An Ab Initio Investigation of the Hydration of Antimony(III)

: The energies, structures, and vibrational frequencies of [Sb(H 2 O) n ] 3+ , n = 0–9, 18 have been calculated at the Hartree–Fock and second-order Møller–Plesset levels of theory using the CEP, LANL2, and SDD effective core potentials in combination with their associated basis sets, or with the 6-31G* and 6-31+G* basis sets. The metal–oxygen distances and totally symmetric stretching frequency of the aqua ions were compared with each other and with related crystal structure measurements where available.


Introduction
Although the structure of many metal ions in solution is known, some remain elusive [1].Many are known to be toxic to man, but this is dependent on the oxidation state and speciation, which often depends on pH and the presence of counterions that solubilize the metal by complex formation.While computational chemistry can assist in supporting and rationalizing proposed speciation models, one drawback is that there are typically few all-electron basis sets that can be used.For elements with a high atomic number, relativistic effects can play an important role.Effective core potentials (ECPs) replace the explicit description of core electrons by a potential, and are paired with basis sets describing the outermost electrons.The ECPs represent the scalar relativistic effects only, but the spin-orbital relativistic effects should be small.In a previous work, we benchmarked some common ECPs for the aqua complexes of the heavy metals mercury(II) and thallium(III), both of which have valence electron configuration 5d 10 [2].It was shown that the ECPs reproduce the known hexacoordination of thallium(III), and supported a hexacoordinate model for mercury(II) over a heptacoordinate model.We also extended this work to lead(II), with valence electron configuration 6s 2 5d 10 [3].The presence of an ns 2 subshell can give rise to either hemidirected structures (which tend to be favored at lower coordination numbers) with ligands that are not symmetrically distributed around the central ion, or holodirected structures with a symmetrical distribution.No consensus exists on the coordination number of lead(II), with predictions ranging from 4 to 9, but our results were most consistent with a hemidirected hexaaqualead(II) species.For the smaller aquatin(II) ion (5s 2 4d 10 ), we found that the preferred hydration mode was a tricoordinate trigonal pyramidal triaquatin(II), agreeing with recent experiments [4].We extend our work now to antimony(III), which has the same valence electron configuration as tin(II) but a higher charge.The structure of aquaantimony(III) is unknown, so one of our aims is to predict its structure.The presence of the ns 2 subshell, as with lead(II) and tin(II), will be shown to have a pronounced effect on the structures compared to those without it.
The literature on the solution chemistry of antimony(III) is sparse.The solubility of rhombic Sb 2 O 3 was examined by Gayer and Garrett over half a century ago, and they proposed that dissolved antimony(III) exists as SbO + , Sb(OH) 3 , and SbO 2 − as the pH is increased [5].This was confirmed spectrophotometrically by Mishra and Gupta, who suggested that the neutral species could be either Sb(OH) 3 or SbO(OH) [6].Potentiometrically, SbO + is equivalent to Sb(OH) to exist only in strongly acidic solutions [7].Ahrland and Bovin examined the solution chemistry of antimony(III) oxide in perchloric and nitric acid [8].At an ionic strength of 5.0 mol/L, maintained by sodium perchlorate or nitrate, the two modifications of Sb 2 O 3 (s) are only metastable above a perchloric acid concentration of 0. .Zakaznova-Herzog and Seward used UV/visible spectroscopy to examine the equilibria of antimonous acid and was able to explain their results using the species H 3 SbO 3 (aq), H 4 SbO 3 + , and H 2 SbO 3 − (aq) from 25-300 • C, pH = 0.8-12.5 at a total antimony concentration of ~10 −4 mol/L [9].

Materials and Methods
Calculations were performed using Gaussian 98 [23].In this program version, the ability to calculate analytical frequencies of molecules in which core electrons are described by effective core potentials was introduced.Therefore, many variants of these were tried.The MP2 calculations use the frozen core approximation.A stepping-stone approach was used for geometry optimization, in which the geometries at the levels HF/CEP-4G, HF/CEP-31G*, HF/CEP-121G*, HF/LANL2MB, HF/LANL2DZ, and HF/SDD were sequentially optimized.For minimum energy structures, the MP2/CEP-31G* and MP2/CEP-121G* calculations were also performed.Calculations were also carried out using the 6-31G* and 6-31+G* basis sets on the atoms of the water molecules (5d) with an effective core potential and basis set on the metal ion (denoted as ECP+6-31G* or 6-31+G*).For shorthand, we denote the mixed basis sets as follows: CEP-121G* on Sb, 6-31G* on O,H, as basis set A; LANL2DZ on Sb, 6-31G* on O, H, as basis set B; SDD on Sb, 6-31G* on O,H, as basis set C; and the corresponding basis sets with diffuse functions are indicated by adding a "+" to the basis set name.Default optimization specifications were used.After each level, where possible, a frequency calculation was performed at the same level and the resulting Hessian was used in the following optimization.Z-matrix coordinates constrained to the appropriate symmetry were used to speed up the optimizations.Because frequency calculations are carried out at each level, any problems with the Z-matrix coordinates would manifest themselves by giving imaginary frequencies corresponding to modes orthogonal to the spanned Z-matrix space.The Hessian was evaluated at the first geometry (opt = CalcFC) for the first level in a series to aid geometry convergence.We note that, for the heavy elements only, the three different CEP basis sets are equivalent (CEP-121G*) but differ for the oxygen and hydrogen atoms.The choice of core electrons defining the pseudopotential depends on the specific core potential (CEP and LANL2, [Kr]4d 10 ; SDD, [Ar]3d 10 ).Gaussian 03 [24] and Gaussian 16 [25] were used to correct errors and omissions.
In many cases to follow, the symmetry of the minimum energy complexes was the same as those previously found for bismuth [26].To confirm these results, starting with high symmetry structures, systematic desymmetrization along the various irreducible representations was carried out [27,28].We did not employ an implicit solvation model for reasons described previously [3].

