Algebraic Determination of Spectral Characteristics of Rovibrational States of Diatomic Molecules. II. Analysis of the Vibration-Rotation Interaction by Means of the Factorization Method

TL;DR

This paper develops an algebraic model using ladder operators to analyze the vibrational-rotational interaction in diatomic molecules, deriving explicit formulas for spectral characteristics and Herman-Wallis coefficients.

Contribution

It introduces a second-order expansion method for vibrational-rotational wave functions and derives algebraic formulas for matrix elements and Herman-Wallis coefficients for arbitrary quantum states.

Findings

Derived explicit algebraic formulas for vibrational dependences of Herman-Wallis coefficients.

Analyzed cases of harmonic oscillator and Morse potential.

Considered non-adiabatic effects on matrix elements.

Abstract

An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter characterizing the vibrational-rotational interaction have been proposed for the potentials whose the creation and annihilation operators can be constructed. Expressions for the expansion of the wave function of the vibrational-rotational states in a set of wave functions of the rotationless vibrational states have been obtained of the second order in the parameter. Using these expressions and the formulas obtained in our previous paper the algebraic expressions for the expansion of the dependences of matrix elements in a set of matrix elements on the wave functions of the rotationless ground vibrational states have been obtained for arbitrary functions of internuclear distance and arbitrary values of the vibrational and rotational quantum numbers of the combined states. The cases of the harmonic oscillator and the Morse potential were analyzed. The explicit algebraic formulas for the vibrational dependences of the first five Herman-Wallis coefficients have been derived for arbitrary values of the vibrational quantum numbers of the combining states. The possibility of taking into account the influence of non-adiabatic effects on the vibrational and rotational dependences of matrix elements is considered.