11 An Evaluation of Density Functional Theory for CO Adsorption on Pt(111)
199
Table 11.1 The calculated singlet-triplet excitation, HOMO, LUMO, HOMO-LUMO energies
(eV) and electronic dipole moment (Debye) of CO and the ratio of HF exchange (%) for several
wavefunction theories (WFT) and density functional theories (DFT)
Level
Method
E S–T
a E S–T
err E HOMO E LUMO E LUMO–HOMO E x
HF μ e
WFT
MP2
6.41
0.09
−14.97
4.14
19.11
100
0.188
WFT
HF
5.19 −1.13
−14.86
4.57
19.43
100 −0.264
Hybrid M06HF
6.29 −0.03
−14.61
3.17
17.77
100 −0.068
Hybrid BMK
6.12 −0.20
−11.47
0.57
12.04
42 −0.001
Hybrid M052X
6.11 −0.21
−12.10
1.16
13.26
56 −0.032
Hybrid wB97
6.03 −0.29
−13.40
2.59
15.99
100
0.022
Hybrid M062X
5.99 −0.33
−11.91
1.08
13.00
54 −0.002
Hybrid wB97X
5.93 −0.39
−13.09
2.26
15.35
100
0.025
Hybrid BHandH
5.92 −0.40
−11.85
1.30
13.15
50 −0.025
Hybrid BHandHLYP 5.91 −0.41
−12.10
1.21
13.31
50 −0.064
Hybrid B1B95
5.90 −0.42
−10.43 −0.03
10.40
28
0.039
Hybrid B3LYP
5.83 −0.49
−10.11 −0.59
9.51
20
0.060
Hybrid PBE0
5.71 −0.61
−10.40 −0.27
10.13
25
0.063
Hybrid B3PW91
5.71 −0.61
−10.14 −0.61
9.53
20
0.068
Hybrid HSE03
5.70 −0.62
−10.27 −0.92
9.35
25
0.057
Hybrid HSE06
5.70 −0.62
−9.98 −0.67
9.31
25
0.062
mGGA M06L
5.66 −0.66
−9.07 −1.42
7.65
0
0.068
GGA
BP86
5.70 −0.62
−8.76 −1.79
6.97
0
0.144
GGA
B97D
5.68 −0.64
−8.70 −1.59
7.12
0
0.103
GGA
PW91
5.64 −0.68
−8.66 −1.71
6.95
0
0.165
GGA
PBE
5.64 −0.68
−8.60 −1.66
6.94
0
0.172
GGA
BLYP
5.73 −0.59
−8.51 −1.55
6.96
0
0.144
LDA
SVWN
5.86 −0.46
−9.13 −2.31
6.82
0
0.186
Exp.
6.32
0.123
a The error of singlet-triplet excitation energies comparing with the experimental result of 6.32 eV
11.3 Results and Discussion
11.3.1 The Properties of CO
Table 11.1 shows the computed single-triplet (S-T) excitations, HOMO, LUMO,
HOMO-LUMO energies and electronic dipole moment of CO and the ratio of HF
exchange energy by HF, MP2 and 21 different level density functional theories. Performance of DFT on excited states can be revealed by examining the S-T excitation
199
Table 11.1 The calculated singlet-triplet excitation, HOMO, LUMO, HOMO-LUMO energies
(eV) and electronic dipole moment (Debye) of CO and the ratio of HF exchange (%) for several
wavefunction theories (WFT) and density functional theories (DFT)
Level
Method
E S–T
a E S–T
err E HOMO E LUMO E LUMO–HOMO E x
HF μ e
WFT
MP2
6.41
0.09
−14.97
4.14
19.11
100
0.188
WFT
HF
5.19 −1.13
−14.86
4.57
19.43
100 −0.264
Hybrid M06HF
6.29 −0.03
−14.61
3.17
17.77
100 −0.068
Hybrid BMK
6.12 −0.20
−11.47
0.57
12.04
42 −0.001
Hybrid M052X
6.11 −0.21
−12.10
1.16
13.26
56 −0.032
Hybrid wB97
6.03 −0.29
−13.40
2.59
15.99
100
0.022
Hybrid M062X
5.99 −0.33
−11.91
1.08
13.00
54 −0.002
Hybrid wB97X
5.93 −0.39
−13.09
2.26
15.35
100
0.025
Hybrid BHandH
5.92 −0.40
−11.85
1.30
13.15
50 −0.025
Hybrid BHandHLYP 5.91 −0.41
−12.10
1.21
13.31
50 −0.064
Hybrid B1B95
5.90 −0.42
−10.43 −0.03
10.40
28
0.039
Hybrid B3LYP
5.83 −0.49
−10.11 −0.59
9.51
20
0.060
Hybrid PBE0
5.71 −0.61
−10.40 −0.27
10.13
25
0.063
Hybrid B3PW91
5.71 −0.61
−10.14 −0.61
9.53
20
0.068
Hybrid HSE03
5.70 −0.62
−10.27 −0.92
9.35
25
0.057
Hybrid HSE06
5.70 −0.62
−9.98 −0.67
9.31
25
0.062
mGGA M06L
5.66 −0.66
−9.07 −1.42
7.65
0
0.068
GGA
BP86
5.70 −0.62
−8.76 −1.79
6.97
0
0.144
GGA
B97D
5.68 −0.64
−8.70 −1.59
7.12
0
0.103
GGA
PW91
5.64 −0.68
−8.66 −1.71
6.95
0
0.165
GGA
PBE
5.64 −0.68
−8.60 −1.66
6.94
0
0.172
GGA
BLYP
5.73 −0.59
−8.51 −1.55
6.96
0
0.144
LDA
SVWN
5.86 −0.46
−9.13 −2.31
6.82
0
0.186
Exp.
6.32
0.123
a The error of singlet-triplet excitation energies comparing with the experimental result of 6.32 eV
11.3 Results and Discussion
11.3.1 The Properties of CO
Table 11.1 shows the computed single-triplet (S-T) excitations, HOMO, LUMO,
HOMO-LUMO energies and electronic dipole moment of CO and the ratio of HF
exchange energy by HF, MP2 and 21 different level density functional theories. Performance of DFT on excited states can be revealed by examining the S-T excitation