Ro-vibrational spectroscopy of molecules represented by a Tietz-Hua oscillator potential

TL;DR

This paper computes accurate ro-vibrational energy levels of six diatomic molecules using the Tietz-Hua potential and a generalized pseudospectral method, providing many first-time reported states and detailed quantum number analysis.

Contribution

It introduces an efficient computational approach for solving the Schrödinger equation with the Tietz-Hua potential, reporting many new ro-vibrational states for diatomic molecules.

Findings

Most states are reported for the first time.

Results show good agreement with existing literature.

Eigenvalues vary systematically with quantum numbers.

Abstract

Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schr\"odinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization. Both $\ell=0$ and rotational states are considered. Ro-vibrational levels of six diatomic molecules \emph{viz.}, H$_2$, HF, N$_2$, NO, O$_2$, O$_2^+$ are obtained with good accuracy. Most of the states are reported here for the first time. A detailed analysis of variation of eigenvalues with $n, \ell$ quantum numbers is made. Results are compared with literature data, wherever possible. These are also briefly contrasted with the Morse potential results.