Page 55 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

34 designation double plus ++ means that diffuse orbitals are present on both hydrogen
and the second-row elements. Split-valence sets are indicated by a sequence defining
CHAPTER 1
the number of Gaussians in each component. Split-valence orbitals are designated by
Chemical Bonding primes, so that a system of three Gaussian orbitals would be designated by single,
and Molecular Structure

double, and triple primes ( , , and ). For example 6-311 + G(d, p) conveys the
following information:
• 6: Core basis functions are represented as a single STO-6G expression.
• 311: The valence set is described by three sets of STO-NG functions; each
set includes an s orbital and three p orbitals. In the 6-311+G(d) basis there
are three such sets. One is composed of three Gaussians (STO-3G expression
of one s-type and three p-type forms) and the other two are represented by a
single Gaussian (STO-1G) representation of the s-p manifold. The collection
of components of the split-valence representation can be designated by a series
of primes.
• +: A STO-1G diffuse s-p manifold is included in the basis set for each
nonhydrogen atom; ++ implies that diffuse functions are also included for the
hydrogen atoms.
• p: A set of p functions placed on each nonhydrogen atom and specifies the
composition.
• d: A set of STO-1G d-functions is placed on each nonhydrogen atom for which
d functions are not used in the ground state configuration. If d functions are so
used, polarization is effected by a manifold of f functions.

The composition of several basis sets is given in Table 1.9.
An important distinguishing feature among ab initio calculations is the extent
to which they deal with electron correlation. Correlation is defined as the difference
between the exact energy of a molecular system and the best energy obtainable by a
SCF calculation in which the wave function is represented by a single determinant. In
single-determinant calculations, we consider that each electron experiences an averaged
electrostatic repulsion defined by the total charge distribution, a mean field approxi-
mation. These are called Hartree-Fock (HF) calculations. Correlation corrections arise
from fluctuations of the charge distribution. Correlations energies can be estimated by
including effects of admixtures of excited states into the Hartree-Fock determinant.

Table 1.9. Abbreviations Describing Gaussian Basis Sets a

Designation H C Functions on second-row atoms

3-21G 2 9 1s ;2s ,32p ;2s ,32p

3-21+G 2 13 1s ;2s ,32p ;2s ,32p ;2s+,32p+
∗
6-31G or 6-31G(d) 2 15 1s;2s ,32p ;2s ,32p ;53d

6-31G ∗∗ or 6-31(d,p) 5 18 1s;2s ,32p ;2s ,32p ;2s ;32p ;53d

6-31+G or 6-31+ d 3 19 1s;2s ,32p ;2s ,32p ;53d;2s+ 32p+
∗

6-311G ∗∗ or 6-311(d,p) 6 18 1s;2s ,32p ;2s ,32p ;2s ;32p ;53d

6-311G(df,p) 6 25 1s;2s ,32p ;2s ,32p;2s ;32p ;53d;74f

6-311G(3df,3pd) 17 35 1s;2s ,32p ;2s ,32p ;2s 3p ;53d,74f

a. From E. Lewars, Computational Chemistry, Kluwer Academic Publishers, Boston, 2003, pp. 225–229.