Theor Chem Acc (2015) 134:116
1 3
Finally, BP86 provided more uniform, though slightly larger,
deviations from the crystal structure data. Simulating the
environment by PCM resulted in an insignifi cant change
in this picture. As seen, one can hardly suggest an optimal
scheme from those investigated. Hence, in the following we
shall selectively pick up results that fi t best to the purpose of
this paper, i.e., those that most closely mimic the available
experimental data.
4.2 Spectral properties
4.2.1 Vibrational spectra
Table 3 contains assignments for selected parts of the vibrational spectra of 1 – 3 . Data for the whole pertinent frequency
range are given in the supplementary material and complement the experimentally recorded IR and Raman spectra
Table 1 Maximal relative
deviations ( max
r ), mean
relative deviations ( ¯
r ), and
mean of the absolute values
of relative deviations ( ¯
abs
r )
of the calculated bond lengths
and bond angles from the
experimental data
Results (in %) are shown separately for ensembles of different bonds and angle types of the complex anions 1 and 2
Functional
Basis
VO bonds
CC, CO bonds
Non-H bonds
max
r
¯
r
¯
abs
r
max
r
¯
r
¯
abs
r
¯
r
¯
abs
r
M06-L
WI
1.91
0.85
0.85
−2.26
−0.23
0.65
0.13
0.72
M06
WI
−1.19
−0.18
0.80
−2.68
−0.56
0.71
−0.43
0.74
M06-2X
WI
−2.60
−0.55
1.32
−1.89
−0.33
0.63
−0.40
0.86
M06-HF
WI
−4.08
−1.31
1.76
−1.69
−0.47
0.73
−0.75
1.07
BP86
WI
2.17
1.23
1.23
1.91
0.80
1.05
0.94
1.11
BP86 PCM
WI
1.93
0.95
0.95
2.00
0.85
1.02
0.88
1.00
BLYP
WI
3.00
1.94
1.94
2.08
1.24
1.37
1.47
1.56
B3LYP
WI
1.52
0.37
0.71
−1.83
0.14
0.68
0.22
0.69
BHHLYP
WI
−2.58
−1.10
1.33
−2.54
−0.91
0.92
−0.97
1.06
HF
WI
−4.72
−1.84
1.98
−2.61
−1.18
1.24
−1.40
1.49
BP86
WII
2.43
1.24
1.24
2.24
0.89
1.13
1.00
1.17
B3LYP
WII
1.65
0.39
0.67
−1.72
0.21
0.72
0.27
0.70
BP86
TZV
2.48
1.87
1.87
4.16
2.11
2.11
2.03
2.03
BLYP
TZV
3.31
2.57
2.57
4.41
2.57
2.57
2.57
2.57
B3LYP
TZV
1.55
0.98
1.01
3.16
1.37
1.37
1.24
1.25
BHHLYP
TZV
−2.03
−0.57
0.62
1.91
0.24
0.60
−0.03
0.60
HF
TZV
−2.99
−1.45
1.45
1.16
−0.06
0.46
−0.52
0.79
Functional
Basis
∠OVO, ∠VOC
∠CCC, ∠CCO, ∠OCO
Non-H angles
max
r
¯
r
¯
abs
r
max
r
¯
r
¯
abs
r
¯
r
¯
abs
r
M06-L
WI
−6.92
0.44
1.84
1.83
0.35
0.92
0.40
1.36
M06
WI
−5.65
0.68
2.12
2.76
0.42
1.00
0.54
1.53
M06-2X
WI
−6.60
0.51
1.81
1.79
0.25
0.93
0.37
1.35
M06-HF
WI
−6.34
0.57
1.78
1.92
0.00
0.99
0.27
1.37
BP86
WI
−5.89
0.68
2.21
3.32
0.51
1.02
0.59
1.59
BP86 PCM
WI
−4.41
0.68
1.96
3.96
0.49
0.90
0.58
1.41
BLYP
WI
−6.04
0.82
2.52
3.73
0.59
1.10
0.70
1.78
B3LYP
WI
−6.51
0.85
2.54
3.28
0.52
1.14
0.68
1.81
BHHLYP
WI
−6.90
0.91
2.60
2.71
0.44
1.13
0.67
1.83
HF
WI
−8.22
1.25
3.18
2.72
0.44
1.15
0.83
2.12
BP86
WII
−5.80
0.76
2.29
3.06
0.50
0.96
0.63
1.60
B3LYP
WII
−6.82
0.96
2.68
3.03
0.51
1.10
0.72
1.85
BP86
TZV
−5.32
0.76
2.18
3.09
0.42
1.13
0.59
1.63
BLYP
TZV
−5.57
0.91
2.48
3.49
0.50
1.19
0.70
1.81
B3LYP
TZV
−6.06
1.03
2.71
3.29
0.42
1.24
0.71
1.94
BHHLYP
TZV
−6.74
1.22
3.49
3.35
0.32
1.28
0.75
2.34
HF
TZV
−8.31
1.60
4.07
3.00
0.28
1.33
0.91
2.64
126
Reprinted from the journal
1 3
Finally, BP86 provided more uniform, though slightly larger,
deviations from the crystal structure data. Simulating the
environment by PCM resulted in an insignifi cant change
in this picture. As seen, one can hardly suggest an optimal
scheme from those investigated. Hence, in the following we
shall selectively pick up results that fi t best to the purpose of
this paper, i.e., those that most closely mimic the available
experimental data.
