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.