Cubic response functions in the multiconfiguration self-consistent field approximation

Abstract

Cubic response functions and various related residues are derived for multiconfigurational self-consistent field reference states. Compact computable expressions are given which render the possibility to simultaneously consider several types of electric and magnetic response properties referring to ground and excited states and to consider multiphoton spectra between ground and excited states or between different excited states. The perturbational expression for the excited-ground state difference in a frequency dependent property can be identified from a double residue of the cubic response function, and from one single reference wave function the property of interest can in principle be given for the whole manifold of excited states. With the present theory calculations for excited state properties can thus be conceived in two ways; by cubic response calculations with the ground state as the reference state and by linear response calculations using the particular excited state as reference state. The two approaches are identical at the full configuration interaction limit, while at the Hartree–Fock level only the former is possible. The applications include calculations of frequency dependent hyperpolarizabilities and excited state polarizabilities of lithium hydride and carbon monoxide and correlated Cotton–Mouton constants for hydrogen fluoride. The results for LiH and CO indicate that the cubic response function approach is quite rewarding already at the self-consistent field level, giving excited state polarizabilities comparable to those obtained from excited state multiconfiguration self-consistent field calculations. At this level the cubic response function calculation scales as ordinary self-consistent field calculations with applicability to large systems. The role of the presently proposed method for quantum chemistry of excited states is briefly discussed.