3.4.9 [B 2 O 2 (OH) 4 ]
−
The diborate ion, [B 2 O 2 (OH) 3 ]
−
, is shown in Fig. 10. Initially, two C 2v structures
were tried. Both had imaginary B 1 , B 2 , and A 2 modes. These lead to C s #1/3, C s #2/
4, and C 2 #1/2, respectively. The structure C s #3 coalesced into C s #1. None of
these structures were stable. The structure C s #1 desymmetrized to C 1 #1. The
structure C s #2, desymmetrized via C 1 #2 to coalesce with C 1 #1. The structure C 2
#1 also desymmetrized via C 1 #3 to coalesce with C 1 #1. The structure C 2 #2
desymmetrized to C 1 #4. The structure C s #4 desymmetrized via C 1 #5 to coalesce
to C 1 #4 (except at MP2/6-311+G*).
3.4.10 [B 2 O 2 (OH) 4 ]
0
The diboric acid, [B 2 O 2 (OH) 2 ]
0 , which is an isomer of metaboric acid, is also given
in Fig. 10. The two forms examined, C 2h and C 2v , were both minima, with C 2h
slightly lower in energy.
3.5 Structural Comparisons
A comparison of the calculated ab initio with the crystallographically observed
boron-oxygen bond lengths is given in Table 6. For ease of reporting, we take
high-symmetry structures in some cases and average the crystal structures
according to the approximate symmetry mentioned. Inspection of Table 6 reveals
that in most instances, calculations with the 6-31+G* and 6-311+G* basis sets are
within 0.01 Å of each other, the exception being [B 4 O 5 (OH) 4 ]
2−
, where the conformation of the hydroxyl on the tetrahedral boron is significantly different. For the
singly and doubly charged anions, the 6-31G* results are, with one exception,
within 0.01 Å of the 6-31+G* results, but the more highly charged anions show
more deviation. The B3LYP and MP2 calculations are usually within 0.01 Å of
each other, except for the highly charged [B 4 O 9 ]
6− anion. The Hartree-Fock calculations tend to be slightly shorter. There seems to be mostly good agreement
between the crystal structures and the correlated calculations with a diffuse basis
set, with the experiments usually being slightly shorter. The agreement between
experiment and theory here is rather remarkable in the sense that the calculations
correspond to a gas-phase ion (no medium effects were included in the calculation),
whereas the experiment corresponds to the solid-state, surrounded by counterions.
We may compare our results to previous ab initio calculations (see Introduction).
Although Zhang et al. [95] completely optimized B 2 O(OH) 4 with symmetry C 2v
(our #3), C s , and C 2 (our #3), our lowest energy structure corresponds to a planar C s
structure with an internal hydrogen bond. However, in most cases, the previous
calculations, if they exist, are comparable to ours.
A Crystallographic Review of Alkali Borate Salts …
135
−
The diborate ion, [B 2 O 2 (OH) 3 ]
−
, is shown in Fig. 10. Initially, two C 2v structures
were tried. Both had imaginary B 1 , B 2 , and A 2 modes. These lead to C s #1/3, C s #2/
4, and C 2 #1/2, respectively. The structure C s #3 coalesced into C s #1. None of
these structures were stable. The structure C s #1 desymmetrized to C 1 #1. The
structure C s #2, desymmetrized via C 1 #2 to coalesce with C 1 #1. The structure C 2
#1 also desymmetrized via C 1 #3 to coalesce with C 1 #1. The structure C 2 #2
desymmetrized to C 1 #4. The structure C s #4 desymmetrized via C 1 #5 to coalesce
to C 1 #4 (except at MP2/6-311+G*).
3.4.10 [B 2 O 2 (OH) 4 ]
0
The diboric acid, [B 2 O 2 (OH) 2 ]
0 , which is an isomer of metaboric acid, is also given
in Fig. 10. The two forms examined, C 2h and C 2v , were both minima, with C 2h
slightly lower in energy.
3.5 Structural Comparisons
A comparison of the calculated ab initio with the crystallographically observed
boron-oxygen bond lengths is given in Table 6. For ease of reporting, we take
high-symmetry structures in some cases and average the crystal structures
according to the approximate symmetry mentioned. Inspection of Table 6 reveals
that in most instances, calculations with the 6-31+G* and 6-311+G* basis sets are
within 0.01 Å of each other, the exception being [B 4 O 5 (OH) 4 ]
2−
, where the conformation of the hydroxyl on the tetrahedral boron is significantly different. For the
singly and doubly charged anions, the 6-31G* results are, with one exception,
within 0.01 Å of the 6-31+G* results, but the more highly charged anions show
more deviation. The B3LYP and MP2 calculations are usually within 0.01 Å of
each other, except for the highly charged [B 4 O 9 ]
6− anion. The Hartree-Fock calculations tend to be slightly shorter. There seems to be mostly good agreement
between the crystal structures and the correlated calculations with a diffuse basis
set, with the experiments usually being slightly shorter. The agreement between
experiment and theory here is rather remarkable in the sense that the calculations
correspond to a gas-phase ion (no medium effects were included in the calculation),
whereas the experiment corresponds to the solid-state, surrounded by counterions.
We may compare our results to previous ab initio calculations (see Introduction).
Although Zhang et al. [95] completely optimized B 2 O(OH) 4 with symmetry C 2v
(our #3), C s , and C 2 (our #3), our lowest energy structure corresponds to a planar C s
structure with an internal hydrogen bond. However, in most cases, the previous
calculations, if they exist, are comparable to ours.
A Crystallographic Review of Alkali Borate Salts …
135