# The spherical-harmonics representation for the interaction between diatomic molecules: the general case and applications to CO-CO and CO-HF

## TL;DR

This paper details the spherical-harmonics expansion method for representing potential energy surfaces of diatomic molecular interactions, generalizing previous models to more complex systems like CO-CO and CO-HF, with applications in spectroscopic and dynamical studies.

## Contribution

It provides a comprehensive mathematical framework for applying spherical-harmonics expansion to complex diatomic systems, extending previous models to lower symmetry cases such as CO-CO and CO-HF.

## Key findings

- Extended the spherical-harmonics method to CO-CO and CO-HF systems.
- Demonstrated the need for more expansion terms in lower symmetry systems.
- Provided a general mathematical description applicable to various diatomic interactions.

## Abstract

The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties, specifically in van der Waals clusters, with applications also to classical and quantum molecular dynamics simulations. The technique consists in the construction (by ab initio or semiempirical methods) of the expanded potential interaction up to terms that provide the generation of a number of leading configurations sufficient to account for faithful geometrical representations. This paper reports the full general description of the method of the spherical-harmonics expansion as applied to diatomic-molecule-diatomic-molecule systems of increasing complexity: the presentation of the mathematical background is given for providing both the application to the prototypical cases considered previously (O2-O2, N2-N2, and N2-O2 systems) and the generalization to: (i) the CO-CO system, where a characteristic feature is the lower symmetry order with respect to the cases studied before, requiring a larger number of expansion terms necessary to adequately represent the potential energy surface; and (ii) the CO-HF system, which exhibits the lowest order of symmetry among this class of aggregates and therefore the highest number of leading configurations.

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Source: https://tomesphere.com/paper/1706.01049