Page 166 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUANTUM CHEMISTRY COMPUTATIONS IN MOMENTUM SPACE 151

Fourier transform of orbital products :

Electronic repulsion term :

Exchange term :

So the first iteration transforms the trial wave functions expressed as linear combinations
of gaussian functions into an expression which involves Dawson functions [62,63]. We
have not been able to find a tabular entry to perform explicitly the normalization of the first
iterate, accordingly this is carried out numerically by the Gauss-Legendre method [64].

One of the drawbacks of the first iteration, however, is that computation of energy
quantities, e.g. orbital and total energies, requires to evaluate the integrals occurring in
Eq. 3 on the basis of the Unfortunately, the transcendental functions in terms of
which the are expressed at the end of the first iteration do not lead to closed form
expressions for these integrals and a numerical procedure is therefore needed. This
constitutes a barrier to carry out further iterations to improve the orbitals by approaching
the HF limit. A compromise has been proposed between a fully numerical scheme and the
simple first iteration approach based on the fact that at the end of each iteration the
entail the main qualitative characteristics of the exact solution and most