpc) -∆Ee (-∆Eecpc) -∆E0 (-∆E0cpc) -∆H (-∆Hcpc) -∆G (-∆Gcpc) 1-A 1-B

30.7 (29.8) 27.2 (26.3)

28.4 (27.5) 26.3 (25.4)

29.3 (28.3) 26.8 (25.9)

19.4 (18.5) 18.4 (17.5)

33.8 (33.0) 29.8 (29.0)

31.5 (30.8) 29.2 (28.4)

32.4 (31.6) 29.8 (29.0)

22.5 (21.8) 20.9 (20.1)

2-A 2-B 2-C

58.3 (56.4) 54.8 (53.0) 56.0 (53.8)

53.7 (51.8) 50.6 (48.8) 51.0 (48.9)

55.3 (53.4) 52.1 (50.3) 52.8 (50.7)

35.7 (33.8) 32.9 (31.1) 32.4 (30.3)

64.3 (62.8) 60.6 (59.1) 61.8 (60.1)

59.5 (58.0) 56.4 (54.9) 57.0 (55.3)

61.2 (59.7) 58.1 (56.6) 58.8 (57.1)

41.5 (40.0) 38.2 (36.7) 38.5 (36.8)

3-A 3-B 3-C 3-D 3-E 3-F 3-G

83.2 (80.4) 80.1 (77.5) 80.4 (77.7) 79.9 (77.0) 79.9 (76.8) 79.8 (76.8) 78.5 (75.4)

76.1 (73.4) 73.3 (70.7) 73.6 (70.9) 72.2 (69.3) 72.6 (69.4) 72.2 (69.2) 71.1 (68.0)

78.4 (75.6) 75.6 (72.9) 75.8 (73.2) 74.9 (72.0) 75.0 (71.9) 74.9 (71.9) 73.6 (70.5)

49.3 (46.5) 46.6 (44.0) 46.8 (44.2) 44.0 (41.1) 44.9 (41.8) 44.1 (41.1) 43.5 (40.4)

91.9 (89.7) 88.5 (86.4) 88.9 (86.7) 87.8 (85.5) 88.8 (86.3) 88.6 (86.1) 87.8 (85.3)

84.6 (82.5) 81.7 (79.5) 81.9 (79.7) 80.2 (77.9) 81.4 (78.9) 81.2 (78.7) 80.2 (77.7)

87.0 (84.9) 84.0 (81.9) 84.3 (82.1) 82.9 (80.6) 83.9 (81.4) 83.9 (81.4) 82.8 (80.3)

57.7 (55.5) 54.5 (52.3) 54.7 (52.5) 52.2 (49.9) 53.6 (51.1) 53.0 (50.5) 52.3 (49.8)

4-A 4-B 4-C 4-D 4-E 4-F 4-G

103.2 (99.6) 101.0 (97.1) 102.9 (99.0) 101.3 (97.7) 102.5 (98.6) 102.4 (98.4) 102.0 (98.0)

93.9 (90.4) 91.3 (87.4) 92.8 (88.9) 92.2 (88.7) 92.0 (88.2) 92.3 (88.4) 91.7 (87.7)

96.8 (93.3) 94.4 (90.4) 96.1 (92.2) 95.1 (91.6) 95.6 (91.8) 95.6 (91.7) 95.2 (91.2)

58.2 (54.7) 54.7 (50.8) 55.7 (51.8) 57.3 (53.8) 54.0 (50.2) 55.1 (51.2) 54.2 (50.2)

114.3 (111.4) 113.1 (109.9) 113.5 (110.5) 110.6 (107.9) 113.7 (110.5) 113.9 (110.7) 112.9 (109.6)

104.7 (101.9) 103.1 (99.9) 103.3 (100.3) 101.7 (99.0) 103.5 (100.3) 103.8 (100.6) 103.0 (99.7)

107.7 (104.9) 106.3 (103.1) 106.7 (103.7) 104.5 (101.8) 107.1 (103.9) 107.2 (104.0) 106.5 (103.2)

68.6 (65.8) 66.1 (62.9) 66.2 (63.2) 67.3 (64.6) 65.7 (62.5) 66.6 (63.4) 65.7 (62.4)

5-A 5-B 5-C 5-D 5-E 5-F 5-G

121.9 (117.6) 123.2 (118.5) 122.3 (117.9) 121.9 (117.7) 122.6 (117.9) 121.1 (116.8) 122.1 (117.6)

110.5 (106.2) 110.3 (105.6) 110.2 (105.8) 110.3 (106.1) 109.3 (104.5) 109.8 (105.5) 109.9 (105.4)

113.9 (109.6) 114.5 (109.8) 113.9 (109.5) 113.8 (109.5) 113.7 (109.0) 113.2 (108.9) 113.8 (109.4)

66.4 (62.1) 63.4 (58.7) 64.5 (60.1) 65.7 (61.5) 61.8 (57.0) 65.6 (61.3) 64.0 (59.5)

135.3 (131.8) 137.1 (133.2) 136.2 (132.5) 135.4 (131.9) 135.3 (131.4) 134.2 (130.7) 135.3 (131.6)

123.2 (119.8) 124.2 (120.3) 123.8 (120.2) 123.3 (119.8) 122.2 (118.3) 122.3 (118.7) 122.8 (119.0)

126.9 (123.4) 128.4 (124.5) 127.7 (124.0) 127.0 (123.5) 126.6 (122.7) 126.0 (122.4) 127.0 (123.2)

78.0 (74.6) 77.2 (73.3) 78.0 (74.3) 77.9 (74.4) 75.0 (71.1) 76.9 (73.4) 76.0 (72.3)

6-A 6-B 6-C 6-D 6-E 6-F 6-G 6-H 6-I

140.8 (135.6) 141.3 (135.9) 140.7 (135.4) 141.1 (135.9) 141.6 (136.1) 139.8 (134.8) 139.9 (134.8) 141.4 (135.8) 139.1 (133.7)

126.0 (120.8) 125.8 (120.4) 125.6 (120.3) 126.0 (120.8) 125.5 (120.0) 125.3 (120.3) 125.5 (120.4) 125.0 (119.5) 124.0 (118.6)

130.6 (125.3) 130.7 (125.4) 130.3 (125.0) 130.8 (125.5) 130.8 (125.3) 129.6 (124.5) 129.7 (124.7) 130.4 (124.9) 128.6 (123.2)

71.1 (65.9) 69.3 (63.9) 70.1 (64.8) 70.4 (65.2) 68.2 (62.7) 70.8 (65.8) 71.2 (66.1) 67.8 (62.3) 68.6 (63.2)

