2.11 Strategy
29
Table 2.14 Comparison of the CCSD(T)_ae/CVQZ bond length between heavy atoms with the
CCSD(T)_ae/CV5Z one and with the most accurate equilibrium structure (all values in pm)
Molecule
r e
Ref.
CVQZ
CV5Z
r e − CVQZ
r e − CV5Z
CO
112.84
a
112.89
112.80
−0.05
0.04
CO 2
116.00
b
116.04
115.98
−0.04
0.02
HCCH
120.28
c
120.34
120.28
−0.06
0.00
N 2
109.75
d
109.81
109.71
−0.06
0.04
F 2
141.08
d
141.13
140.92
−0.05
0.16
HF
091.71
d
091.58
091.54
0.13
0.17
HCN
115.32
e
115.38
115.30
−0.06
0.02
CH 2 O
120.45
e
120.43
120.41
0.02
0.05
CH 2 =CH 2
133.08
e
133.12
133.06
−0.04
0.02
HNC
116.87
e
116.93
116.86
−0.06
0.01
HNO
120.81
e
120.85
120.77
−0.04
0.03
Median
−0.04
0.04
MAD
0.04
0.02
s f
0.06
0.03
a Experimental: Authier et al. (1993)
b Experimental: Teffo and Ogilvie (1993)
c Experimental: Tamassia et al. (2016)
d CCSD(T)/V∞Z + core + T + Q: Ruden et al. (2004)
e CCSD(T)/V∞Z + core + T + Q: Puzzarini et al. (2008)
f Standard deviation calculated from MAD, see (9.36)
r
BO
e
= r e
CCSD(T) − ae/wCVTZ
+ r e (MP2 − ae/wCVQZ)
− r e (MP2 − ae/wCVTZ)
(2.31)
The accuracy of this equation, which is based on the additivity of small corrections,
was confirmed many times and, the example given in Table 2.15 shows that the loss
of accuracy is quite small. The MAD of the residuals is 0.02 pm for the bond lengths
and 0.02° for the angles.
For still larger molecules, the structure may be optimized at the CCSD(T)_fc/VTZ
level and the effects of basis set enlargement (VTZ → VQZ) and core correlation are then estimated at a lower level. In this case, only the valence electrons are
correlated (the so-called frozen core approximation). The estimation of the core
correlation is discussed in Sect. 2.7.2. The calculation of the correction (AVTZ
→ AVQZ) is presented in Table 2.16 (when an electronegative atom is present, the
addition of diffuse functions—augmented basis sets—may be necessary). Inspection
of Table 2.16 shows that the extension of the basis set can be accurately calculated
at the CCSD level of theory. The MP2 method is slightly less accurate; nevertheless,
it allows us to estimate the extension with an acceptable accuracy. As the correction
(AVQZ → AV5Z) is smaller, it is estimated with a better accuracy.
29
Table 2.14 Comparison of the CCSD(T)_ae/CVQZ bond length between heavy atoms with the
CCSD(T)_ae/CV5Z one and with the most accurate equilibrium structure (all values in pm)
Molecule
r e
Ref.
CVQZ
CV5Z
r e − CVQZ
r e − CV5Z
CO
112.84
a
112.89
112.80
−0.05
0.04
CO 2
116.00
b
116.04
115.98
−0.04
0.02
HCCH
120.28
c
120.34
120.28
−0.06
0.00
N 2
109.75
d
109.81
109.71
−0.06
0.04
F 2
141.08
d
141.13
140.92
−0.05
0.16
HF
091.71
d
091.58
091.54
0.13
0.17
HCN
115.32
e
115.38
115.30
−0.06
0.02
CH 2 O
120.45
e
120.43
120.41
0.02
0.05
CH 2 =CH 2
133.08
e
133.12
133.06
−0.04
0.02
HNC
116.87
e
116.93
116.86
−0.06
0.01
HNO
120.81
e
120.85
120.77
−0.04
0.03
Median
−0.04
0.04
MAD
0.04
0.02
s f
0.06
0.03
a Experimental: Authier et al. (1993)
b Experimental: Teffo and Ogilvie (1993)
c Experimental: Tamassia et al. (2016)
d CCSD(T)/V∞Z + core + T + Q: Ruden et al. (2004)
e CCSD(T)/V∞Z + core + T + Q: Puzzarini et al. (2008)
f Standard deviation calculated from MAD, see (9.36)
r
BO
e
= r e
CCSD(T) − ae/wCVTZ
+ r e (MP2 − ae/wCVQZ)
− r e (MP2 − ae/wCVTZ)
(2.31)
The accuracy of this equation, which is based on the additivity of small corrections,
was confirmed many times and, the example given in Table 2.15 shows that the loss
of accuracy is quite small. The MAD of the residuals is 0.02 pm for the bond lengths
and 0.02° for the angles.
For still larger molecules, the structure may be optimized at the CCSD(T)_fc/VTZ
level and the effects of basis set enlargement (VTZ → VQZ) and core correlation are then estimated at a lower level. In this case, only the valence electrons are
correlated (the so-called frozen core approximation). The estimation of the core
correlation is discussed in Sect. 2.7.2. The calculation of the correction (AVTZ
→ AVQZ) is presented in Table 2.16 (when an electronegative atom is present, the
addition of diffuse functions—augmented basis sets—may be necessary). Inspection
of Table 2.16 shows that the extension of the basis set can be accurately calculated
at the CCSD level of theory. The MP2 method is slightly less accurate; nevertheless,
it allows us to estimate the extension with an acceptable accuracy. As the correction
(AVQZ → AV5Z) is smaller, it is estimated with a better accuracy.