Biomedical Engineering Reference
In-Depth Information
also shown to be nearly independent of the number of Gaussian functions. A standard set of ζ
values for use in molecular calculations is suggested on the basis of this study and is shown
to be adequate for the calculation of total and atomization energies, but less appropriate for
studies of the charge distribution.
As we increase the number of primitive GTOs in the expansion, the resultant looks more
and more like an STO, except at the nucleus where it can never attain the correct shape (the
cusp). I show the comparison in Figure 16.7 for the STO/3G basis set.
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
Distance/a0
Figure 16.7
The STO/3G expansion
We therefore regard a minimal molecular basis set as comprised of STOs, except for
integral evaluation where we use a linear expansion of
n
GTOs.
Many molecular properties depend on the valence electrons rather than the shape of the
wavefunction at a nucleus, two exceptions being properties such as electron spin resonance
and nuclear magnetic resonance parameters.
Tables of exponents and expansion coefficients are given in the original reference, and
these all refer to an STO exponent of 1. These original GTO basis sets were 'universal' in
that they applied to every atom irrespective of the atomic configuration; to convert from the
STO exponent 1 to an exponent ζ you simply multiply the primitive exponents by ζ
3/2
. For
reasons of computational efficiency, all basis functions in a given valence shell are taken
to have the same primitive GTOs (but with different contraction coefficients).
16.9.2
STO/4-31G
Such STO/
n
G calculations were common in the literature of the 1970s. It soon became
apparent that they give poor results in a number of circumstances. There are particular
problems for molecules containing atoms towards the end of the first period, such as oxygen
