Non-relativistic energy equations for diatomic molecules constrained in a deformed hyperbolic potential function

Area of Science:

• Quantum Mechanics
• Molecular Physics
• Computational Chemistry

Background:

• The deformed hyperbolic potential is a key model in molecular physics.
• Determining accurate energy levels for diatomic molecules is crucial for understanding their behavior.
• Existing methods may have limitations in precision or applicability.

Purpose of the Study:

• To derive approximate analytical energy equations for the deformed hyperbolic potential.
• To apply these equations to determine the vibrational energy spectra of specific diatomic molecules.
• To validate the obtained results against experimental data and alternative theoretical approaches.

Main Methods:

• Utilized the Nikiforov-Uvarov approach and semi-classical WKB approximation.
• Applied the Pekeris approximation to solve the non-relativistic wave equation.
• Transformed the potential function using Varshni conditions for molecular applications.
• Employed the MATHEMATICA program for numerical data acquisition.

Main Results:

• Obtained approximate analytical energy equations for the deformed hyperbolic potential.
• Calculated the molecular vibrational energy spectra for diatomic molecules like CO, HCl, and H2.
• Results showed good agreement with experimental data and other analytical methods.
• Energy values were found to be bounded and increase with quantum numbers.

Conclusions:

• The derived approximate analytical energy equations are effective for diatomic molecules.
• The method provides a reliable approach for calculating molecular vibrational energy spectra.
• Slight discrepancies with literature are attributed to analytical methods and computational accuracy.