3.6 Hints for Calculations
147
considering their calculation purpose. Those frequently used, within the Pople type
(Ditchfield et al. 1971) as an example, are listed as follows:
(1) Minimal basis set
This is the least basis set and useful to qualitative analysis of the electronic structure
of molecules. The least necessary orbitals are allotted for the inner-shell and valenceshell electrons in terms of Slater-type orbitals (STO’s) (see Sect. 3.1.1). The minimal
basis set is usually expressed as STO-NG (N = 3, 4, 6, etc.), where N signifies the
number of the Gaussian-type orbitals (GTO’s) to expand an STO.
The minimal basis set requires a comparatively short time for computation and
it gives a pretty good result for the orbital patterns when considering the orbital
interaction toward chemical reaction analysis. Actually, the orbital pattern pictures
afforded by the minimal basis set are rather visible. The basis set consisting of too
many basis functions is apt to result in over-delocalized MO’s from the viewpoint
of orbital patterns. Due to the same reason, the delocalization of electrons in the
concerning molecule tends to be suppressed in the calculation using the minimal
basis set, leading to rather rigid atomic net charges, for instance.
(2) Split-valence basis set
This is the basis set employing double or triple GTO sets with different orbital
exponents to expand the STO’s of the valence orbitals, which is called split valence.
Different orbital exponent (also called zeta) results in different spatial extensions
giving more quantitative results in energies compared with those by the minimal
basis set. The split-valence basis set is usually expressed as N-KLG or N-KLMG
for double zeta or triple zeta, case, respectively. The index N indicates the number
of GTO’s to expand the inner-shell orbital(s), and K, L or K, L, M the numbers of
GTO’s to expand the valence-shell orbitals for double zeta or triple zeta, respectively.
Typical examples are: 3-21G, 4-31G, 6-31G (double zeta), and 6-311G (triple zeta).
Split-valence basis set gives more quantitative results in energies compared with
those by the minimal basis set but necessitates more computation time.
(3) Polarized basis set
Addition of polarization functions (d or p functions) to the most outer orbital of the
split-valence basis set. The d functions are added to the most outer p orbitals in the
case of the atoms larger than Li atoms, and p functions for H atom. These d and p
signs are added in the parentheses. Typical examples are: 6-31G(d), 6-31G(d, p), and
6-311G (d, p). The (d) or (d, p) is also indicated as * or **, respectively, as 6-31G*
and 6-31G**.
A polarized basis set is good for the description of molecules having inner polarization since this can describe the polarization effect or deviation of electron distribution
in the molecule. However, on one hand, the computation time becomes considerably
longer with employing the polarized basis set.
147
considering their calculation purpose. Those frequently used, within the Pople type
(Ditchfield et al. 1971) as an example, are listed as follows:
(1) Minimal basis set
This is the least basis set and useful to qualitative analysis of the electronic structure
of molecules. The least necessary orbitals are allotted for the inner-shell and valenceshell electrons in terms of Slater-type orbitals (STO’s) (see Sect. 3.1.1). The minimal
basis set is usually expressed as STO-NG (N = 3, 4, 6, etc.), where N signifies the
number of the Gaussian-type orbitals (GTO’s) to expand an STO.
The minimal basis set requires a comparatively short time for computation and
it gives a pretty good result for the orbital patterns when considering the orbital
interaction toward chemical reaction analysis. Actually, the orbital pattern pictures
afforded by the minimal basis set are rather visible. The basis set consisting of too
many basis functions is apt to result in over-delocalized MO’s from the viewpoint
of orbital patterns. Due to the same reason, the delocalization of electrons in the
concerning molecule tends to be suppressed in the calculation using the minimal
basis set, leading to rather rigid atomic net charges, for instance.
(2) Split-valence basis set
This is the basis set employing double or triple GTO sets with different orbital
exponents to expand the STO’s of the valence orbitals, which is called split valence.
Different orbital exponent (also called zeta) results in different spatial extensions
giving more quantitative results in energies compared with those by the minimal
basis set. The split-valence basis set is usually expressed as N-KLG or N-KLMG
for double zeta or triple zeta, case, respectively. The index N indicates the number
of GTO’s to expand the inner-shell orbital(s), and K, L or K, L, M the numbers of
GTO’s to expand the valence-shell orbitals for double zeta or triple zeta, respectively.
Typical examples are: 3-21G, 4-31G, 6-31G (double zeta), and 6-311G (triple zeta).
Split-valence basis set gives more quantitative results in energies compared with
those by the minimal basis set but necessitates more computation time.
(3) Polarized basis set
Addition of polarization functions (d or p functions) to the most outer orbital of the
split-valence basis set. The d functions are added to the most outer p orbitals in the
case of the atoms larger than Li atoms, and p functions for H atom. These d and p
signs are added in the parentheses. Typical examples are: 6-31G(d), 6-31G(d, p), and
6-311G (d, p). The (d) or (d, p) is also indicated as * or **, respectively, as 6-31G*
and 6-31G**.
A polarized basis set is good for the description of molecules having inner polarization since this can describe the polarization effect or deviation of electron distribution
in the molecule. However, on one hand, the computation time becomes considerably
longer with employing the polarized basis set.