Page 167 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

152 M. DEFRANCESCHI ET AL.

importantly the right asymptotic decay. The idea is thus to fit the iterated analytical
functions obtained at the step on a finite set of gaussian functions and then use
these fitted functions as a new set of trial functions The advantage is twofold.

First, with exponents and linear coefficients specific for each orbital, energies and
functions are quickly improved. Second, the problematic convolution products and
integrals are efficiently computed in terms of the gaussian functions obtained to represent
the The analytical functions are represented as linear combinations of
gaussian functions, This fit is carried out using a modified version of the
Gausfit package [65] developed by Stewart [66] for gaussian fits of Slater functions. The
resulting functions are analytically orthonormalized.

For atoms, the radial part of is expressed as a linear combination of spherical
gaussians, which, in the case of 2p orbitals writes as :

Given a radial function to fit, one minimizes the variance,

where is a function which weights the contributions to the integral according their

expected importance [28]. From several tests on Be and Ne we have found that the
following weight functions are quite efficient:

Gaussian functions do not have the right asymptotic decay due to too low amplitudes in
regions of large p values, therefore representations in terms of gaussians are of much
slower convergence than Slater functions. Since contributions from high momenta are
essential to the energy, a second degree polynomial, Eq. 35, is used to enforce them in the
valence orbitals.
A set of nine gaussians allows a satisfactory fit with low variance, Eq. 34, values : about
for the 1s and 2p orbitals and for the 2s orbital. The valence orbitals having
node(s) are slightly more difficult to fit. Under these conditions, the iterative scheme