157.0 (152.6) 157.8 (153.2) 157.0 (152.5) 156.4 (152.0) 157.1 (152.4) 156.0 (151.8) 156.1 (151.8) 156.5 (151.8) 155.8 (151.2)

141.9 (137.5) 142.4 (137.8) 141.7 (137.2) 141.1 (136.7) 141.2 (136.6) 141.1 (136.8) 141.1 (136.9) 140.6 (135.9) 140.6 (136.1)

146.7 (142.3) 147.5 (142.9) 146.5 (142.1) 146.1 (141.7) 146.5 (141.8) 145.6 (141.4) 145.6 (141.4) 145.9 (141.2) 145.3 (140.8)

86.1 (81.7) 85.6 (81.0) 85.8 (81.4) 84.9 (80.5) 84.2 (79.6) 86.0 (81.8) 86.1 (81.9) 83.6 (78.9) 85.0 (80.5)

9

190.0 (182.6)

166.7 (159.3)

173.7 (166.4)

82.2 (74.9)

213.7 (207.2)

190.4 (183.8)

197.7 (191.1)

105.4 (98.9)

a

Counterpoise corrected values (superscript “cpc”) are given in parentheses. All other values are not corrected for the BSSE. The highest values in a column for a given n are underlined.

lowest energy structure according to all DFT methods. This structure is similar to the lowest energy structure 3-A of the SeO32-(H2O)3 cluster, yet with another water molecule donating one H-bond to a selenite oxygen and the other to a water molecule. This H-bond accepting water molecule is doubly H-bonded according to the M05-2X and PBE0 functionals (H-O · · · O angles of 27.4° and 29.2°, respectively), but only singly H-bonded according to B3LYP (H-O · · · O angle: 30.2°), so that one of the selenite oxygens is accepting either three or two H-bonds. Geometry optimizations of the anionic SeO3-(H2O)4 cluster with 4-A as the initial structure lead to structures with only two water molecules doubly H-bonded to selenite oxygen atoms according to all three functionals (Figure S1). Beginning with the SeO32-(H2O)5 clusters, it becomes difficult to distinguish between several energetically low-lying structures. As can be seen in Tables 2 and 3, there is a strong dependence on the used density functional as well as on which energy term is considered. Structure 5-A is the lowest energy structure at the B3LYP level using the ZPE correction (B3LYP/∆E0), and also in terms of the Gibbs free energy regardless of the functional. On the other hand, structure 5-B is the energetically most favorable cluster geometry with both the M05-2X and the PBE0 functionals regardless of ZPE correction and for all three functionals in terms of the enthalpy.

The comparison between the energies for the geometry 5-E and the other structures underlines the increasing importance of the water-water interactions. In this structure, one water molecule resides in the second hydration shell and donates two H-bonds to the first hydration shell, while accepting an H-bond from that. Despite its relatively weak selenite-water interaction as compared to the other structures, 5-E is the second most favorable structure in terms of B3LYP/∆Ee, PBE0/∆Ee, and PBE0/∆H, while it is only 1.20 or 1.06 kcal/mol higher in energy than the respective lowest energy structure 5-A or 5-B with the ZPE correction. In the case of the M05-2X functional, geometry optimizations of the anions with either 5-A or 5-B as the initial structures yield qualitatively similar structures, albeit with weaker selenite-water interaction. The same holds for the B3LYP and PBE0 functionals and structure 5-B. Consistent with the findings for structure 4-A, the arrangement of water molecules around the SeO3- anion is noticeably different from the dianionic case, when 5-A is studied with the B3LYP or PBE0 functional (Figure S2). Figure 3 gives an overview of the nine studied structures containing six water molecules. As can be seen in Tables 2 and 3, the C1 structure 6-A is the lowest energy geometry only in terms of B3LYP/∆E0 and PBE0/∆E0cpc. Notably, structure 6-E with one water molecule in the second hydration shell is

Microhydration of the Selenite Dianion

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TABLE 3: PBE0 and FC-MP2 Results (kcal/mol) for the Binding Energies (-∆Ee), ZPE-Corrected Binding Energies (-∆E0), Binding Enthalpies (-∆H), and Binding Gibbs Free Energies (-∆G) at 298.15 K and 1 atm for SeO32-(H2O)1-9 or SeO32-(H2O)1-3a PBE0/6-311++G(3df,2pd)

FC-MP2/6-311++G(3df,2pd)

structure -∆Ee (-∆Ee ) -∆E0 (-∆E0 ) -∆H (-∆H ) -∆G (-∆G ) -∆Ee (-∆Ee ) -∆E0 (-∆E0cpc) -∆H (-∆Hcpc) -∆G (-∆Gcpc) cpc

cpc

cpc

cpc

cpc

1-A 1-B

32.2 (31.3) 28.4 (27.5)

30.0 (29.0) 27.6 (26.7)

30.9 (29.9) 28.1 (27.2)

20.9 (20.0) 19.5 (18.5)

32.1 (29.9) 27.7 (25.5)

29.8 (27.6) 26.7 (24.5)

30.7 (28.4) 27.3 (25.0)

21.2 (18.9) 19.2 (16.9)

2-A 2-B 2-C

61.1 (59.2) 57.6 (55.8) 58.9 (56.7)

56.5 (54.6) 53.2 (51.4) 54.0 (51.7)

58.2 (56.3) 54.9 (53.0) 55.8 (53.6)

38.5 (36.6) 35.1 (33.2) 35.2 (33.0)

61.3 (57.0) 57.7 (53.5) 59.1 (54.5)

56.5 (52.3) 53.1 (48.9) 54.1 (49.4)

58.2 (53.9) 54.8 (50.6) 55.9 (51.3)

39.3 (35.0) 35.8 (31.5) 36.1 (31.5)

3-A 3-B 3-C 3-D 3-E 3-F 3-G

87.1 (84.4) 84.1 (81.4) 84.4 (81.7) 84.1 (81.1) 84.1 (80.9) 84.1 (80.9) 82.4 (79.4)

80.2 (77.4) 77.3 (74.5) 77.5 (74.8) 76.4 (73.5) 76.8 (73.6) 76.5 (73.3) 75.9 (72.9)

82.6 (79.8) 79.6 (76.9) 79.9 (77.2) 79.3 (76.3) 79.3 (76.1) 79.3 (76.1) 78.2 (75.2)

53.3 (50.5) 50.2 (47.5) 50.4 (47.7) 48.1 (45.1) 48.9 (45.7) 48.1 (45.0) 49.2 (46.2)

87.8 (81.7) 84.7 (78.6) 84.9 (78.8) 84.5 (78.1) 85.0 (78.4) 85.0 (78.3) 83.8 (77.2)