A Survey of Structures
Antimony(III) might be expected to show similar properties to tin(II), although the higher charge would cause stronger interactions with water molecules.The point group symmetry for mono-through octaaquaantimony(III) was initially usually found to be , and S 8 , respectively.The diaquaantimony(III) species, like lead and tin, ascended in symmetry to a planar C 2v structure at HF/LANL2MB.Initially, all attempts to generate a stable 7-coordinate antimony resulted in two water molecules moving to the second hydration sphere.We initially did not find a stable D 3 enneaaquaantimony(III) structure.
The results of the systematic desymmetrization procedure [27] for aquaantimony(III) are as follows (see Figures 1 and S1): • The monoaquaantimony(III) remains C 2v at all levels.

•
The 5+1] structures were stationary points, they were lower in energy than the [6+0] forms by about 25 kJ/mol.In some cases, they were actually minima (HF/CEP-121G*, all HF mixed basis sets).Given how shallow (or in some cases, nonexistent) the barrier to proton transfer is to give the deprotonated forms, it is reasonable to conclude that the aquaantimony(III) species would only exist in an extremely acidic solution.Combined with the results for the pentaaquaantimony(III), this suggests that antimony(III) is actually pentacoordinate square pyramidal.structures.This exemplifies the power of the systematic desymmetrization procedure in finding minimum energy structures that would otherwise be difficult to locate.In all cases where a seven-coordinate minimum energy structure exists (HF/CEP-31G*, HF/CEP-121G*, MP2/CEP-31G*, MP2/CEP-121G*, HF/C, HF/A+, HF/B+, HF/C+, MP2/A+), it is less stable than a [5+2] or [6+1] structure (or a proton transferred version thereof).The 7-coordinate structures are unlikely to have any significant population in an aqueous solution under ambient conditions.To summarize these results, it appears that the square pyramidal pentaaquaantimony(III) ion is the most stable aqua ion.There is a strong propensity to react with secondshell water molecules to form hydroxo complexes.While stable structures with coordination numbers between six and nine do exist at some levels of theory, the corresponding structures in which some waters have moved to the second hydration shell are more stable (in some cases, with proton transfer).These higher-coordination aqua complexes might exist at high pressures.The aqua ion, if it exists, would only exist at a very low pH.To summarize these results, it appears that the square pyramidal pentaaquaantimony(III) ion is the most stable aqua ion.There is a strong propensity to react with second-shell water molecules to form hydroxo complexes.While stable structures with coordination numbers between six and nine do exist at some levels of theory, the corresponding structures in which some waters have moved to the second hydration shell are more stable (in some cases, with proton transfer).These higher-coordination aqua complexes might exist at high pressures.The aqua ion, if it exists, would only exist at a very low pH.

The Sb-O Distance
In Figure 2, a plot of the dependence of the average Sb-O distance as a function of the coordination number n is given for all of the levels investigated.The Sb-O distance lengthened with the increase in coordination number.With the exception of HF/LANL2MB, the results were fairly uniform (for the most part, within 0.05 Å).The HF/LANL2MB level is the only Hartree-Fock level calculation using a minimal basis set on the valence shell of all atoms, and therefore does not have enough flexibility to fully describe the bonding between antimony(III) and oxygen.The pairs HF/CEP-31G* and HF/CEP-121G*, and MP2/CEP-31G* and MP2/CEP-121G*, were nearly coincident with each other, with the latter pair giving slightly longer bond lengths.The variation in the Sb-O distance with the level of theory was smaller than that of Sn-O [4].Based on our calculations, if the coordination number is indeed 5, then we would expect an average Sb-O distance of around 2.25 Å.

