Rovibrational Spectroscopy of Diatomic Molecules in a Modified Morse Potential using Nikiforov-Uvarov Functional Analysis

TL;DR

This paper applies the Nikiforov-Uvarov Functional Analysis method to solve the Schrödinger equation for various diatomic molecules using a modified Morse potential, providing new energy levels and wavefunctions with high accuracy.

Contribution

It introduces the NUFA method as a simple, general, and accurate approach for solving diatomic molecular spectra with a modified Morse potential, including previously unreported states.

Findings

Accurate energy eigenvalues for multiple diatomic molecules.

New high-lying vibrational and rotational states reported.

Excellent agreement with literature for certain molecules.

Abstract

The radial time-independent Schr\"odinger equation is solved for the diatomic molecules: H2, LiH, HCl, CO, VH, CrH, CuLi, TiC, NiC, and ScN using the recently developed Nikiforov-Uvarov Functional Analysis (NUFA) method. A modified Morse potential is considered and the Pekeris approximation is used to accommodate the centrifugal term. Accurate energy eigenvalues and eigenfunction solutions are obtained for vibrational ($\mathit{n}$) and rotational ($\ell$) states. For H2, LiH, HCl, and CO, excellent agreement is observed between present values and literature, provided that the Pekeris approximation remains valid. For other molecules, a collection of low and high-lying states not found in literature are reported. The NUFA method is a simple, general and accurate approach that may be applied to other interatomic potentials.