Canonical Potentials and Spectra within the Born-Oppenheimer Approximation

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Theoretical Chemistry

Background:

• The Born-Oppenheimer approximation is fundamental in molecular quantum chemistry.
• Accurate intermolecular potentials are crucial for predicting molecular behavior.
• Canonical transformations offer a framework for analyzing molecular systems.

Purpose of the Study:

• To investigate the concept of a canonical potential within the Born-Oppenheimer approximation.
• To rigorously evaluate canonical transformations using accurate intermolecular potential data.
• To generate and test canonical potentials for various molecular systems.

Main Methods:

• Utilized a generalized formulation of canonical transformations and spectra.
• Employed accurate ground electronic state pairwise intermolecular potentials for H2, HD, D2, HeH(+), and LiH.
• Generated canonical potentials using algebraic functions derived from H2(+) parameters.
• Compared predicted vibrational state eigenvalues with known Born-Oppenheimer eigenvalues.

Main Results:

• Canonical potentials were generated for H2, HD, D2, HeH(+), and LiH.
• Predicted vibrational eigenvalues deviated by less than 2 cm(-1) from accurate Born-Oppenheimer values for all systems.
• An average standard deviation of 0.27 cm(-1) was observed across 87 vibrational states.

Conclusions:

• The canonical potential approach provides highly accurate predictions of vibrational states within the Born-Oppenheimer approximation.
• This method demonstrates significant efficacy for a range of diatomic molecular systems.
• The findings have important implications for advancing molecular quantum chemistry calculations.