tried. The D 2d structure was stable at B3LYP/6-31G* and MP2/6-31G*, but had an
imaginary E mode at the other levels, suggesting desymmetrization to either a C 2 #1
or C s #1. The C 2 #1 is stable at all levels except HF/6-31+G* and HF/6-31+G*, for
which the C s #1 is stable. The D 2h structure is unstable at all levels. Desymmetrization along an imaginary A u mode at all levels results in ascension in symmetry to the D 2d structure. Desymmetrization along the B 2u , B 3u , and B 3g modes
give unstable C 2v #1 (all levels except B3LYP/6-31G*), C 2v #2 (MP2/6-31+G* and
MP2/6-311+G*), and C 2h (B3LYP/6-31+G* and B3LYP/6-311+G*) structures.
Desymmetrization of these structures leads to structures already observed.
3.4.2 [B 2 (OH) 7 ]
−
In the polyborate structures discussed thus far, any oxygen that is bound to two
boron atoms is not bound to a hydrogen. However, the diborate species [B 2 (OH) 7 ]
−
with a bridging hydroxide was postulated as the intermediate to explain the boric
acid–borate interchange in aqueous solution as studied by
11 B NMR [101]. Such an
intermediate may lie on the reaction path to condensation to form the other
polyborates. It is expected that the hydrogen of the bridging oxygen would be quite
acidic and easily lost.
The diborate ion, [B 2 (OH) 7 ]
− , is given in Fig. 5. Initially, two C 2v structures
were tried. These had numerous imaginary A 2 , B 1 , and B 2 frequencies, which
suggested desymmetrization to two C 2 and four C s structures. Neither C 2 structure
was stable, possessing an imaginary B mode. The C s #1 and C s #2 structures,
derived from C 2v #1, were not stable, containing A” imaginary frequencies. The C s
#3 and C s #4 structures, derived from C 2v #2, either dissociated into a hydrogen
bonded [B(OH) 4 ]
−
…B(OH) 3 hydrogen bonded complex (C s #3) or coalesced into
C s #2. The C 2 structures desymmetrized into the corresponding stable C 1 #1 and #2
structures. The C s structures desymmetrized into the corresponding stable C 1 #3 and
#4 structures. The four stable structures are quite close in energy, and the gas-phase
association energy of boric acid and borate is in the range −47.9 to 108.5 kJ/mol.
3.4.3 [B 2 (OH) 6 ]
0
We were curious to see whether a dimer of boric acid could exist possessing a
single hydroxyl bridge. The bridge necessarily converts one of the boron atoms into
tetrahedral, and under the constraint of C s symmetry, results in eight possible
structures. None of these are stable at the HF/6-31G* level, resulting in fragmentation of the B-O bond to give hydrogen bonded structures. In addition, structure C s
#1 is unstable at all levels investigated. These results suggest that such a structure
does not exist.
Next, a dimer of boric acid containing two bridging hydroxyls was investigated.
The optimized structures are shown in Fig. 6. Initially two structures of D 2h
symmetry were considered. Neither of these structures were stable, possessing
128
C. C. Pye
imaginary E mode at the other levels, suggesting desymmetrization to either a C 2 #1
or C s #1. The C 2 #1 is stable at all levels except HF/6-31+G* and HF/6-31+G*, for
which the C s #1 is stable. The D 2h structure is unstable at all levels. Desymmetrization along an imaginary A u mode at all levels results in ascension in symmetry to the D 2d structure. Desymmetrization along the B 2u , B 3u , and B 3g modes
give unstable C 2v #1 (all levels except B3LYP/6-31G*), C 2v #2 (MP2/6-31+G* and
MP2/6-311+G*), and C 2h (B3LYP/6-31+G* and B3LYP/6-311+G*) structures.
Desymmetrization of these structures leads to structures already observed.
3.4.2 [B 2 (OH) 7 ]
−
In the polyborate structures discussed thus far, any oxygen that is bound to two
boron atoms is not bound to a hydrogen. However, the diborate species [B 2 (OH) 7 ]
−
with a bridging hydroxide was postulated as the intermediate to explain the boric
acid–borate interchange in aqueous solution as studied by
11 B NMR [101]. Such an
intermediate may lie on the reaction path to condensation to form the other
polyborates. It is expected that the hydrogen of the bridging oxygen would be quite
acidic and easily lost.
The diborate ion, [B 2 (OH) 7 ]
− , is given in Fig. 5. Initially, two C 2v structures
were tried. These had numerous imaginary A 2 , B 1 , and B 2 frequencies, which
suggested desymmetrization to two C 2 and four C s structures. Neither C 2 structure
was stable, possessing an imaginary B mode. The C s #1 and C s #2 structures,
derived from C 2v #1, were not stable, containing A” imaginary frequencies. The C s
#3 and C s #4 structures, derived from C 2v #2, either dissociated into a hydrogen
bonded [B(OH) 4 ]
−
…B(OH) 3 hydrogen bonded complex (C s #3) or coalesced into
C s #2. The C 2 structures desymmetrized into the corresponding stable C 1 #1 and #2
structures. The C s structures desymmetrized into the corresponding stable C 1 #3 and
#4 structures. The four stable structures are quite close in energy, and the gas-phase
association energy of boric acid and borate is in the range −47.9 to 108.5 kJ/mol.
3.4.3 [B 2 (OH) 6 ]
0
We were curious to see whether a dimer of boric acid could exist possessing a
single hydroxyl bridge. The bridge necessarily converts one of the boron atoms into
tetrahedral, and under the constraint of C s symmetry, results in eight possible
structures. None of these are stable at the HF/6-31G* level, resulting in fragmentation of the B-O bond to give hydrogen bonded structures. In addition, structure C s
#1 is unstable at all levels investigated. These results suggest that such a structure
does not exist.
Next, a dimer of boric acid containing two bridging hydroxyls was investigated.
The optimized structures are shown in Fig. 6. Initially two structures of D 2h
symmetry were considered. Neither of these structures were stable, possessing
128
C. C. Pye