Bayesian Analysis of Theoretical Rotational Constants from Low-Cost Electronic Structure Methods

Area of Science:

• Computational Chemistry
• Molecular Spectroscopy

Background:

• Microwave spectroscopy relies heavily on accurate theoretical predictions of rotational constants.
• There is a growing need to evaluate the performance of cost-effective electronic structure methods for these predictions.

Purpose of the Study:

• To benchmark the accuracy of various low-level ab initio and density functional methods for predicting rotational constants.
• To assess the uncertainty associated with these theoretical predictions.
• To identify optimal computational strategies for rotational spectroscopy.

Main Methods:

• Systematic benchmarking of quantum chemical methods and basis sets using a dataset of 6916 optimized geometries.
• Bayesian analysis with Hamiltonian Monte Carlo sampling to determine prediction uncertainties.
• Analysis of 76 species with available high-resolution experimental gas-phase rotational constants.

Main Results:

• Newer functionals (Minnesota family, ωB97X-D) show higher accuracy and lower uncertainty than traditional methods (B3LYP, MP2).
• The ωB97X-D functional with a 6-31+G(d) basis set offers optimal performance-to-cost ratio.
• Statistical scaling factors were derived to correct for vibration-rotation effects, improving accuracy.

Conclusions:

• The study provides a hierarchy of accuracy for common computational methods in rotational spectroscopy.
• Theoretical uncertainties can be leveraged for cross-correlation with experimental spectra, aiding molecule identification.
• Optimized computational approaches can enhance the efficiency and accuracy of microwave spectroscopy experiments.