Electric and magnetic multipole integrals in STO basis sets: an analytical approach

A new method for the evaluation of one- and two-centre magnetic and electric multipole integrals for Slater-type functions is presented. The method is strictly analytical in that no approximations of any kind are involved. Two simple functions, J(1)(aug) and J(2)(aug), are introduced, which employ only functions that are well known in electronic structure theory. With the use of augmentation exponents these functions apply to multipole integrals as well as other one-electron integrals, such as nuclear attraction integrals. The proposed method includes the analytic determination of derivatives of the integrals with respect to atomic displacements. Some illustrative test calculations are presented and compared to results from the literature.