Matrix elements for anharmonic potentials: Application to I₂ morse oscillator

Area of Science:

• Quantum mechanics
• Molecular spectroscopy
• Computational chemistry

Background:

• Analytical expressions for Morse oscillator matrix elements are widely used.
• Previous methods have limitations or complexities in application.

Purpose of the Study:

• To discuss the advantages of existing analytical expressions for Morse oscillator matrix elements.
• To propose and validate a comprehensive numerical method for calculating these matrix elements.

Main Methods:

• Review and discussion of established analytical methods.
• Development of a full numerical approach for matrix element calculation.
• Comparative analysis using the I2 molecular system.

Main Results:

• The study highlights the benefits of current analytical techniques.
• A novel numerical method is presented for calculating matrix elements.
• Comparison of numerical results with analytical methods (Gallas, Vasan, Cross) and the variational method for I2.

Conclusions:

• The proposed numerical method offers a viable alternative for calculating Morse oscillator matrix elements.
• The findings facilitate a deeper understanding and accurate computation in molecular systems.