Vibrational levels of a generalized Morse potential

Area of Science:

• Quantum Chemistry
• Computational Physics
• Spectroscopy

Background:

• The Morse Potential (MP) has limitations in accurately describing long-range molecular interactions.
• A Generalized Morse Potential (GMP) was developed to address these limitations with an additional exponential term.
• The complexity of GMP prevents analytical solutions for vibrational energy levels.

Purpose of the Study:

• To present and evaluate numerical methods for solving the vibrational problem of the Generalized Morse Potential.
• To apply these methods to calculate vibrational levels for diatomic molecules B2, O2, and F2.
• To compare the efficiency and accuracy of these numerical methods against existing techniques.

Main Methods:

• Galerkin methods, including the Laguerre Polynomial Method (LPM), Symmetrized LPM, and Polynomial Expansion Method (PEM).
• Application to the vibrational energy levels of homonuclear diatomic molecules (B2, O2, F2).
• Comparison with the Colbert-Miller Discrete Variable Representation (CN-DVR) method.

Main Results:

• The Laguerre Polynomial Method (LPM) achieved spectroscopic accuracy of 0.01 cm⁻¹.
• LPM demonstrated 1-2 orders of magnitude faster convergence compared to CN-DVR.
• Fewer basis functions/grid points were required with LPM for accurate results.

Conclusions:

• Numerical methods, particularly LPM, provide accurate and efficient solutions for the vibrational states of the Generalized Morse Potential.
• The developed methods are suitable for analyzing diatomic molecules with accurate potential energy surfaces.
• A publicly available Python library facilitates the use of GMP and similar potentials.