agreement with the IR spectra measured in an argon matrix, and with most modes
of solid and aqueous boric acid. However, the in-plane BO 3 deformation, HOB
deformation, and OH stretching frequencies differ, which would be expected,
because in solid boric acid, the molecules are held together by a network of
hydrogen bonds. It might be expected that aqueous solutions may exhibit similar
behavior to the solid. The vibrational spectra of the higher-energy C s #2 conformation is also given in Table 6. The E modes correlate with 2A modes of the same
reflection symmetry. The main differences in the vibrational frequencies of the C s
#2 conformer are that the BOH torsion is much lower, the in plane BO 3 deformation
is somewhat higher in frequency, the out of plane BO 3 deformation is slightly
lower, the symmetric BO stretch is slightly higher, one component of the HOB
deformation and asymmetric B-O stretch is somewhat lower, and the OH frequencies slightly higher.
Table 4 Geometrical Parameters of the C 3h form of B(OH) 3 . n/r = not reported
Level
B-O (Å)
O-H (Å)
B-O-H angle (deg.)
HF/6-31G*
1.3581
0.9466
112.56
HF/6-31+G*
1.3584
0.9471
113.69
HF/6-311+G*
1.3553
0.9401
113.99
B3LYP/6-31G*
1.3721
0.9675
110.90
B3LYP/6-31+G*
1.3729
0.9683
112.46
B3LYP/6-311+G*
1.3691
0.9630
113.01
MP2/6-31G*
1.3762
0.9700
110.38
MP2/6-31+G*
1.3780
0.9722
111.77
MP2/6-311+G*
1.3709
0.9614
112.25
Literature
HF/STO-3G [2, 47]
1.389
n/r
114 (fixed)
HF/STO-3G [48]
1.364
0.98
110
HF/4-31G [48]
1.364
0.95
121
HF/3-21G* [49]
1.377
0.962
n/r
HF/6-31G [49]
1.370
0.947
n/r
HF/6-31G* [49]
1.358
0.947
n/r
HF/6-31G* [2, 49]
1.358
0.947
112.6
MP2/6-31G** [50]
1.357
0.942
113.0
B3LYP/6-311++G** [51]
1.380
0.971
112.6
B3LYP/6-311++G** [52]
1.370
0.962
112.8
MP2/6-311++G** [52]
1.373
0.961
110.7
B3LYP/aug-cc-pVQZ [53]
1.369
0.960
113.1
MP2/aug-cc-pVTZ [53]
1.374
0.962
111.5
MP2/aug-cc-pVQZ [53]
1.370
0.959
111.8
QCISD/6-311++G** [53]
1.371
0.959
111.1
B3LYP/aug-cc-pVDZ [54]
1.376
n/r
n/r
An Ab Initio Study of Boric Acid, Borate …
151
of solid and aqueous boric acid. However, the in-plane BO 3 deformation, HOB
deformation, and OH stretching frequencies differ, which would be expected,
because in solid boric acid, the molecules are held together by a network of
hydrogen bonds. It might be expected that aqueous solutions may exhibit similar
behavior to the solid. The vibrational spectra of the higher-energy C s #2 conformation is also given in Table 6. The E modes correlate with 2A modes of the same
reflection symmetry. The main differences in the vibrational frequencies of the C s
#2 conformer are that the BOH torsion is much lower, the in plane BO 3 deformation
is somewhat higher in frequency, the out of plane BO 3 deformation is slightly
lower, the symmetric BO stretch is slightly higher, one component of the HOB
deformation and asymmetric B-O stretch is somewhat lower, and the OH frequencies slightly higher.
Table 4 Geometrical Parameters of the C 3h form of B(OH) 3 . n/r = not reported
Level
B-O (Å)
O-H (Å)
B-O-H angle (deg.)
HF/6-31G*
1.3581
0.9466
112.56
HF/6-31+G*
1.3584
0.9471
113.69
HF/6-311+G*
1.3553
0.9401
113.99
B3LYP/6-31G*
1.3721
0.9675
110.90
B3LYP/6-31+G*
1.3729
0.9683
112.46
B3LYP/6-311+G*
1.3691
0.9630
113.01
MP2/6-31G*
1.3762
0.9700
110.38
MP2/6-31+G*
1.3780
0.9722
111.77
MP2/6-311+G*
1.3709
0.9614
112.25
Literature
HF/STO-3G [2, 47]
1.389
n/r
114 (fixed)
HF/STO-3G [48]
1.364
0.98
110
HF/4-31G [48]
1.364
0.95
121
HF/3-21G* [49]
1.377
0.962
n/r
HF/6-31G [49]
1.370
0.947
n/r
HF/6-31G* [49]
1.358
0.947
n/r
HF/6-31G* [2, 49]
1.358
0.947
112.6
MP2/6-31G** [50]
1.357
0.942
113.0
B3LYP/6-311++G** [51]
1.380
0.971
112.6
B3LYP/6-311++G** [52]
1.370
0.962
112.8
MP2/6-311++G** [52]
1.373
0.961
110.7
B3LYP/aug-cc-pVQZ [53]
1.369
0.960
113.1
MP2/aug-cc-pVTZ [53]
1.374
0.962
111.5
MP2/aug-cc-pVQZ [53]
1.370
0.959
111.8
QCISD/6-311++G** [53]
1.371
0.959
111.1
B3LYP/aug-cc-pVDZ [54]
1.376
n/r
n/r
An Ab Initio Study of Boric Acid, Borate …
151