80.7 (74.6) 77.6 (71.5) 77.8 (71.7) 76.6 (70.2) 77.5 (70.9) 77.2 (70.5) 76.2 (69.6)

83.1 (76.9) 80.0 (73.9) 80.3 (74.1) 79.5 (73.1) 80.1 (73.5) 80.0 (73.3) 78.8 (72.2)

55.0 (48.9) 51.6 (45.5) 51.9 (45.8) 49.6 (43.2) 50.8 (44.2) 50.0 (43.3) 49.5 (42.9)

4-A 4-B 4-C 4-D 4-E 4-F 4-G

108.3 (104.7) 106.4 (102.4) 108.2 (104.2) 106.2 (102.6) 108.0 (104.0) 107.8 (103.7) 107.4 (103.2)

99.0 (95.4) 96.8 (92.7) 98.2 (94.2) 97.2 (93.6) 97.6 (93.5) 97.8 (93.7) 97.1 (92.9)

102.0 (98.4) 99.9 (95.9) 101.6 (97.6) 100.2 (96.6) 101.3 (97.2) 101.2 (97.1) 100.7 (96.6)

63.0 (59.4) 59.9 (55.8) 60.9 (56.9) 62.2 (58.6) 59.4 (55.3) 60.3 (56.2) 59.3 (55.2)

5-A 5-B 5-C 5-D 5-E 5-F 5-G

128.0 (123.6) 129.8 (124.9) 128.7 (124.1) 128.1 (123.7) 129.2 (124.1) 127.0 (122.5) 128.3 (123.7)

116.4 (112.0) 116.9 (112.0) 116.5 (112.0) 116.4 (112.0) 115.9 (110.9) 115.5 (111.0) 116.1 (111.5)

120.0 (115.6) 121.3 (116.3) 120.4 (115.9) 120.0 (115.7) 120.5 (115.5) 119.1 (114.6) 120.2 (115.6)

71.4 (67.0) 69.7 (64.8) 70.6 (66.1) 71.3 (67.0) 68.1 (63.1) 71.0 (66.5) 70.1 (65.4)

6-A 6-B 6-C 6-D 6-E 6-F 6-G 6-H 6-I

148.3 (142.9) 149.1 (143.3) 148.3 (142.7) 148.5 (142.9) 149.4 (143.6) 147.2 (141.9) 147.3 (142.0) 149.2 (143.3) 146.7 (141.1)

133.4 (127.9) 133.5 (127.8) 133.1 (127.6) 133.1 (127.6) 133.3 (127.4) 132.7 (127.4) 132.8 (127.5) 132.9 (127.1) 131.6 (126.0)

138.2 (132.7) 138.7 (132.9) 138.0 (132.4) 138.2 (132.6) 138.8 (132.9) 137.1 (131.9) 137.2 (132.0) 138.5 (132.6) 136.4 (130.7)

77.6 (72.2) 76.6 (70.8) 77.1 (71.5) 77.0 (71.5) 75.8 (70.0) 77.8 (72.6) 78.0 (72.7) 75.5 (69.6) 75.8 (70.2)

9

200.9 (193.0)

177.5 (169.6)

184.9 (177.0)

92.5 (84.6)

a

Counterpoise corrected values (superscript “cpc”) are given in parentheses. All other values are not corrected for the BSSE. The highest values in a column for a given n are underlined.

energetically most favorable in terms of B3LYP/∆Ee, PBE0/ ∆Ee, and PBE0/∆H. The M05-2X calculations yield the approximately Cs symmetric cluster 6-B as the lowest energy structure in terms of ∆Ee, ∆E0, and ∆H, like the PBE0 calculations do in terms of ∆E0. Structure 6-D is the lowest energy structure in terms of B3LYP/∆H, while all three density functionals yield 6-G as the structure with the lowest Gibbs free energy. The C3 symmetric structure 6-I, which includes three water molecules doubly H-bonded to selenite oxygens as well as a cyclic structure of three singly H-bonded water molecules, is relatively unfavorable according to all functionals. The five lowest energy structures presented, 6-A, 6-B, 6-D, 6-E, and 6-G, have only two (6-A, 6-E) or one (6-B, 6-D, 6-G) water molecule doubly H-bonded to selenite oxygen atoms, further highlighting the decreased importance of the selenite-water interaction as compared to water-water interactions. Geometry optimizations of the anionic cluster yielded qualitatively similar arrangements of the water molecules with 6-A as the initial structure and the M05-2X functional or with 6-B and all functionals. When structure 6-A is used in conjunction with the B3LYP or PBE0 functionals, the number of doubly H-bonded water molecules in the anionic cluster is reduced by one as compared to the dianion (Figure S3). SeO32-(H2O)9. The extensive search for minimum energy structures of more than six water molecules was not within the

scope of the present study, and only one structure of the SeO32-(H2O)9 cluster was calculated as presented in Figure 4 for the B3LYP optimized geometry. Geometry optimizations of the dianion using the M05-2X or PBE0 functionals and optimizations of the anion with the dianion structure as the initial geometry yielded qualitatively very similar structures, which are in very good approximation C3 symmetric. In this cluster, the pattern of surface hydration, which was already apparent for the lowest energy structures of the smaller clusters, is continued. Differently from the smaller clusters, there are no water molecules doubly H-bonded to selenite oxygens. Each water molecule donates a single H-bond to a selenite oxygen, all of which thus accept three H-bonds. As a result, of the nine water molecules, there are three each accepting two, one, or no H-bonds. 3.2. Structural Stability of Selenite. The geometry of the selenite substructure is distorted as a result of the selenite-water interaction. Figure 5a shows the average bond length between the selenium atom and the selenite oxygens for the various cluster sizes. The shortest average bond length is reached for the bare selenite dianion in the range between 1.687 Å for M052X and 1.706 Å for B3LYP with the longest average bond length of 1.712, 1.696, and 1.693 Å for B3LYP, PBE0, and M05-2X, respectively, observed in the cluster with four water molecules. For FC-MP2, the longest average bond length of

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Figure 3. Optimized structures of SeO32-(H2O)6 at the B3LYP/6311++G(3df,2pd) level. H-bonds are indicated by dotted double lines.

Figure 2. Optimized structures of SeO32-(H2O)4-5 at the B3LYP/6311++G(3df,2pd) level. H-bonds are indicated by dotted double lines.

