Zero-Field Splittings. IV. Gaussian Approximation of Integrals

Zero-field splitting integrals over Slater 2pz atomic orbitals are evaluated by substituting for each orbital an approximating linear combination of Gaussians differing in their orbital exponents. Each linear combination is derived a priori for maximum overlap with the Slater orbital. The accuracy of the method for successively higher orders of approximation is assayed by direct comparison with exact Slater values. It is found that a three-term expansion is sufficient to give molecular Slater integrals needed in triplet calculations to 0.1% accuracy.