  Accurate prediction of molecular vibrational frequencies is important to
identify spectroscopic signatures and reaction thermodynamics. In this work, we
develop a method to quantify uncertainty associated with density functional
theory predicted harmonic vibration frequencies utilizing the built-in error
estimation capabilities of the BEEF-vdW exchange-correlation functional. The
method is computationally efficiency by estimating 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 bounds the self-consistent calculations of six exchange
correlation functionals for small molecules, rare gas dimers, and molecular
complexes from the S22 dataset. Ten rare-gas dimers and the S22 dataset of
molecular complexes provide a rigorous test as they are systems with
complicated vibrational motion and non-covalent interactions. Using coefficient
of variation as a uncertainty metric, we find that modes involving bending or
torsional motion and those dominated by non-covalent interactions are found to
have higher uncertainty in their predicted frequencies than covalent stretching
modes. Given the simplicity of the method, we believe that this method can be
easily adopted and should form a routine part of DFT-predicted harmonic
frequency analysis.
