Monomer Basis Representation Method For Calculating The Spectra Of Molecular Clusters I. The Method And Qualitative Models

TL;DR

This paper introduces the Monomer Basis Representation (MBR) method, which uses symmetry adaptation and optimized monomer bases to efficiently compute vibration-rotation-tunneling spectra of molecular clusters.

Contribution

It develops a new MBR method that generates orthogonal optimized bases for molecular clusters using symmetry adaptation, improving spectral calculations.

Findings

MBR method simplifies the eigenvalue problem for molecular spectra.

Sequential symmetry adaptation effectively generates small, symmetry-adapted bases.

The method is applicable regardless of primitive basis types.

Abstract

Firstly, a sequential symmetry adaptation procedure is derived for semidirect product groups. Then, this sequential symmetry adaptation procedure is used in the development of new method named Monomer Basis Representation (MBR) for calculating the vibration-rotation-tunneling (VRT) spectra of molecular clusters. The method is based on generation of optimized bases for each monomer in the cluster as a linear combination of some primitive basis functions and then using the sequential symmetry adaptation procedure for generating a small symmetry adapted basis for the solution of the full problem. It is seen that given an optimized basis for each monomer the application of the sequential symmetry adaptation procedure leads to a generalized eigenvalue problem instead of a standard eigenvalue problem if the procedure is used as it is. In this paper, MBR method will be developed as a solution of that problem such that it leads to generation of an orthogonal optimized basis for the cluster being studied regardless of the nature of the primitive bases that are used in the generation of optimized bases of the monomers.