4.2 Spectral properties
4.2.1 Vibrational spectra
Table 3 contains assignments for selected parts of the vibrational spectra of 1 – 3 . Data for the whole pertinent frequency
range are given in the supplementary material and complement the experimentally recorded IR and Raman spectra
Table 1 Maximal relative
deviations ( max
r ), mean
relative deviations ( ¯
r ), and
mean of the absolute values
of relative deviations ( ¯
abs
r )
of the calculated bond lengths
and bond angles from the
experimental data
Results (in %) are shown separately for ensembles of different bonds and angle types of the complex anions 1 and 2
Functional
Basis
VO bonds
CC, CO bonds
Non-H bonds
max
r
¯
r
¯
abs
r
max
r
¯
r
¯
abs
r
¯
r
¯
abs
r
M06-L
WI
1.91
0.85
0.85
−2.26
−0.23
0.65
0.13
0.72
M06
WI
−1.19
−0.18
0.80
−2.68
−0.56
0.71
−0.43
0.74
M06-2X
WI
−2.60
−0.55
1.32
−1.89
−0.33
0.63
−0.40
0.86
M06-HF
WI
−4.08
−1.31
1.76
−1.69
−0.47
0.73
−0.75
1.07
BP86
WI
2.17
1.23
1.23
1.91
0.80
1.05
0.94
1.11
BP86 PCM
WI
1.93
0.95
0.95
2.00
0.85
1.02
0.88
1.00
BLYP
WI
3.00
1.94
1.94
2.08
1.24
1.37
1.47
1.56
B3LYP
WI
1.52
0.37
0.71
−1.83
0.14
0.68
0.22
0.69
BHHLYP
WI
−2.58
−1.10
1.33
−2.54
−0.91
0.92
−0.97
1.06
HF
WI
−4.72
−1.84
1.98
−2.61
−1.18
1.24
−1.40
1.49
BP86
WII
2.43
1.24
1.24
2.24
0.89
1.13
1.00
1.17
B3LYP
WII
1.65
0.39
0.67
−1.72
0.21
0.72
0.27
0.70
BP86
TZV
2.48
1.87
1.87
4.16
2.11
2.11
2.03
2.03
BLYP
TZV
3.31
2.57
2.57
4.41
2.57
2.57
2.57
2.57
B3LYP
TZV
1.55
0.98
1.01
3.16
1.37
1.37
1.24
1.25
BHHLYP
TZV
−2.03
−0.57
0.62
1.91
0.24
0.60
−0.03
0.60
HF
TZV
−2.99
−1.45
1.45
1.16
−0.06
0.46
−0.52
0.79
Functional
Basis
∠OVO, ∠VOC
∠CCC, ∠CCO, ∠OCO
Non-H angles
max
r
¯
r
¯
abs
r
max
r
¯
r
¯
abs
r
¯
r
¯
abs
r
M06-L
WI
−6.92
0.44
1.84
1.83
0.35
0.92
0.40
1.36
M06
WI
−5.65
0.68
2.12
2.76
0.42
1.00
0.54
1.53
M06-2X
WI
−6.60
0.51
1.81
1.79
0.25
0.93
0.37
1.35
M06-HF
WI
−6.34
0.57
1.78
1.92
0.00
0.99
0.27
1.37
BP86
WI
−5.89
0.68
2.21
3.32
0.51
1.02
0.59
1.59
BP86 PCM
WI
−4.41
0.68
1.96
3.96
0.49
0.90
0.58
1.41
BLYP
WI
−6.04
0.82
2.52
3.73
0.59
1.10
0.70
1.78
B3LYP
WI
−6.51
0.85
2.54
3.28
0.52
1.14
0.68
1.81
BHHLYP
WI
−6.90
0.91
2.60
2.71
0.44
1.13
0.67
1.83
HF
WI
−8.22
1.25
3.18
2.72
0.44
1.15
0.83
2.12
BP86
WII
−5.80
0.76
2.29
3.06
0.50
0.96
0.63
1.60
B3LYP
WII
−6.82
0.96
2.68
3.03
0.51
1.10
0.72
1.85
BP86
TZV
−5.32
0.76
2.18
3.09
0.42
1.13
0.59
1.63
BLYP
TZV
−5.57
0.91
2.48
3.49
0.50
1.19
0.70
1.81
B3LYP
TZV
−6.06
1.03
2.71
3.29
0.42
1.24
0.71
1.94
BHHLYP
TZV
−6.74
1.22
3.49
3.35
0.32
1.28
0.75
2.34
HF
TZV
−8.31
1.60
4.07
3.00
0.28
1.33
0.91
2.64
126
Reprinted from the journal