Reducing and Solving Electric Multipole Moment Integrals

Abstract

Electric multipole moment integrals with the same screening parameters are calculated using Slater type orbitals (STOs) translation formulae and the Fourier transform method. First, multipole moment operators which appear in the three-center electric multipole moment integrals are translated from the 0-center to the b-center. After the translation procedure and using Fourier transform convolution theorem, three-center electric multipole moment integrals were reduced to two-center molecular integrals. Then, the analytical expressions obtained were written in terms of overlap integrals. The numerical values for electric multiple moment integrals are useful especially for high quantum numbers and atomic parameters.