The Sb-O Distance
In Figure 2, a plot of the dependence of the average Sb-O distance as a function of the coordination number n is given for all of the levels investigated.The Sb-O distance lengthened with the increase in coordination number.With the exception of HF/LANL2MB, the results were fairly uniform (for the most part, within 0.05 Å).The HF/LANL2MB level is the only Hartree-Fock level calculation using a minimal basis set on the valence shell of all atoms, and therefore does not have enough flexibility to fully describe the bonding between antimony(III) and oxygen.The pairs HF/CEP-31G* and HF/CEP-121G*, and MP2/CEP-31G* and MP2/CEP-121G*, were nearly coincident with each other, with the latter pair giving slightly longer bond lengths.The variation in the Sb-O distance with the level of theory was smaller than that of Sn-O [4].Based on our calculations, if the coordination number is indeed 5, then we would expect an average Sb-O distance of around 2.25 Å.

The Sb-O Vibrational Frequency
In Figure 3, a plot of the dependence of the frequency of the most intense Raman Sb-O stretching mode as a function of the coordination number n is given for all of the levels investigated.As expected, this frequency drops with hydration number n.The minimal basis set levels HF/LANL2MB, and to some extent, HF/CEP-4G, are different than the others, having higher values.The CEP-4G basis set is a minimal basis set on oxygen and hydrogen, but is actually using the triple-zeta valence basis set (CEP-121G) on the antimony atom.There is a levelling off of the frequency, and then a bigger drop at n = 6.For n = 4 and 5, the vibrational mode is somewhat more localized, being due predominantly to either the equatorial oxygen motion (n = 4) or the apical oxygen motion (n = 5).The HF/CEP-31G*, HF/CEP-121G*, MP2/CEP-31G*, MP2/CEP-121G*, and MP2/A+ levels form the group with the lowest vibrational frequencies.The HF calculations using the SDD basis set on Sb form a group with the highest vibrational frequencies.For the levels using split

The Sb-O Vibrational Frequency
In Figure 3, a plot of the dependence of the frequency of the most intense Raman Sb-O stretching mode as a function of the coordination number n is given for all of the levels investigated.As expected, this frequency drops with hydration number n.The minimal basis set levels HF/LANL2MB, and to some extent, HF/CEP-4G, are different than the others, having higher values.The CEP-4G basis set is a minimal basis set on oxygen and hydrogen, but is actually using the triple-zeta valence basis set (CEP-121G) on the antimony atom.There is a levelling off of the frequency, and then a bigger drop at n = 6.For n = 4 and 5, the vibrational mode is somewhat more localized, being due predominantly to either the equatorial oxygen motion (n = 4) or the apical oxygen motion (n = 5).The HF/CEP-31G*, HF/CEP-121G*, MP2/CEP-31G*, MP2/CEP-121G*, and MP2/A+ levels form the group with the lowest vibrational frequencies.The HF calculations using the SDD basis set on Sb form a group with the highest vibrational frequencies.For the levels using split valence basis sets, if the coordination number is indeed 5, then the predictions for the Sb-O symmetric stretching motion center around 450 ± 30 cm −1 .In solution, the effect of the second hydration shell would increase this by an estimated 60 cm −1 , meaning that our best guess for the Sb-O mode in an aqueous solution would be 510 cm −1 .
Liquids 2024, 4, FOR PEER REVIEW 8 valence basis sets, if the coordination number is indeed 5, then the predictions for the Sb-O symmetric stretching motion center around 450 ± 30 cm −1 .In solution, the effect of the second hydration shell would increase this by an estimated 60 cm −1 , meaning that our best guess for the Sb-O mode in an aqueous solution would be 510 cm −1 .

Conclusions
The common CEP, LANL2, and SDD pseudopotentials were paired with various basis sets to study the hydrated antimony(III) ion.Calculations using minimal basis sets (HF/LANL2MB, HF/CEP-4G) performed poorly.The calculated structures of the aqua

Conclusions
The common CEP, LANL2, and SDD pseudopotentials were paired with various basis sets to study the hydrated antimony(III) ion.Calculations using minimal basis sets (HF/LANL2MB, HF/CEP-4G) performed poorly.The calculated structures of the aqua complexes compared favorably with the crystal structures of the oxides/hydroxides.Symmetry can be used to guide the search for new structures and to rule out structures.For the smaller coordination numbers, the effect of the ns 2 subshell is clearly to form a hemidirected structure in which the electrons act similarly as a ligand or lone pair would.

Figure 1 .
Figure 1.The minimum energy structures of aquaantimony(III) and related species.

Figure 1 .
Figure 1.The minimum energy structures of aquaantimony(III) and related species.

Figure 2 .
Figure 2. The dependence of the average Sb-O distance (Å) in Sb(H2O)n 3+ on the coordination number n and level of theory.

Figure 2 .
Figure 2. The dependence of the average Sb-O distance (Å) in Sb(H 2 O) n 3+ on the coordination number n and level of theory.

Figure 3 .
Figure 3.The dependence of the most intense Raman Sb-O frequency (cm −1 ) in Sb(H2O)n 3+ on the coordination number n and level of theory.

Figure 3 .
Figure 3.The dependence of the most intense Raman Sb-O frequency (cm −1 ) in Sb(H 2 O) n 3+ on the coordination number n and level of theory.