Connection between the SU(2) Lie algebraic approach and configuration space: application to methylene chloride

Abstract

The $SU(2)$-Lie algebraic approach based on the dynamical group $U_1(2)\times U_2(2)\times \cdots \times U_n(2)$ to describe a set of n local oscillators is analysed from the point of view of its connection with configuration space. First, the matrix elements of a general Hamiltonian involving Casimir operators of the two dynamical algebras $S{O}_{ij}(2)$ and $S{U}_{ij}(2)$ are revised and subsequently the equivalent Hamiltonian in configuration space is established. This relationship permits us to evaluate the order of the interactions traditionally taken into account in the $SU(2)$ vibron model with the additional advantage of providing the connection with force constants. Starting from configuration space our analysis is applied to the description of vibrational excitations of the molecule of methylene chloride including both stretching and bending degrees of freedom.

GRAPHICAL ABSTRACT

Keywords:

• $U(2)$ lie algebras
• connection with configuration space
• vibrational excitations
• methylene chloride

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (DGAPA-UNAM), Mexico [grant number IN-212020].