(Section 5.5.2.2b) use as part of their procedure single-point HF (rather than post-
HF) level calculations with very large basis sets, and geometry optimizations with
large basis sets were performed at both HF and post-HF levels in studies of the
theoretically and experimentally challenging oxirene system [ 53 ].
5.3.3.6 Correlation-Consistent Basis Sets
All the previously explicitly designated basis sets, from STO-3G through
6–311þþG(3df,3pd) (in large basis sets), are Pople (from the group of John
Pople; see above) basis sets. Another class of popular basis sets was developed
by the research group of Dunning [ 54 ]. These are specially designed for post-
Hartree–Fock calculations (Section 5.4), in which electron correlation is better
taken into account than at the Hartree–Fock level. Because they are intended,
ideally, to give with such calculations improved results in step with (correlated
with) their increasing size, they are called correlation-consistent (cc) basis sets.
Ideally, they systematically improve results with increasing basis set size, and
permit extrapolation to the infinite basis set limit. The cc-sets are designated cc-
pVXZ, where p stands for polarization functions, V for valence, X for the number of
shells the valence functions are split into, and Z for zeta (cf.split valence and
double-zeta basis sets, above). Thus we have cc-pVDZ (cc polarized valence
doubly-split zeta), cc-pVTZ (cc polarized valence triply-split zeta), cc-pVQZ (cc
polarized valence quadruply-split zeta), and cc-pV5Z (cc polarized valence five-
fold-split zeta). These basis sets can be augmented with diffuse and extra polariza-
tion functions, giving aug-cc-pVXZ sets. The number of basis functions on CH 2
using some Dunning sets (cf. the data on Pople sets, above) is CþHþH):
cc-pVDZ 14þ 5 þ 5 ¼24 functions
cc-pVTZ 30þ 14 þ 14 ¼58 functions
cc-pVQZ 55þ 30 þ 30 ¼115 functions
cc-pV5Z 91þ 55 þ 55 ¼201 functions
We see that only the cc-pVDZ is (roughly) comparable in size to the 6–31G*
(15þ 2 þ 2 ¼19 functions); the other cc sets are much bigger. Correlation-
consistent basis sets sometimes [ 55 ] but do not necessarily [ 56 ] give results superior
to those with Pople sets that require about the same computational time.
5.3.3.7 Effective Core Potentials (Pseudopotentials)
At about the third row (potassium to krypton) of the periodic table, the large number
(19 or more) of electrons in each atom begins to have a significant slowing effect on
conventional ab initio calculations, because of the many two-electron repulsion
integrals they engender. The usual way of avoiding this problem is to add to the
Fock operator a one-electron operator that takes into account in a collective way the
effect of the core electrons on the valence electrons, which latter are still considered
explicitly. This “average core effect” operator is called an effective core potential
5.3 Basis Sets 251