Comparison of the polarizabilities and hyperpolarizabilities obtained from finite basis set and finite difference Hartree–Fock calculations for diatomic molecules: III. The ground states of N2, CO and BF**This paper is dedicated to Victor R Saunders, on his official retirement from Daresbury Laboratory.

Abstract

We investigate the accuracy with which the electric dipole polarizability, αzz, and the hyperpolarizability, βzzz, can be calculated by using the algebraic approximation, i.e. finite basis set expansions, and by means of the finite difference method in calculations for the ground states of the 14 electron systems N2, CO and BF within the Hartree–Fock model at their respective experimental equilibrium geometries. For a well-chosen grid, the finite difference technique can provide Hartree–Fock energy and dipole moment expectation values approaching machine precision which can be used to assess the accuracy of corresponding calculations carried out within the algebraic approximation. The finite field approximation is used to determine polarizabilities and hyperpolarizabilities from finite difference Hartree–Fock dipole moment expectation values. The results are compared with finite basis set calculations of the corresponding quantities which are carried out analytically using coupled perturbed Hartree–Fock theory. For the N2 molecule, the Hartree–Fock polarizability is found to be 14.9512 au within the finite basis set approximation and 14.945 au within the finite difference approach. For the CO molecule, the corresponding results are 14.4668 au and 14.4668 au, whilst for the BF molecule the values are 16.6450 au and 16.6450 au, respectively. The Hartree–Fock hyperpolarizability of the CO molecule is found to be 31.4081 au and 31.411 au within the finite basis set and finite difference approximations, respectively. The corresponding hyperpolarizability values for the BF molecule are 63.9687 au and 63.969 au, respectively.