Γ vib = 5A R, p
ð
Þ+ 6B IR; R, dp
ð
Þ+ 5E IR; R, dp
ð
Þ .
The BOH deformations appear from 1000 to 1300 cm
−1
, the B-O stretching
motions from 720 to 1100 cm
−1 , the BO 4 deformations from 230 to 570 cm
−1 , and
the BOH torsions from 180 to 440 cm
−1 .
Table 8 Relative energies of B(OH) 4
− (kJ/mol)
D 2d #1
D 2d #2
S 4 #1
S 4 #2
S 4 #3
HF/6-31G*
67.6
7.4
0.0
9.7
n/a
HF/6-31+G*
68.9
8.7
0.0
10.5
n/a
HF/6-311+G*
74.6
9.6
0.0
12.4
n/a
B3LYP/6-31G*
63.3
7.4
0.0
5.6
5.6
B3LYP/6-31+G*
66.0
8.2
0.0
8.0
7.8
B3LYP/6-311+G*
70.9
9.0
0.0
9.0
8.7
MP2/6-31G*
71.3
7.0
0.0
8.1
6.7
MP2/6-31+G*
72.3
8.1
0.0
9.1
8.0
MP2/6-311+G*
77.8
8.8
0.0
11.1
8.7
Table 9 Geometrical parameters of the S 4 #1 form of B(OH) 4
−
Level
B-O (Å)
O-H (Å)
B-O-H angle (deg.)
HF/6-31G*
1.4722
0.9454
105.63
HF/6-31+G*
1.4717
0.9451
107.63
HF/6-311+G*
1.4702
0.9390
107.81
B3LYP/6-31G*
1.4876
0.9674
103.05
B3LYP/6-31+G*
1.4873
0.9673
106.20
B3LYP/6-311+G*
1.4854
0.9626
106.52
MP2/6-31G*
1.4897
0.9689
102.67
MP2/6-31+G*
1.4904
0.9710
105.63
MP2/6-311+G*
1.4829
0.9610
106.00
Literature
HF/STO-3G [69] (D 2d )
1.48
114 (fixed)
HF/STO-3G [47] (D 2d )
1.492
114 (fixed)
HF/6-31G* [51] (D 2d )
1.474
0.946
104
HF/6-31G* [70]
1.472
0.945
105.6
HF/6-31G* [2]
1.472
0.954
105.4
B3LYP/aug-cc-pVDZ [54]
1.486
n/r
n/r
B3LYP/6-311++G**
1.489
0.960
n/r
MP2/6-311++G**
1.486
0.960
n/r
160
C. C. Pye
ð
Þ+ 6B IR; R, dp
ð
Þ+ 5E IR; R, dp
ð
Þ .
The BOH deformations appear from 1000 to 1300 cm
−1
, the B-O stretching
motions from 720 to 1100 cm
−1 , the BO 4 deformations from 230 to 570 cm
−1 , and
the BOH torsions from 180 to 440 cm
−1 .
Table 8 Relative energies of B(OH) 4
− (kJ/mol)
D 2d #1
D 2d #2
S 4 #1
S 4 #2
S 4 #3
HF/6-31G*
67.6
7.4
0.0
9.7
n/a
HF/6-31+G*
68.9
8.7
0.0
10.5
n/a
HF/6-311+G*
74.6
9.6
0.0
12.4
n/a
B3LYP/6-31G*
63.3
7.4
0.0
5.6
5.6
B3LYP/6-31+G*
66.0
8.2
0.0
8.0
7.8
B3LYP/6-311+G*
70.9
9.0
0.0
9.0
8.7
MP2/6-31G*
71.3
7.0
0.0
8.1
6.7
MP2/6-31+G*
72.3
8.1
0.0
9.1
8.0
MP2/6-311+G*
77.8
8.8
0.0
11.1
8.7
Table 9 Geometrical parameters of the S 4 #1 form of B(OH) 4
−
Level
B-O (Å)
O-H (Å)
B-O-H angle (deg.)
HF/6-31G*
1.4722
0.9454
105.63
HF/6-31+G*
1.4717
0.9451
107.63
HF/6-311+G*
1.4702
0.9390
107.81
B3LYP/6-31G*
1.4876
0.9674
103.05
B3LYP/6-31+G*
1.4873
0.9673
106.20
B3LYP/6-311+G*
1.4854
0.9626
106.52
MP2/6-31G*
1.4897
0.9689
102.67
MP2/6-31+G*
1.4904
0.9710
105.63
MP2/6-311+G*
1.4829
0.9610
106.00
Literature
HF/STO-3G [69] (D 2d )
1.48
114 (fixed)
HF/STO-3G [47] (D 2d )
1.492
114 (fixed)
HF/6-31G* [51] (D 2d )
1.474
0.946
104
HF/6-31G* [70]
1.472
0.945
105.6
HF/6-31G* [2]
1.472
0.954
105.4
B3LYP/aug-cc-pVDZ [54]
1.486
n/r
n/r
B3LYP/6-311++G**
1.489
0.960
n/r
MP2/6-311++G**
1.486
0.960
n/r
160
C. C. Pye