The identification of nonlinear molecular systems by spectroscopic methods

The Wiener functional expansion method for the analysis of nonlinear systems is applied to identify and analyze both nonlinear and linear molecular systems by spectroscopic methods. As the sampling filter (monochromator) of any spectroscopic apparatus may be defined by a Weber-Hermite polynomial, an analysis of the refracted or scattered light by orthogonal polynomials is easily achieved. Time averaging obtains the Weber-Hermite coefficients which permit the characterization of the molecular system with respect to the polarization of the incident and scattered light. In the case of two series of measurements made with incident and emerging light polarized in different directions: the identification of the JonesM matrices for the molecular system irradiated is possible. In the case of three series of measurements made, for example, with incident and emerging light (a) circularly polarized corotating, (b) circularly polarized contrarotating, and (c) plane polarized perpendicular: the identification of the molecular system's McClain invariants related to the vibrational symmetry group for Raman inelastic light scattering is possible. The analysis presents a unified picture of elastic and inelastic light scattering and one-photon and two-photon processes. The apparatus described would detect those instances in molecular systems for which Beer's law does not apply.