Spin-unrestricted time-dependent Hartree-Fock theory of frequency-dependent linear and nonlinear optical properties

A self-consistent time-dependent unrestricted Hartree-Fock (TDUHF) theory of linear and nonlinear optical properties is presented. Expressions are derived to calculate the elements of the linear polarizability tensor alpha, the first-hyperpolarizability tensor beta, and the second-hyperpolarizability tensor gamma, in terms of spin-adapted perturbed density matrices. For the hyperpolarizability tensors, beta and gamma, expressions are also derived from the lower-order solutions to the TDUHF equations. A novel feature of the present formulation is that it automatically allows for the separation of the contributions to (hyper)polarizability tensors from individual spin. Results obtained from the calculations of alpha(omega(sigma);alpha(a)) for H, C, N, O, F, Si, P, S, Cl, O-2, NO, and OH and of beta(-omega(sigma);omega(a),omega(b)) corresponding to various second-order nonlinear optical processes for NO and OH radicals are presented. The present results for alpha show excellent agreement with the literature data. The calculated result for beta(parallel to) in the case of the NO radical is too small and has a different sign in comparison to the published experimental data. For both NO and OH, the beta tensor for different second-order nonlinear optical processes show the order: beta(-2 omega;omega,omega)>beta(-omega;0,omega) =beta(0;omega,-omega)>beta(0;0,0). (C) 1996 American Institute of Physics.