2.7 Choice of the Basis Sets
23
Table 2.8 Effect of diffuse functions on the geometrical parameters: AVnZ − VnZ (lengths in pm
and angles in degrees)
Molecule
Bond
VTZ
VQZ
V5Z
V6Z
HF
0.38
0.15
0.06
−0.04
N 2
0.02
0.02
0.01
0.00
F 2
0.23
0.01
−0.01
−0.01
CO
0.03
0.04
0.02
0.01
HC≡CH
C≡C
0.05
0.04
0.01
0.01
C–H
0.03
0.02
0.01
0.01
NH 3
N–H
0.06
0.04
0.03
0.02
HNH
0.72
0.34
0.02
CH 3 F
C–F
0.78
0.29
0.08
C–H
0.03
0.02
0.02
HCF
−0.46
−0.17
−0.04
H 2 O
O–H
0.22
0.10
0.04
0.02
HOH
0.60
0.25
0.06
0.02
H 2 O 2
O–H
0.25
0.08
0.04
O–O
0.31
0.10
0.03
All calculations were performed at the CCSD(T) level of theory
Reprinted from Journal of Molecular Structure, 1023. Demaison J, Császár AG. Equilibrium CO
bond lengths, 7–14. Copyright 2012, with permission from Elsevier
Table 2.9 Convergence of the basis set for a few bond lengths (in pm) at the CCSD(T) level of
theory
HF
N 2
F 2
CO
AVTZ
92.10
110.40
141.81
113.60
QZ-TZ a
−0.33
−0.35
−0.51
−0.42
5Z-QZ a
−0.04
−0.10
−0.21
−0.09
6Z-5Z a
0.00
−0.03
−0.08
−0.03
AV6Z
91.73
109.92
141.01
113.06
AV∞Z b
91.72
109.88
140.93
113.02
Source Ruden et al. (2004)
a r[AVnZ] − r[AV(n − 1)Z]
b Extrapolated value, see Sect. 2.7.4
2.7.4.1 Extrapolation to Complete Basis Set (CBS) (Puzzarini 2009)
It is established that the HF energy converges much faster than the correlation correction. The basis set limit may be estimated by extrapolating them separately. For the HF
energy, the following empirical formula is often used with the correlation-consistent
basis sets