1.700 Å is reached for the cluster with three water molecules. Figure 5b separates the Se-O bond lengths depending on the number of H-bonds accepted by selenite oxygens and reveals that the distance between selenium and a selenite oxygen strongly increases with the latter number. Yet, for a given number of accepted H-bonds, the Se-O bond length decreases with a growing size of the water cluster, as the disturbing effect of water is better distributed over the selenite substructure. These two different effects lead to the nonmonotonic dependence of the average bond length on the cluster size shown in Figure 5a. The calculated values are in good agreement with the extended X-ray absorption fine structure value of 1.70 ( 0.01 Å for the Se-O bond length in aqueous solution.16 The corresponding results for the anionic SeO3-(H2O)n clusters are shown in Figures S4a and S4b. In these systems, the average Se-O bond lengths are considerably shorter than for the dianion and, in absolute terms, less influenced by the hydration. Differently from the dianionic case, the average Se-O bond length varies between 1.661 Å for the bare SeO3structure and 1.665 Å for SeO3-(H2O)9 with UB3LYP, or between 1.639 and 1.643 Å (UM05-2X) or 1.645 and 1.648 Å (UPBE0). Figure 6 shows the average O-Se-O angle of selenite and the height of the selenite tetrahedron in dependence of the cluster

Figure 4. Optimized structure of SeO32-(H2O)9 at the B3LYP/6311++G(3df,2pd) level. H-bonds are indicated by dotted double lines.

size. Both quantities are correlated, and the strictly monotonic decrease of the O-Se-O angle is accompanied by the strictly monotonic increase of the tetrahedron height, with a maximum difference between the various methods of 0.4° and 0.01 Å, respectively. Figure S5 shows the corresponding results for the anionic clusters. A comparison of the values for the dianionic and anionic clusters reveals that the SeO3- substructure remains much closer to the trigonal planar structure of the neutral SeO3 molecule than the dianionic system. Depending on the functional, the O-Se-O angles are on average 6.3-7.0° larger in the anionic case (the differences between dianion and anion generally increase with the cluster size, with the only exception being the B3LYP results for the clusters with six and nine water molecules). Accordingly, the tetrahedron heights are, on average, larger by 0.19-0.20 Å in the dianionic case, for which they fall into the range ∼0.64-0.73 Å. These values are in good agreement with X-ray standing wave experiments, which have yielded tetrahedron heights of 0.63 ( 0.11 and 0.76 ( 0.09 Å for selenite dianions adsorbed on two different crystallographic faces of calcite.13

Microhydration of the Selenite Dianion

J. Phys. Chem. A, Vol. 114, No. 34, 2010 8955 TABLE 4: Charges on the Selenite Substructure, the Selenium Atom, and the Selenite Oxygen Atoms structurea

methodb

SeO3c

Sec

∑OSec

SeO32-

B3LYP M05-2X PBE0 B3LYP M05-2X PBE0 B3LYP M05-2X PBE0 B3LYP M05-2X PBE0 B3LYP M05-2X PBE0 B3LYP M05-2X PBE0 B3LYP M05-2X PBE0 B3LYP M05-2X PBE0

-2.00 -2.00 -2.00 -1.87 -1.92 -1.88 -1.79 -1.86 -1.80 -1.72 -1.82 -1.73 -1.66 -1.79 -1.69 -1.65 -1.72 -1.58 -1.52 -1.70 -1.57 -1.45 -1.66 -1.49

0.79 0.93 0.79 1.01 1.03 1.01 1.13 1.07 1.12 1.21 1.07 1.19 1.23 1.08 1.20 1.22 1.03 1.13 1.17 1.04 1.11 0.98 0.90 0.91

-2.79 -2.93 -2.79 -2.88 -2.95 -2.88 -2.92 -2.93 -2.91 -2.94 -2.89 -2.92 -2.89 -2.86 -2.89 -2.87 -2.76 -2.71 -2.70 -2.74 -2.68 -2.43 -2.55 -2.40

1-A 2-A 3-A 4-A

Figure 5. Average bond length dSe-O (Å) between the selenium atom and the oxygen atoms of the selenite substructure for the four different methods (B3LYP, black; M05-2X, blue; PBE0, red; FC-MP2, orange) with the 6-311++G(3df,2pd) basis set. The average bond length is calculated either on the basis of all three Se-O bonds (a) or using only selenite oxygen atoms with the same number of accepted H-bonds (b). In the latter case, this number falls into the range 0-3 for the different cluster sizes and is used as a symbol in the graph. All values refer to the lowest energy structures including the ZPE correction.

Figure 6. Average O-Se-O angle RO-Se-O (deg) of the selenite substructure (left ordinate, full symbols) and the height h of the selenite tetrahedron (Å), defined as the distance between the selenium atom and the plane of the selenite oxygen atoms (right ordinate, empty symbols), for the four different methods (B3LYP, black 9; M05-2X, blue b; PBE0, red [; FC-MP2, orange 2) with the 6-311++G(3df,2pd) basis set. All values refer to the lowest energy structures including the ZPE correction.

The above results evidence that SeO32- is preserved as a structural entity, but undergoes a considerable perturbation upon hydration. This is accompanied by the continuous transfer of negative charge from the selenite substructure to the water molecules as revealed by Mulliken population analysis100–103 results presented in Table 4. In the SeO32-(H2O)6 cluster, selenite has a negative charge that is lower by 0.48|e| (B3LYP), 0.30|e| (M05-2X), or 0.43|e| (PBE0) than for the isolated selenite dianion. The loss of negative charge proceeds even further with three more waters added, the respective differences between the cluster with nine water molecules and the isolated dianion being 0.55|e|, 0.34|e|, and 0.51|e|. For n ) 1-3, negative charge is primarily lost from the selenium atom, with the biggest loss occurring upon addition of one water molecule to the bare selenite dianion, whereas the

5-A 5-B 5-B 6-A 6-B 6-B 9

a Lowest energy structures of the SeO32-(H2O)n clusters in terms of ZPE-corrected total energies. b In all cases, the 6-311++ G(3df,2pd) basis set was used in conjunction with the different density functionals. c Mulliken population analysis charges in multiples of |e|.

