Use of symmetry in coupled Hartree-Fock calculation of non-linear response tensor in molecules

A new computational scheme for electric dipole hyperpolarizabilities has been devised within the coupled Hartree-Fock method. Only the projection of second-order perturbed orbitals onto the subspace spanned by unperturbed virtual orbitals is computed. The entire molecular symmetry is exploited to reduce computational effort: a reduced two-electron integral file containing only symmetry-distinct matrix elements over the atomic basis functions is processed at each iteration. In addition, only symmetry-independent first- and second-order perturbed density matrices need to be calculated. An efficient computer program implementing the present approach has been developed.