Distributed first and second order hyperpolarizabilities: An improved calculation of nonlinear optical susceptibilities of molecular crystals

The method of calculating distributed polarizabilities is extended to the f irst and second dipole hyperpolarizabilities, in order to describe more acc urately the molecular response to strong and inhomogeneous external time-de pendent electric fields. The dipolar response is expressed in terms of both potential related charge-density response functions and electric field rel ated dipole-density response functions. The macroscopic linear, quadratic, and cubic optical dipole susceptibilities of molecular crystals are express ed in terms of the distributed (hyper) polarizabilities. This formulation d iffers from previous theories using distributed dipoles in that it allows f or a rigorous treatment of both local induced dipoles and charge flow betwe en different regions of the molecule. As an example, the distributed polari zabilities and first hyperpolarizabilities of urea at the self-consistent-f ield level are used to calculate the linear and quadratic susceptibilities of the urea crystal. The linear susceptibility does not differ substantiall y from that calculated with previous less rigorous models for distributed r esponse, but the quadratic susceptibility is about 50% of that calculated w ith previous models. This indicates that the present treatment of distribut ed response should give a quadratic susceptibility in good agreement with e xperimental data, once the effects of electronic correlation, frequency dis persion, and the permanent crystal field are taken into account. (C) 2000 A merican Institute of Physics. [S0021-9606(00)30111-8].