Floquet gauge-invariant coupled perturbation theory in calculations of the optical susceptibilities of molecules

Abstract

A trial wave function applied in variational calculations of the dynamic hyperpolarizabilities of molecules in the Floquet theory is analyzed. It is proved that, when a variational parameter is introduced into the phase multiplier of the trial function, the two methods of description of the interaction between a molecule and a field of a light wave in the dipole approximation with the use of scalar or vector potentials turn out to be identical, as in the rigorous theory. The concept of the gauge-invariant Floquet method as a method of approximate calculation in a finite basis is introduced. Based on the Floquet theory, this method yields identical results in both gauges. A system of equations for the variational parameters is obtained in terms of the suggested method. The perturbation theory is developed on the basis of this system of equations, and the formulas for the first and second derivatives of the Fourier component of the electronic dipole moment of the molecule are derived. These formulas, in combination with the formulas of numerical differentiation, allow one to calculate the dynamic polarizabilities and the first and second hyperpolarizabilities of molecules with the use of the gauge-invariant method.