Morse potential derived from first principles

TL;DR

This paper establishes a fundamental quantum basis for the Morse potential, linking it to the harmonic potential through a non-additive translation operator, and explains anharmonicity in diatomic molecules from first principles.

Contribution

It introduces a novel quantum theoretical approach that derives the Morse potential from first principles, connecting it to the harmonic oscillator via a deformed space framework.

Findings

Morse potential can be derived from quantum principles using a non-additive translation operator.

The approach reveals a quantum origin for anharmonicity in molecular interactions.

Provides insights into properties like dissociation energy and metal deformation from first principles.

Abstract

We show that a direct connection can be drawn, based on fundamental quantum principles, between the Morse potential, extensively used as an empirical description for the atomic interaction in diatomic molecules, and the harmonic potential. This is conceptually achieved here through a non-additive translation operator, whose action leads to a perfect equivalence between the quantum harmonic oscillator in deformed space and the quantum Morse oscillator in regular space. In this way, our theoretical approach provides a distinctive first principle rationale for anharmonicity, therefore revealing a possible quantum origin for several related properties as, for example, the dissociation energy of diatomic molecules and the deformation of cubic metals.