Computational Chemistry

much if any improvement over the results now being obtained with a minimal
valence basis, since once the basic MNDO-type method has been chosen, the key to
good results is careful parameterization. There might be some improvement in
properties which depend on a good description of the electron density near the
nucleus, but there are few such of general interest to chemists – even NMR
chemical shifts are affected mainly by (the tails of) valence orbitals [1].
The disadvantage is that the time of calculations would be increased, particularly
for elements beyond the first full row (Na and beyond).

Reference

1. Cramer CJ (2004) Essentials of computational chemistry, 2nd edn. Wiley, UK, p 345

Chapter 6, Harder Questions, Answers

Q6

In SCF SE methods major approximations lie in the calculation of theHrscore,(rs|
tu), and (ru|ts) integrals of the Fock matrix elementsFrs(Eq. 6.1). Suggest an
alternative approach to approximating one of these integrals.
So much thought and experimentation (checking calculated results against
experimental ones) have gone into devising semiempirical parameters that a sug-
gestion here is unlikely to be much of an improvement. The easiest integral to
modify is probably the core one, because it does not involve electron-electron
repulsion.Hrscorein theFrsFock matrix element is:

Hcorers ð 1 Þ¼ frð 1 ÞH^

core

ð 1 Þ

fsð 1 Þ

DE

where H^

core

ð 1 Þ¼#

1

2

r^21 #

X

allm

Zm

rm 1

So the integralHrscorecan be taken as the energy (kinetic plus potential) of
an electron moving in thefr,fsoverlap region under the attraction of all the
chargesZm. In ab initio calculations these charges are nuclear, in SE calculations
they are the net charges of nuclei plus non-valence electrons. A crude attempt to
capture the physical meaning of this might be to takeHrscoreas the average of
the valence-state ionization energies of an electron infrandfsplus the energy
needed to remove the electron to infinity against the attraction of the other (non-r
and non-s) cores.

632 Answers