Ro-vibrational energy and thermodynamic properties of molecules subjected to Deng-Fan potential through an improved approximation

TL;DR

This paper presents an improved analytical approach to solve the Schrödinger equation with Deng-Fan potential, deriving energy levels and thermodynamic properties for molecules, and analyzing the impact of a new approximation method and quantum corrections.

Contribution

It introduces a modified Pekeris-type approximation with an adjustable parameter for better accuracy in solving the Schrödinger equation with Deng-Fan potential.

Findings

The new approximation improves eigenvalue calculations for H₂, LiH, HCl, and CO.

Analytical expressions for thermodynamic properties are derived.

Quantum corrections significantly affect thermodynamic calculations.

Abstract

Accurate solution of the Schr\"odinger equation with Deng-Fan potential is presented by means of Nikiforov-Uvarov method. A modified Pekeris-type approximation is proposed for the centrifugal term, from a linear combination of the $r \to 0$ and $r \to r_e$ limits. It can potentially offer a series of approximations (depending on an adjustable parameter $\lambda$). The existing approximations in the literature can then be recovered in certain special cases. Its efficiency and feasibility is demonstrated by a critical comparison of eigenvalues produced at various $\lambda$'s for four molecules, \emph{viz.}, H$_2$, LiH, HCl and CO. Analytical expressions are derived for energies, eigenfunctions and the thermodynamic properties such as vibrational mean free energy, vibrational free energy, vibrational entropy and vibrational specific heat. The effect of quantum correction on partition function and thermodynamic properties is discussed by including the correction up to 10th-order, for H$_2$ and LiH. The effect of $\lambda$ parameter on these properties is also studied.