RACAH ALGEBRA AND TALMI TRANSFORMATION IN THE THEORY OF MULTI-CENTRE INTEGRALS OF GAUSSIAN ORBITALS

The multi-centre integrals of spherical Gaussian atomic orbitals are expressed in an algebraically correct tensor form, which consists of invariants, 3jm symbols, and spherical harmonics. The invariants are calculated using the Talmi transformation and the Moshinsky-Smirnov coefficients of nuclear shell theory. Effective calculation procedures of the Moshinsky-Smirnov coefficients are discussed. The integral types investigated are: overlap, electric dipole transition, kinetic energy, three-centre nuclear attraction, four-centre electron repulsion, and three-centre spin-orbit interaction.