amount of negative charge on the selenite oxygens is even increased (B3LYP, PBE0) or stays approximately constant (M05-2X). For n g 4, negative charge is increasingly lost from the selenite oxygens and is regained by the selenium atom, which apparently corresponds to the decrease of the number of water molecules doubly H-bonded to the selenite dianion. According to the M05-2X calculation, the selenium atom is even less positively charged in the SeO32-(H2O)9 cluster than in the bare selenite dianion. A comparison with sulfate-water clusters29 shows that the charge delocalization from selenite to water is one order of magnitude larger. The calculated charge difference between the clusters with one and six water molecules equals only 0.02|e| for sulfate,29 whereas it is as high as 0.35|e| (B3LYP), 0.22|e| (M05-2X), or 0.31|e| (PBE0) for selenite. 3.3. Hydration Shell Structure. As discussed in section 3.1, selenite-water interactions become less important as compared to water-water interactions upon an increase of the cluster size. This is further demonstrated by Figures 7 and S6, which show that the average distance between the selenium atom and the first hydration shell oxygens, dSe-O1HS, increases with the size of the dianionic and anionic clusters, respectively. In the case of the dianion, the values for dSe-O1HS increase from 3.42-3.47 Å (n ) 1) to 3.75-3.80 Å (n ) 9) depending on the functional. The calculations of the anion predict the larger dSe-O1HS values of 3.48-3.55 Å (n ) 1) and 3.78-3.92 Å (n ) 9), which corresponds to the weaker selenite-water interactions in this case. Notably, especially in the dianionic case, the agreement between the density functionals M05-2X and PBE0 as well as FC-MP2 is very good. B3LYP yields somewhat higher values than the other two functionals (except for n ) 6), which is due to the different lowest energy structure for B3LYP (6-A instead of 6-B).

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Figure 7. Average distance dSe-O1HS (Å) between the selenium atom and the first hydration shell oxygen atoms for the lowest energy structures (including ZPE correction) for the B3LYP (9), M05-2X (blue b), PBE0 (red [), and FC-MP2 (orange 2) methods.

Figure 8. Average H-bond distance dO(Se) · · · H (Å) between the selenite oxygens and respective hydrogens of the first hydration shell. All values refer to the lowest energy structures (including ZPE correction) for the B3LYP (9), M05-2X (blue b), PBE0 (red [), and FC-MP2 (orange 2) methods. Part a depicts the average H-bond lengths, while part b differentiates between doubly (full symbols) and singly (empty symbols) H-bonded water molecules.

The selenium-water distances are in reasonable agreement with those for other oxyanions. For sulfite- and sulfate-water clusters, an experimental value of ∼3.80 Å has been determined,104 while MP2/6-31+G(d) calculations of SO42-(H2O)1-6 have yielded 3.43-3.50 Å.31 For nitrate-water clusters, an experimental value in the range 3.14-3.50 Å has been reported, while the selenium-water oxygen distance has been assumed to be 3.95 Å for hydrated selenate.104 For some other oxyanions, ClO4-, CrO42-, MoO42-, WO42-, and PO43-, the average distance between the central atom and the oxygen atom of the first hydration shell has been experimentally determined to fall into the range 3.6-4.1 Å.104 The average H-bond lengths between selenite or the SeO3substructure and water for the dianionic SeO32-(H2O)n clusters and the anionic SeO3-(H2O)n clusters are presented in Figures 8 and S7, respectively. As can be seen, the H-bond length strongly depends on whether a water molecule is singly or doubly H-bonded to the selenite or SeO3- substructure, with the former H-bonds being shorter than the latter by 0.16-0.22 Å (B3LYP), 0.09-0.13 Å (M05-2X), or 0.07-0.16 Å (PBE0) for the dianion and by 0.19-0.24 Å (UB3LYP), 0.05-0.08 Å

Wicke and Meleshyn

Figure 9. Average bond lengths dO-H (Å) (left ordinate, solid lines, full symbols) and bond angles RH-O-H (deg) (right ordinate, dotted lines, empty symbols) for the first hydration shell water molecules. All values refer to the lowest energy structures (including ZPE correction) for the B3LYP (black 9), M05-2X (blue b), PBE0 (red [), and FC-MP2 (orange 2) methods.

(UM05-2X), or 0.03-0.23 Å (UPBE0) for the anion, depending on the cluster size. This dependence explains the increase of the average H-bond length from n ) 1 to n ) 3, and its tendency to decline for n > 4. As a result of this decline, the average H-bond length for the cluster with nine water molecules is very similar to that with only one water molecule, with the largest difference being just ∼0.02 Å for the anionic cluster according to UPBE0. A comparison of theory levels shows the best agreement between the M05-2X and PBE0 functionals, with the latter agreeing best with the FC-MP2 values for n ) 1-3. The average H-bond lengths, which fall into the range 1.85-1.93 Å (B3LYP), 1.82-1.90 Å (M05-2X), or 1.81-1.89 Å (PBE0) for the dianion and 2.03-2.16 Å (UB3LYP), 2.05-2.11 Å (UM05-2X), or 2.05-2.12 Å (UPBE0) for the anion, are in reasonable agreement with other quantum chemical investigations for the hydrated oxyanions nitrate and sulfate. H-bond lengths vary between 1.8 and 2.3 Å for nitrate clusters with one to eight water molecules studied at the B3LYP level, depending on the basis set.25–27 The average MP2/6-31+G(d) values for sulfate-water clusters with 1-12 water molecules fall into the range 1.86-2.02 Å.31,35 Similar to the case of the selenite-water clusters, upon increase of the cluster size the average H-bond length in sulfate-water clusters shows an initial increase,31 followed by a decrease for n > 8.35 The average oxygen-oxygen H-bond lengths between the selenite substructure and water fall into the range 2.78-2.83 Å (B3LYP), 2.75-2.80 Å (M05-2X), or 2.74-2.79 Å (PBE0) and are higher by 5.5-7.4% for the anion. For SO42-(H2O)1-6, MP2/ 6-31+G(d) calculations have yielded similar values of 2.81-2.90 Å.31 The average H-bond angle (H-O · · · O) between selenite and water is 7.8°-8.3° for n ) 9, depending on the functional, while the anionic values are higher by ∼70%. The average bond lengths and bond angles of the water molecules are shown in Figures 9 and S8 for the dianionic and anionic clusters, respectively. For the dianionic clusters, the bond lengths decrease by 0.012-0.013 Å from n ) 1 to n ) 9, indicating the decreasing influence of the selenite dianion as the cluster grows larger. For the anionic clusters, the corresponding difference is only 0.002 Å, highlighting the smaller influence of the singly charged anion. The average H-O-H bond angles, on the contrary, increase with increasing n. The difference between the clusters with n ) 9 and n ) 1 is 6.2°-8.7° for the dianionic system and 5.0°-5.2° for the anionic system. Figure 10 provides the average interwater H-bond lengths dO · · · H in the first hydration shell for both the dianionic and the

