A dynamical Lie algebraic approach to the second order polarizability of the substituted benzenes

Abstract

The dynamical Lie algebraic (DLA) method is used to study the second-order nonlinear optical properties of substituted benzene molecules. In this formulation a dynamical Lie algebra is generated for the Pariser–Parr–Pople π-electron Hamiltonian of the molecule, and the time evolution operator is then given in terms of the group parameters. The group parameters can be determined by solving a set of coupled nonlinear differential equations. Thus, statistical average values of the dipole moment of the molecule are obtained in terms of the density operator formalism in statistical mechanics. The method is applied to the calculation of the second order polarizability of the para-disubstituted benzene molecules. Comparison with other quantum calculations is made. The results demonstrate that DLA method appears to provide an effective means for calculating the second-order nonlinear optical properties of certain classes of conjugated organic molecules.