Semiclassical theory of molecular nonlinear optical polarization

The calculation of linear and nonlinear optical response as well as nonadiabatic curve crossing processes depends on the time evolution of the electronic coherences ~off-diagonal elements of the density matrix!. Unlike their diagonal counterparts, the off-diagonal elements do not have an obvious classical limit. A semiclassical approximation for the nonlinear optical response function, which reveals the classical orbit structure underlying the electronic coherences between Born– Oppenheimer surfaces, is developed. The resulting numerical propagation, which applies to arbitrary anharmonic potentials, is based on integrating the time-dependent Schrödinger equation using the semiclassical time evolution operator, Van Vleck propagator. Using the present formalism it is possible to describe semiclassically multiphoton processes involving several Born–Oppenheimer surfaces. © 1995 American Institute of Physics.