Microhydration of the Selenite Dianion

J. Phys. Chem. A, Vol. 114, No. 34, 2010 8957 sulfate SO42-, are not stable with respect to the removal of an electron from the highest occupied molecular orbital (HOMO).29,44,45 Using this experimental technique in conjunction with a theoretical approach very similar to the one employed in the present work, it has been shown that at least three water molecules are necessary to electronically stabilize the sulfate dianion.29 Adiabatical and vertical electron binding energies calculated in the present study for the microhydrated selenite clusters are given in Table 5. As can be seen, the three density functionals do not agree on the amount of water molecules necessary to stabilize the dianionic selenite-water cluster. The B3LYP and PBE0 calculations predict that the dianion becomes electronically stable only after addition of five water molecules as the ADE becomes positive. The M05-2X calculations, on the contrary, predict electronic stability after the addition of four water molecules. Further, more refined calculations and, ultimately, experiments are necessary to resolve this discrepancy. Comparable to the case of sulfate,29 the incremental stabilization due to the additional water molecules decreases rather sharply from n ) 1 to n ) 4 (Figure S10), while being almost constant for the larger clusters as also indicated by the ADE differences between the clusters with six and nine water molecules. The first three water molecules clearly have the strongest stabilizing effect, similar to the first four water molecules in sulfate-water clusters.29 The calculated ADE is associated with an ionization of electrons from the SeO3 structural unit of the [SeO3(H2O)n]2cluster, and not from the water molecules, because in all cases investigated, the HOMO of the dianion has an appearance similar to the lowest unoccupied β molecular orbital (β-LUMO) of the anion, as both are approximately linear combinations of the selenite oxygen p orbitals and a selenium hybrid orbital (shown exemplary in Figure S11 for the cluster with n ) 3). As in the case of SO42- though,32 not all of the high-lying molecular orbitals in the dianionic selenite-water clusters can be matched to respective R and β molecular orbitals of the anionic systems, highlighting the orbital relaxation and charge redistribution due to the ionization.32 3.5. Hydration Energies. The water molecule binding energies (Tables 2 and 3) that were already discussed in section 3.1 in the light of the relative stability of the clusters for the different numbers of water molecules show a very good agreement (in terms of -∆Eecpc, -∆E0cpc, and -∆Hcpc) between the B3LYP

Figure 10. Average interwater H-bond lengths dO · · · H (Å) for the first hydration shell water molecules of both the dianionic SeO32-(H2O)n (solid lines, full symbols) and the anionic SeO3-(H2O)n clusters (dotted lines, empty symbols) for the (U)B3LYP (black 9), (U)M05-2X (blue b), and (U)PBE0 (red [) methods. In the dianionic case, all values refer to the lowest energy structures (including ZPE correction), while the anionic results are based on structures optimized with these lowest energy structures as initial structures.

anionic clusters. The most important observation from this figure is that the difference between the dianionic and the anionic cluster becomes very small for n ) 9, underlining that the influence of the additional negative charge on the interwater H-bonding pattern becomes negligible. A similar pattern is observed for the O · · · O distances (2.92-3.09 Å for the dianionic clusters) as well as the H-O · · · O angles of the interwater H-bonds (for the dianionic clusters: 27.6°-29.7° for n ) 4 and 17.5°-18.0° for n ) 9). The dO · · · H values for the M05-2X and PBE0 functionals (2.00-2.20 Å) are in reasonable agreement with the results of minimum energy structures of SO42-(H2O)6-12 at the MP2/6-31+G(d) level (1.83-2.12 Å),35 whereas the B3LYP results are slightly higher (2.06-2.30 Å). The orientation angles of first hydration shell water molecules (according to a definition by Ohtaki and Radnai for ion-water clusters104) relative to the selenium atom strongly depend on whether a water molecule is singly or doubly H-bonded to selenite (see Figure S9). The values for singly or doubly H-bonded waters show only a slight variation across the cluster sizes. 3.4. Electronic Stability. Electrospray and photodetachment photoelectron spectroscopy has been used to probe the electronic stability of microsolvated oxyanion clusters and has revealed that some bare oxyanions, for example, selenate SeO42- and

TABLE 5: Adiabatic and Vertical Detachment Energies (eV) for Selenite-Water Clusters, Calculated with the 6-311++G(3df,2pd) Basis Set structure SeO3

2-

1-A

2-A

3-A

4-A

5-Ad

5-Be

6-Af

6-Bg

6-Eh

9

B3LYP ADEa VDEb

-2.55 -2.30

-1.82 -1.48

-1.15 -0.74

-0.56 -0.08

-0.14c 0.44

0.26c 0.90

0.23 0.78

0.58c 1.26

0.61 1.17

0.45 1.04

1.63 2.33

M05-2X ADEa VDEb

-2.46 -2.11

-1.69 -1.24

-0.99 -0.46

-0.36 0.25

0.12 0.79

0.56 1.29

0.48 1.16

0.94 1.67

0.88 1.57

0.71 1.44

1.96 2.79

PBE0 ADEa VDEb

-2.74 -2.45

-1.97 -1.60

-1.29 -0.83

-0.67 -0.14

-0.23c 0.39

0.18c 0.88

0.13 0.74

0.50c 1.24

0.52 1.14

0.36 1.01

1.57 2.33

a Adiabatic detachment energy based on an unrestricted calculation of the anion, including the ZPE correction, that is, taking into account the frequency calculation for the anion. b Vertical detachment energy based on an unrestricted calculation of the anion. c The geometry of this anion is qualitatively different from the geometry of the corresponding dianion. d Lowest energy structure (ZPE corrected) for SeO32-(H2O)5 at the B3LYP level. e Lowest energy structure (ZPE corrected) for SeO32-(H2O)5 at the M05-2X and PBE0 levels. Also the lowest energy structure at the B3LYP level, when the ZPE correction is not included. f Lowest energy structure (ZPE corrected) for SeO32-(H2O)6 at the B3LYP level. g Lowest energy structure (ZPE corrected) for SeO32-(H2O)6 at the M05-2X and PBE0 levels. h Lowest energy structure for SeO32-(H2O)6 at the B3LYP level, when the ZPE correction is not included.

