their sodium salts (Table 1). The calculated B-O bond distance of BO 3
3− (Table 13)
is slightly longer than what is observed experimentally in the sodium salt, and this
is partly due to the neglect of the sodium counterion and crystal packing. For
BO 2 (OH)
2−
, the B-O distances for the unprotonated oxygens are in reasonable
agreement with experiment, whereas the B-O(H) distance is quite long. It is
expected that hydrogen bonding present in the crystal structure would shorten the
corresponding B-O(H) distance considerably.
The calculated vibrational frequencies of BO 3
3− are shown in Table 14. There is
a quite surprising dependence of the level of theory and basis set. The stretching
frequencies decrease when going from Hartree-Fock to the correlated levels, as
expected, as well as when going from nondiffuse to diffuse basis sets. It is more
surprising that the deformation modes are affected even more when going from
nondiffuse to diffuse basis sets at the correlated levels. This may be an artifact of
using a correlated level on a system, which, in the gas-phase, is likely unbound with
respect to electron detachment.
The calculated vibrational frequencies of BO 2 (OH)
2− are shown in Table 15.
The dependence of the frequency on the level of theory and basis set is not as
Table 13 Geometrical parameters of BO 3
3− and BO 2 (OH)
2−
Level
B-O distances (Å)
BO 3
3−
BO 2 (OH)
2−
s-BO 2 (OH)
2−
a-BO 2 (OH)
2−
HF/6-31G*
1.4186
1.5941
1.3347
1.3188
HF/6-31+G*
1.4135
1.5556
1.3440
1.3251
HF/6-311+G*
1.4127
1.5613
1.3405
1.3209
B3LYP/6-31G*
1.4411
1.6307
1.3551
1.3332
B3LYP/6-31+G*
1.4234
1.5731
1.3637
1.3413
B3LYP/6-311+G*
1.4211
1.5812
1.3587
1.3359
MP2/6-31G*
1.4461
1.6296
1.3616
1.3401
MP2/6-31+G*
1.4363
1.5781
1.3755
1.3513
MP2/6-311+G*
1.4299
1.5741
1.3679
1.3437
Table 14 Vibrational frequencies (cm
−1
) of the D 3h form of BO 3
3−
Level
BO 3 i.p def E′
BO str. A 1 ′
BO 3 o.o.p. def A 2 ″
BO str. E′
HF/6-31G*
581
848
876
1216
HF/6-31+G*
536
829
851
1085
HF/6-311+G*
535
826
844
1062
B3LYP/6-31G*
530
764
773
1107
B3LYP/6-31+G*
271
791
679
897
B3LYP/6-311+G*
227
785
680
867
MP2/6-31G*
533
769
788
1124
MP2/6-31+G*
358
767
659
843
MP2/6-311+G*
344
768
654
824
An Ab Initio Study of Boric Acid, Borate …
173
3− (Table 13)
is slightly longer than what is observed experimentally in the sodium salt, and this
is partly due to the neglect of the sodium counterion and crystal packing. For
BO 2 (OH)
2−
, the B-O distances for the unprotonated oxygens are in reasonable
agreement with experiment, whereas the B-O(H) distance is quite long. It is
expected that hydrogen bonding present in the crystal structure would shorten the
corresponding B-O(H) distance considerably.
The calculated vibrational frequencies of BO 3
3− are shown in Table 14. There is
a quite surprising dependence of the level of theory and basis set. The stretching
frequencies decrease when going from Hartree-Fock to the correlated levels, as
expected, as well as when going from nondiffuse to diffuse basis sets. It is more
surprising that the deformation modes are affected even more when going from
nondiffuse to diffuse basis sets at the correlated levels. This may be an artifact of
using a correlated level on a system, which, in the gas-phase, is likely unbound with
respect to electron detachment.
The calculated vibrational frequencies of BO 2 (OH)
2− are shown in Table 15.
The dependence of the frequency on the level of theory and basis set is not as
Table 13 Geometrical parameters of BO 3
3− and BO 2 (OH)
2−
Level
B-O distances (Å)
BO 3
3−
BO 2 (OH)
2−
s-BO 2 (OH)
2−
a-BO 2 (OH)
2−
HF/6-31G*
1.4186
1.5941
1.3347
1.3188
HF/6-31+G*
1.4135
1.5556
1.3440
1.3251
HF/6-311+G*
1.4127
1.5613
1.3405
1.3209
B3LYP/6-31G*
1.4411
1.6307
1.3551
1.3332
B3LYP/6-31+G*
1.4234
1.5731
1.3637
1.3413
B3LYP/6-311+G*
1.4211
1.5812
1.3587
1.3359
MP2/6-31G*
1.4461
1.6296
1.3616
1.3401
MP2/6-31+G*
1.4363
1.5781
1.3755
1.3513
MP2/6-311+G*
1.4299
1.5741
1.3679
1.3437
Table 14 Vibrational frequencies (cm
−1
) of the D 3h form of BO 3
3−
Level
BO 3 i.p def E′
BO str. A 1 ′
BO 3 o.o.p. def A 2 ″
BO str. E′
HF/6-31G*
581
848
876
1216
HF/6-31+G*
536
829
851
1085
HF/6-311+G*
535
826
844
1062
B3LYP/6-31G*
530
764
773
1107
B3LYP/6-31+G*
271
791
679
897
B3LYP/6-311+G*
227
785
680
867
MP2/6-31G*
533
769
788
1124
MP2/6-31+G*
358
767
659
843
MP2/6-311+G*
344
768
654
824
An Ab Initio Study of Boric Acid, Borate …
173