Accurate evaluation of molecular potential energy functions through vibrational quantum defect analysis

Area of Science:

• Molecular Quantum Mechanics
• Spectroscopy
• Computational Chemistry

Background:

• Accurate modeling of vibrational energy levels is crucial for understanding molecular behavior.
• Existing energy functions may not perfectly represent the complex interactions within diatomic molecules.
• Spectroscopic data provides high-fidelity information on molecular energy levels.

Purpose of the Study:

• To introduce and validate the vibrational quantum defect (VQD) as a metric for selecting optimal molecular energy functions.
• To assess the sensitivity of the VQD method in evaluating the accuracy of different oscillator models.
• To demonstrate a straightforward graphical analysis of VQD for practical application.

Main Methods:

• Utilized experimental RKR (Rydberg-Klein-Rees) energy data obtained from spectroscopy.
• Calculated vibrational quantum deviations (VQD) for various molecular potentials using diverse energy functions.
• Analyzed VQD plotted against vibrational energy to identify the best-fitting energy function.

Main Results:

• The VQD method successfully differentiated between energy functions, highlighting those that best model vibrational energy levels.
• VQD graphs provided a clear and simple means to select the energy function with minimal deviation.
• The VQD approach proved highly sensitive in detecting inaccuracies in oscillator models, particularly for ground-state potentials.

Conclusions:

• The vibrational quantum defect (VQD) is a reliable and sensitive tool for selecting accurate energy functions for diatomic molecules.
• Graphical analysis of VQD offers a practical method for evaluating molecular model performance.
• This method enhances the precision of theoretical predictions for molecular vibrational spectra.