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

## TL;DR

This paper introduces a computationally efficient method to quantify uncertainty in density functional theory predictions of molecular vibrational frequencies, improving confidence in spectroscopic and thermodynamic analyses.

## Contribution

The authors develop a novel, low-cost uncertainty estimation technique for DFT vibrational frequencies using BEEF-vdW functional's error bounds, applicable to various molecular systems.

## Key findings

- Uncertainty estimates reliably bound different exchange-correlation functionals.
- Modes with bending, torsional, or non-covalent interactions show higher uncertainty.
- The method is simple, efficient, and suitable for routine vibrational frequency analysis.

## Abstract

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.