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Figure 11. Differential water molecule binding energy ∆∆Eecpc(n) ) ∆Eecpc(n - 1) - ∆Eecpc(n) (kcal/mol) versus the number of water molecules for selenite at the B3LYP (9), M05-2X (blue b), PBE0 (red [), and FC-MP2 (orange 2, only for up to three water molecules) levels with the 6-311++G(3df,2pd) basis set. For the SeO32-(H2O)5 and SeO32-(H2O)6 clusters, the values for the lowest energy structures without ZPE correction are shown, that is, 5-B for all functionals, 6-B for M05-2X, and 6-E for B3LYP and PBE0 (see Tables 4 and 5). The values for the cluster with nine water molecules are (∆Eecpc(6) ∆Eecpc(9))/3. For comparison, previously reported values for sulfate29 and nitrate25 are also included. SO42- values have been calculated at the B3LYP/(aug-)cc-pVTZ//B3LYP/TZVP+ level, where the aug-ccpVTZ basis has been used on sulfur and oxygen and the cc-pVTZ basis on hydrogen atoms.29 The interaction of NO3- with water has been studied at the B3LYP/aug-cc-pVDZ level.25

functional and the FC-MP2 method for the lowest energy structures with up to three water molecules (1-A, 2-A, and 3-A). The PBE0 and M05-2X functionals produce consistently higher values, with PBE0 still providing better agreement with the B3LYP and FC-MP2 results than does M05-2X. The differential binding energy of the water molecules (Figure 11) drops very sharply at n ) 4 due to the perturbance of one of the three symmetrically doubly H-bonded water molecules from the SeO32-(H2O)3 cluster (Figure 1) by the fourth water molecule in the SeO32-(H2O)4 system (Figure 2). The only modest reduction of the differential binding energies for n g 4 is due to the growing importance of the water-water interaction relative to the selenitewater interaction for the larger clusters, as discussed above. Figure 11 also displays hydration energies for sulfate and nitrate reported previously by Wang et al.25,29 It can be seen that for n ) 1-3, the values for selenite are similar to those for sulfate, and are lower by ∼4 kcal/mol for n ) 4-6, whereas they are larger by at least ∼8 kcal/mol than those for nitrate. To estimate the free energy of hydration of the selenite dianion, cluster/continuum calculations were conducted. For the single-point continuum solvation calculations of selenite-water clusters, the optimized structures with the lowest Gibbs free energy were used, that is, 1-A, 2-A, 3-A, 4-A, 5-A, and 6-G for all theory levels (Tables 2 and 3). The extended results of these calculations are presented in Tables S1-S3, with the B3LYP functional generally showing the highest values for the hydration free energy and M05-2X the lowest. PBE0 and FCMP2 fall into the middle, exhibiting relatively good mutual agreement for n ) 1-3. The optimum number of explicit water molecules to be included in the cluster/continuum calculations can be assumed to correspond to the lowest free energy of hydration according to a variational principle.80,82 For the CPCM solvation method with UAKS atomic radii, the lowest hydration free energy corresponds to n ) 0, both for the monomer and for the cluster cycles; that is, in this case the cluster/continuum approach does not appear to improve upon the ordinary continuum solvation

Wicke and Meleshyn

Figure 12. Free energy of selenite hydration (kcal/mol) calculated according to the cluster/continuum approach using the CPCM solvation model with Klamt atomic radii at the B3LYP (black 9), M05-2X (blue b), PBE0 (red [), and FC-MP2 (orange 2, only for up to three water molecules) levels with the 6-311++G(3df,2pd) basis set. Both monomer (solid lines, full symbols) and cluster cycle results (dotted lines, empty symbols) are shown.

calculation results. On the other hand, the CPCM method with Klamt atomic radii yields a shallow minimum at n ) 2 or n ) 3 for all theory levels with the monomer cycle, while the cluster cycle produces the lowest values for the highest number of explicit water molecules (n ) 9 for the DFT methods and n ) 3 for FC-MP2) with local minima at n ) 3 for the DFT methods (Figure 12). Similarly, the IPCM solvation method shows (in all but one case) the lowest value for the highest number of explicit water molecules. These observations indicate that at least for the cluster cycle CPCM calculations with Klamt radii and the IPCM calculations, the inclusion of an even higher number of explicit water molecules may improve the estimated free energy of selenite hydration. Furthermore, improvements may be obtained by considering more than one geometry of water clusters and hydrated selenite clusters for a given number of water molecules83 or by carrying out geometry optimizations of the clusters in the solvent reaction field instead of singlepoint calculations.82 The exploration of these options was beyond the scope of the present study and should be the subject of a subsequent investigation. Here, the lowest calculated values for the free energy of selenite hydration for the different theory levels and continuum solvation methods are regarded as the best estimates. These values are summarized in Table 6 along with the respective cluster sizes. Because of lacking experimental or theoretical determinations of the free energy of selenite hydration, the values listed in Table 6 can only be compared to experimental values for related oxyanions, that is, sulfite SO32- (-309.5 kcal/mol), sulfate SO42(-258.1 kcal/mol), and selenate SeO42- (-215.1 kcal/mol),46 which are based on the choice of -252.4 kcal/mol for the free energy of hydration of the proton.46 The absolute values for selenite fall into the range 224.6-245.5 kcal/mol (Table 6) and are higher than the absolute value for selenate, which is in agreement with the ordering of the hydration free energies for sulfite and sulfate. The ratio of the values for sulfite and sulfate, if conveyed to selenite and selenate, results in an estimated hydration free energy of ∼ -258 kcal/mol for selenite, which is reasonably close to the calculated values. 4. Conclusions A detailed analysis of energetically low-lying structures of selenite-water clusters shows that for n ) 1-3, water molecules are doubly H-bonded to the selenite substructure in the lowest

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J. Phys. Chem. A, Vol. 114, No. 34, 2010 8959

TABLE 6: Free Energy of Hydration (kcal/mol) of Selenite SeO32-, Calculated with the 6-311++G(3df,2pd) Basis Set and the Cluster/Continuum Approach for Different Continuum Solvation Methods monomer cycle

cluster cycle

na

∆G*solv(SeO32-)

na

∆G*solv(SeO32-)

B3LYP CPCM/UAKSb CPCM/Klamtc IPCM

0 1 6

-230.0 -225.7 -224.6

0 9 6

-230.0 -229.9 -232.5

M05-2X CPCM/UAKSb CPCM/Klamtc IPCM

0 3 6

-234.1 -233.8 -237.8

0 9 6

-234.1 -245.5 -240.7

PBE0 CPCM/UAKSb CPCM/Klamtc IPCM

0 2 6

-231.2 -229.2 -231.6

0 9 6

-231.2 -235.3 -236.1

FC-MP2 CPCM/UAKSb CPCM/Klamtc IPCM

0 3 3

-229.7 -229.8 -229.8

0 3 3

-229.7 -232.9 -229.9

a Number of explicit water molecules that produces the lowest value of ∆G*solv(SeO32-) in the cluster/continuum approach. n ) 0 refers to the CPCM or IPCM value for bare selenite. b The CPCM continuum solvation method with the atomic radii dubbed UAKS in Gaussian 03. c The CPCM continuum solvation method with the atomic radii dubbed Klamt in Gaussian 03.

