Analytical and numerical development for the two-centre overlap-like quantum similarity integrals over Slater-type functions

Abstract

In molecular quantum similarity measure between two molecules, using the molecular electron density, the major task involves the accurate numerical evaluation of overlap between the two electron densities in the integral measure. By expanding the electron densities in terms of atomic orbitals, using the linear combination of atomic orbitals approach, a large number of overlap-like quantum similarity integrals over the basis functions in the two molecules will be required accurately for the calculation of a meaningful quantum similarity measure. Improvement of the computational methods of these integrals would be indispensable to a further development in computational studies of large molecular systems. Analytic expressions were obtained for these overlap-like quantum similarity integrals over Slater-type functions, in terms of the usual two-centre overlap integrals over B functions. Different approaches were developed for the numerical evaluation of these two-centre overlap integrals over B functions, which can be used for the numerical evaluation of the two-centre overlap-like quantum similarity integrals over Slater-type functions. In this work we present our approach which is based on the use of nonlinear transformations for improving convergence of highly oscillatory integrals. In the case of more complicated multicentre integrals, this approach is shown to be able to produce remarkably good results. We also present different representations, which were obtained by Steinborn group, and which can be used for a fast and accurate computation of the two-centre overlap-like quantum similarity integrals over Slater-type functions.