Uncertainty Quantification in First-Principles Predictions of Harmonic Vibrational Frequencies of Molecules and Molecular Complexes

Accurate prediction of molecular vibrational frequencies is important to identify spectroscopic signatures and reaction thermodynamics. In this work, we develop a method to quantify the uncertainty associated with density functional theory-predicted harmonic vibrational frequencies using the built-in error estimation capabilities of the Bayesian error estimation functional with van der Waals exchange–correlation functional. The method is computationally efficient as it estimates the uncertainty at nearly the same computational cost as a single vibrational frequency calculation. We demonstrate the utility and robustness of the method by showing that the uncertainty estimates bound the self-consistent calculations of 6 exchange–correlation functionals for 10 small molecules, 10 rare-gas dimers, and molecular complexes from the S22 dataset. The rare-gas dimers and the S22 dataset provide a rigorous test, as they are systems with complicated vibrational motion and noncovalent interactions. Using the coefficient of variation as an uncertainty metric, we find that modes involving bending or torsional motion and those dominated by noncovalent interactions have higher uncertainty in their predicted frequencies than covalent stretching modes. Given its simplicity, we believe that this method can be easily adopted and should form a routine part of density functional theory-predicted harmonic frequency analysis.