A dynamical Lie algebraic treatment for the optical nonlinearity of disubstituted benzenes

The dynamical Lie algebraic (DLA) method is applied to the study of nonlinear optical properties of the para-disubstituted benzene systems. It is shown how to generate a dynamical Lie algebra for given Hamiltonian and to construct the corresponding time evolution operator, which is written as a function of the group parameters. The group parameters can be then determined by means of solving a system of nonlinear differential equations. The statistical average values of the dipole moment for the disubstituted benzenes are obtained in terms of the density operator formalism in statistical mechanics. Thus, expressions for the first and second hyperpolarizabilities of the para-disubstituted benzene systems are explicitly given. Comparison with other quantum mechanical calculations shows that the DLA method appears to have a wide range of validity for describing the nonlinear optical properties of a variety of conjugated organic molecules. (C) 2002 Elsevier Science B.V. All rights reserved.