Semiclassical theory of Fermi resonance between stretching and bending modes in polyatomic molecules

Abstract

Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two-state model, and a uniform semiclassical approximation (USC) based on Mathieu functions are each used to determine the splittings and state mixing involved in these stretch-bend Fermi resonances. For small perturbations, approximate analytic semiclassical expressions are obtained for the system treated. These analytic expressions are given for the splittings using a two-state or USC method and for the overlaps of the zeroth order states with the eigenstates of the molecule using a USC method.

Vibrational spectrum of a 1D oscillator: The quantum, the Wigner, and the classical ways

“…Methods mixing quantum wavefunction information and classical propagation, so‐called mixed quantum‐classical or semiclassical (SC) methods, have also been developed. [ 7–12 ]…”

“…Methods mixing quantum wavefunction information and classical propagation, so-called mixed quantum-classical or semiclassical (SC) methods, have also been developed. [7][8][9][10][11][12] In the QM approach, the common method is to solve for the eigenstates, wave functions, and eigenvalues of the quantum Hamiltonian. [13][14][15] These values are used to calculate the peak position and absorption intensity.…”

Pressure‐induced Fermi resonance between fundamental modes in 7,7,8,8‐tetracyanoquinodimethane

“…Consequently, Fermi resonances are used to aid assignment of peaks probed in Raman scattering and infrared absorption spectra that do not correspond with known fundamental vibrations. The investigation of Fermi resonance has great significance not only in the areas of physics and chemistry, such as the establishment of Fermi resonance modeling, solvent effects, isotopic effects, ion–molecule interaction, vibrational lifetime and hydrogen bond, but also for practical applications in the field of material science, biology (protein transfer), geology and sensor . Although past research has yielded fruitful results, it is still a significant challenge to fully explore the mechanisms of Fermi resonance.…”