Abstract
A fully coupled variational formulation has been presented for calculating the electric dipole hyperpolarizability (γ) of open and closed-shell atomic systems. For the Li sequence the open-shell formalism of Roothaan has been adopted. The sign of γ for ions of the Li sequence agree well with earlier results although the magnitude for Li atom is somewhat smaller. The value of γ for the Be atom has been found to agree fairly well with other results, both in the order of magnitude and sign, while for B+ and C++ the sign is found to be negative.