Evaluation of molecular spin-orbit integrals by a gaussian expansion method

A method is presented for the evaluation of molecular multi-centre spin-orbit integrals of Coulomb, hybrid and exchange types using cartesian gaussian functions. It is shown that if gaussian bases are employed the spin-same-orbit integrals reduce to one-electron field integrals and the spin-other-orbit integrals to two-electron field integrals. The final formulae for these integrals are found to be convenient for computer programming. Some relationships among the nuclear attraction, the field and the field-gradient integrals as well as among the electronic repulsion, the two-electron field, and the zero-field splitting integrals are discussed in connection with the spin-orbit integrals. Some calculations are carried out for the radicals CH₂ and NH.