A new method of approximative calculation of polycentric integrals used in the quantum mechanical study of molecular structure

Abstract

This report begins with a short review of approximative methods which have been used for the calculation of polycentric integrals. Against this background a new method is proposed which replaces the product of two atomic orbitals by the sum of two squares of approximate atomic orbitals. The parameters and localization of these orbitals are so chosen that the approximative expression has the same monopole, dipole, quadrupole and octupole moments as the approximated one. The investigation of the accuracy of approximative methods hitherto used as well as of the new approximative method is carried out for twelve types of integrals. It is shown that in most cases the proposed method provides much better results than the methods hitherto applied.