Resonant light-scattering spectra of molecules with double-well vibrational potentials

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Introduction. Oscillators, the motion of which is determined by a potential with a single minimum for a molecule in both the ground and excited electronic states, are used as a model for the vibrational subsystem in the overwhelming majority of theoretical studies of Raman scattering (RS) of light by molecules. The success of the theory is due mainly to the fact that the overlap integrals for wave functions of oscillators for the ground and excited electronic states of the molecule that are required to derive expressions for the RS line intensity are used in the analytical form. However, many vibrational states of various molecules should be examined using models of oscillators characterized by a potential with two minima (double-well potential). For example, this refers to models describing the Jahn–Teller and Renner–Teller effects, the rotation dynamics of a fragment of an organic molecule around a single or double bond, and the states of a proton in an intra- or intermolecular hydrogen bond (H-bond). Exact expressions for the steady-state wave functions of a particle in a double-well potential have not been obtained in the analytical form. Therefore, approximate wave functions that were found by numerical solution of the corresponding Schrodinger equation with the sought wave functions represented as a linear combination of the eigenfunctions of a harmonic oscillator were used as the vibrational wave functions in one of the first theoretical studies [1] of RS of light by a molecule with a vibrational subsystem characterized by a double-well potential in the lower of two interacting electronic states taking into account Jahn–Teller and Renner–Teller effects. Superpositions of two harmonic oscillator functions, each of which belonged to one of the potential wells, were taken as the approximate vibrational wave functions in theoretical studies [2–4] of RS of light by a molecule with a vibrational subsystem, the motion of which was determined by a double-well potential in the ground electronic state also. Obviously such an examination has a very limited scope of application. Only qualitative conclusions about certain features of the RS process in molecules with double-well vibrational potentials were drawn. Moreover, knowledge of the rules for RS of light by molecules with a double-well potential for the examined vibrational mode is of purely theoretical and great practical interest because RS spectroscopy, especially for irradiation of molecules in the frequency range of their self-absorption [resonance RS spectroscopy (RRS)], is an effective method for establishing, e.g., the mechanism of the position change of a proton in an intramolecular H-bond in the excited electronic state of the molecule during light transformation by it (proton phototransfer). Much attention has re