energy clusters. This pattern does not persist for the larger systems as water-water interactions gain relative importance as compared to the selenite-water interaction. Accordingly, selenium-water distances increase with the cluster size. Furthermore, intrawater O-H bond lengths increase and H-O-H bond angles decrease as the clusters grow larger, both changing toward the values characteristic for the water monomer. The number of doubly H-bonded water molecules gradually decreases to zero for n ) 9, while structures with water molecules in the second hydration become energetically competitive. Obtained structural parameters of the selenite hydration shell (selenium-water distances, selenite-water H-bond lengths, and interwater H-bond lengths) exhibit reasonable agreement with available experimental and theoretical results for other hydrated oxyanions as nitrate, sulfate, or selenate. The selenite substructure is preserved as a distinct structural entity upon hydration, although the calculations evidence considerable perturbations accompanied by the continuous transfer of negative charge from the selenite substructure to the water molecules. The calculated charge difference between the clusters with one and six water molecules amounts to 0.22|e|-0.35|e|, depending on the functional, and, notably, is thereby one order of magnitude larger than for sulfate.29 The additional negative charge in the dianionic system leads to stronger selenite-water interaction and a bigger influence on the intrawater geometry as compared to the anionic clusters. This discrepancy between dianion and anion is itself reduced with growing cluster size and becomes negligible for n ) 9. The calculated electron binding energies (adiabatic detachment energies) predict the electronic stability of the selenite-water clusters only for systems containing at least four or five water molecules, depending on the employed functional. More refined calculations and, ultimately, experiments are necessary to resolve this discrepancy. A comparison of the employed theoretical methods with regard to the hydration shell structure yielded the best agreement

between the M05-2X and PBE0 functionals, which also agree best with FC-MP2 for n ) 1-3. The B3LYP results deviate somewhat, exhibiting longer selenium-water distances, selenite-water H-bond lengths, and interwater H-bond lengths. Using a cluster/continuum approach and three different continuum solvation methods, the absolute value of the free energy of selenite hydration was determined to fall into the range 224.6-245.5 kcal/mol. While further refined studies may eventually provide an improved calculated value, the present result shows a reasonable agreement with the estimate based on available experimental values for sulfite, sulfate, and selenate. Acknowledgment. This work was supported by the German Research Foundation (DFG) under Project No. ME 3128/1-1. The calculations for this work were partially conducted on the computing clusters of the Regional Computing Centre for Lower Saxony (RRZN). We are grateful for the helpful comments from the anonymous reviewers. Supporting Information Available: Extensive figures and tables. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Morris, V. C.; Levander, O. A. J. Nutr. 1970, 100, 1383. (2) Young, V. R.; Nahapetian, A.; Janghorbani, M. Am. J. Clin. Nutr. 1982, 35, 1076. (3) Opinion of the Scientific Committee on Food on the Tolerable Upper Intake Level of Selenium, European Commission - Scientific Committee on Food, SCF/CS/NUT/UPPLEV/25 Final, 2000. (4) Bruno, J.; Ewing, R. C. Elements 2006, 2, 343. (5) Jiang, S.-S.; He, M.; Diao, L.-J.; Guo, J.-R.; Wu, S.-Y. Chin. Phys. Lett. 2001, 18, 746. (6) Technical Report 02-05 - Project Opalinus Clay - Safety Report; Nagra, Wettingen, Switzerland, 2002. (7) GRS-247 Endlagerung wa¨rmeentwickelnder radioaktiVer Abfa¨lle in Deutschland; Gesellschaft fu¨r Anlagen-und Reaktorsicherheit (GRS) ¨ ko-Institut e.V., 2008. mbH, O (8) Elrashidi, M. A.; Adriano, D. C.; Workman, S. M.; Lindsay, W. L. Soil Sci. 1987, 144, 141. (9) Se´by, F.; Potin-Gautier, M.; Giffaut, E.; Donard, O. F. X. Analusis 1998, 26, 193. (10) Johnson, T. M.; Bullen, T. D. ReV. Mineral. Geochem. 2004, 55, 289. (11) Bradbury, M. H.; Baeyens, B. J. Contam. Hydrol. 2003, 61, 329. (12) Madsen, F. T. Clay Miner. 1998, 33, 109. (13) Cheng, L.; Lyman, P. F.; Sturchio, N. C.; Bedzyk, M. J. Surf. Sci. 1997, 382, L690. (14) Schulthess, C. P.; Hu, Z. Soil Sci. Soc. Am. J. 2001, 65, 710. (15) Catalano, J. G.; Zhang, Z.; Fenter, P.; Bedzyk, M. J. J. Colloid Interface Sci. 2006, 297, 665. (16) Peak, D.; Saha, U. K.; Huang, P. M. Soil Sci. Soc. Am. J. 2006, 70, 192. (17) Behnsen, J.; Riebe, B. Appl. Geochem. 2008, 23, 2746. (18) Dousˇova´, B.; Fuitova´, L.; Herzegova´, L.; Grygar, T.; Kolousˇek, D.; Machovicˇ, V. Acta Geodyn. Geomater. 2009, 6, 193. (19) Charlet, L.; Scheinost, A. C.; Tournassat, C.; Greneche, J. M.; Ge´hin, A.; Ferna´ndez-Martı´nez, A.; Coudert, S.; Tisserand, D.; Brendle, J. Geochim. Cosmochim. Acta 2007, 71, 5731. (20) Scheinost, A. C.; Charlet, L. EnViron. Sci. Technol. 2008, 42, 1984. (21) Lo´pez de Arroyabe Loyo, R.; Nikitenko, S. I.; Scheinost, A. C.; Simonoff, M. EnViron. Sci. Technol. 2008, 42, 2451. (22) Scheinost, A. C.; Kirsch, R.; Banerjee, D.; Ferna´ndez-Martı´nez, A.; Zaenker, H.; Funke, H.; Charlet, L. J. Contam. Hydrol. 2008, 102, 228. (23) Missana, T.; Alonso, U.; Scheinost, A. C.; Granizo, N.; Garcı´aGutie´rrez, M. Geochim. Cosmochim. Acta 2009, 73, 6205. (24) Long, J. C. S.; Ewing, R. C. Annu. ReV. Earth Planet Sci. 2004, 32, 363. (25) Wang, X.-B.; Yang, X.; Wang, L.-S.; Nicholas, J. B. J. Chem. Phys. 2002, 116, 561. (26) Pathak, A. K.; Mukherjee, T.; Maity, D. K. J. Phys. Chem. A 2008, 112, 3399. (27) Goebbert, D. J.; Garand, E.; Wende, T.; Bergmann, R.; Meijer, G.; Asmis, K. R.; Neumark, D. M. J. Phys. Chem. A 2009, 113, 7584. (28) Cannon, W. R.; Pettitt, B. M.; McCammon, J. A. J. Phys. Chem. 1994, 98, 6225.

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