Computational Analysis of the Energy States of the Hydrogen Molecule H2, and Lithium Hydride LiH

Abstract

This study investigates the rovibrational energy spectra of the hydrogen molecule and lithium hydride using Exact quantization rule (EQR) within the framework of the non-relativistic Schrödinger equation. The molecular interaction is modelled with a combined Kratzer plus generalized inverse quadratic Yukawa potential, which incorporates the long-range molecular interaction and short-range screening effects. The radial Schrödinger equation is formulated and solved analytically using EQR to obtain the bound-state energy eigenvalues and the corresponding eigenfunctions. The effects of the potential parameters, vibrational and rotational quantum numbers, on the energy spectra are examined. The spectroscopic constants are used to assess the suitability of the proposed potential in describing the molecular structure and vibrational behaviour of H₂ and LiH. The theoretical predictions are compared with available literature to establish the accuracy and reliability of the model. The study further provides insights into the applicability of the exact quantization rule to diatomic molecular systems and demonstrates the potential of the combined interaction model for investigating molecular vibrational spectra.