initially to result in partial hydrolysis into discrete structural motifs already present
in the solid state, followed by equilibration in solution.
Ab initio calculations have been carried out on some of the discrete ions seen in
the crystal structures. Gupta and Tossell fixed the symmetry of B 2 O(OH) 4 to C 2v
(B-O fixed at 1.353 Å (HF/STO-3G) and 1.375 Å (4-31G), and found that the B-O-B
linkage was bent [94]. They also found B-O distances of 1.430 Å and 1.279 Å for
B 3 O 6
3− at HF/STO-3G, which compares well with the crystal structure. Zhang et al.
[95] completely optimized B 2 O(OH) 4 with symmetry C 2v (HF/STO-3G, 6-31G*), C s
(HF/6-31G) and C 2 (HF/STO-3G, 3-21G*, 4-31G, 6-31G, 6-31G*). They also
calculated the B 2 O(OH) 6
2− (C 2v ), B 2 O(OH) 5
− (C s ), B 3 O 3 (OH) 4
− (C 2v ) and B 3 O 3
(OH) 5
2− (C s ) ions at HF/STO-3G. Oi calculated B 2 O(OH) 4 (C 2 ), B 2 O(OH) 5
− (C 1 ), and
B 2 O(OH) 6
2− (C 2 ) at HF/6-31G* [96]. In addition, Oi also calculated B 3 O 3 (OH) 4
−
(C 2 ), B 3 O 3 (OH) 5
2− (C 1 ), B 4 O 5 (OH) 4
2− (C 2 ), and B 5 O 6 (OH) 4
− (S 4 ) at HF/6-31G* [97].
A combined Raman and DFT (B3LYP/aug-cc-pVDZ) investigation of B 2 O(OH) 4 ,
B 2 O(OH) 5
−
, B 2 O(OH) 6
2−
, B 3 O 3 (OH) 4
−
, B 3 O 3 (OH) 5
2−
, B 3 O 3 (OH) 6
3− , B 4 O 5 (OH) 4
2−
,
and B 5 O 6 (OH) 4
− was presented by Zhou et al [98]. In addition to these ions, two
heptamers B 7 O 9 (OH) 5
2− were calculated by Beckett et al. at B3LYP/6-311++G(d, p)
[99].
2 Methods
Calculations were performed using Gaussian 03 [100]. The MP2 calculations use
the frozen core approximation. The geometries were optimized using a stepping
stone approach, in which 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 orbitals 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.
A Crystallographic Review of Alkali Borate Salts …
119
in the solid state, followed by equilibration in solution.
Ab initio calculations have been carried out on some of the discrete ions seen in
the crystal structures. Gupta and Tossell fixed the symmetry of B 2 O(OH) 4 to C 2v
(B-O fixed at 1.353 Å (HF/STO-3G) and 1.375 Å (4-31G), and found that the B-O-B
linkage was bent [94]. They also found B-O distances of 1.430 Å and 1.279 Å for
B 3 O 6
3− at HF/STO-3G, which compares well with the crystal structure. Zhang et al.
[95] completely optimized B 2 O(OH) 4 with symmetry C 2v (HF/STO-3G, 6-31G*), C s
(HF/6-31G) and C 2 (HF/STO-3G, 3-21G*, 4-31G, 6-31G, 6-31G*). They also
calculated the B 2 O(OH) 6
2− (C 2v ), B 2 O(OH) 5
− (C s ), B 3 O 3 (OH) 4
− (C 2v ) and B 3 O 3
(OH) 5
2− (C s ) ions at HF/STO-3G. Oi calculated B 2 O(OH) 4 (C 2 ), B 2 O(OH) 5
− (C 1 ), and
B 2 O(OH) 6
2− (C 2 ) at HF/6-31G* [96]. In addition, Oi also calculated B 3 O 3 (OH) 4
−
(C 2 ), B 3 O 3 (OH) 5
2− (C 1 ), B 4 O 5 (OH) 4
2− (C 2 ), and B 5 O 6 (OH) 4
− (S 4 ) at HF/6-31G* [97].
A combined Raman and DFT (B3LYP/aug-cc-pVDZ) investigation of B 2 O(OH) 4 ,
B 2 O(OH) 5
−
, B 2 O(OH) 6
2−
, B 3 O 3 (OH) 4
−
, B 3 O 3 (OH) 5
2−
, B 3 O 3 (OH) 6
3− , B 4 O 5 (OH) 4
2−
,
and B 5 O 6 (OH) 4
− was presented by Zhou et al [98]. In addition to these ions, two
heptamers B 7 O 9 (OH) 5
2− were calculated by Beckett et al. at B3LYP/6-311++G(d, p)
[99].
2 Methods
Calculations were performed using Gaussian 03 [100]. The MP2 calculations use
the frozen core approximation. The geometries were optimized using a stepping
stone approach, in which 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 orbitals 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.
A Crystallographic Review of Alkali Borate Salts …
119