determine the effect of hydration where appropriate. We also examine the mechanism of interconversion of orthoboric acid and tetrahydroxoborate, which leads to a
discussion of the crystallography unobserved oxodihydroxoborate anion. We then
discuss the related crystallographically observed trioxoborate and dioxohydroxoborate anions.
2 Methods
Calculations were performed using Gaussian 03 [46]. The MP2 calculations utilize
the frozen core approximation, which is valid in nearly all cases except where
excessive core/valence mixing occurs (denoted c/v). The geometries were optimized using a stepping stone approach, in which the geometries at the levels HF/
6-31G*, HF/6-31+G*, HF/6-311+G*, B3LYP/6-31G*, B3LYP/6-31+G*, B3LYP/
6-311+G*, MP2/6-31G*, MP2/6-31+G*and MP2/6-311+G* were sequentially
optimized, with the geometry and molecular orbital reused for the subsequent level.
Default optimization specifications were normally 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 as required to speed up the optimizations.
Because frequency calculations are done 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 in
order to aid geometry convergence. To facilitate comparison with results from
gas-phase, solution, and solid phase measurements, no solvent corrections were
applied except via the supermolecule approach (explicit water molecules).
3 Results and Discussion
3.1 Orthoboric Acid, H 3 BO 3
Six forms of (ortho)boric acid were investigated (Fig. 1). Two of these (C 3h and C s #2)
were minima, with the C 3h structure being lower in energy by 22–26 kJ/mol
(Table 3). The C 3v structure, a third-order saddle point, was much higher in energy
(139–152 kJ/mol). The other three structures were transition states linking the minima.
Both the C s #1 and C s #3 linked the C s #2 structure to itself, whereas the C 1 structure
linked the C 3h and C s #2 structures. The C 1 structure was 38–43 kJ/mol higher than
the C 3h structure, whereas the C s #1 and C s #3 structures were 34–38 and
20–22 kJ/mol, respectively, higher than the C s #2.
An Ab Initio Study of Boric Acid, Borate …
149
discussion of the crystallography unobserved oxodihydroxoborate anion. We then
discuss the related crystallographically observed trioxoborate and dioxohydroxoborate anions.
2 Methods
Calculations were performed using Gaussian 03 [46]. The MP2 calculations utilize
the frozen core approximation, which is valid in nearly all cases except where
excessive core/valence mixing occurs (denoted c/v). The geometries were optimized using a stepping stone approach, in which the geometries at the levels HF/
6-31G*, HF/6-31+G*, HF/6-311+G*, B3LYP/6-31G*, B3LYP/6-31+G*, B3LYP/
6-311+G*, MP2/6-31G*, MP2/6-31+G*and MP2/6-311+G* were sequentially
optimized, with the geometry and molecular orbital reused for the subsequent level.
Default optimization specifications were normally 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 as required to speed up the optimizations.
Because frequency calculations are done 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 in
order to aid geometry convergence. To facilitate comparison with results from
gas-phase, solution, and solid phase measurements, no solvent corrections were
applied except via the supermolecule approach (explicit water molecules).
3 Results and Discussion
3.1 Orthoboric Acid, H 3 BO 3
Six forms of (ortho)boric acid were investigated (Fig. 1). Two of these (C 3h and C s #2)
were minima, with the C 3h structure being lower in energy by 22–26 kJ/mol
(Table 3). The C 3v structure, a third-order saddle point, was much higher in energy
(139–152 kJ/mol). The other three structures were transition states linking the minima.
Both the C s #1 and C s #3 linked the C s #2 structure to itself, whereas the C 1 structure
linked the C 3h and C s #2 structures. The C 1 structure was 38–43 kJ/mol higher than
the C 3h structure, whereas the C s #1 and C s #3 structures were 34–38 and
20–22 kJ/mol, respectively, higher than the C s #2.
An Ab Initio Study of Boric Acid, Borate …
149