Uncertainties in scaling factors for ab initio vibrational frequencies

Vibrational frequencies determined from ab initio calculations are often scaled by empirical factors. An empirical scaling factor partially compensates for the errors arising from vibrational anharmonicity and incomplete treatment of electron correlation. These errors are not random but are systematic biases. We report scaling factors for 40 combinations of theory and basis set, intended for predicting the fundamental frequencies from computed harmonic frequencies. An empirical scaling factor carries uncertainty. We quantify and report, for the first time, the uncertainties associated with the scaling factors. The uncertainties are larger than generally acknowledged; the scaling factors have only two significant digits. For example, the scaling factor for HF/6-31G(d) is 0.8982 +/- 0.0230 (standard uncertainty). The uncertainties in the scaling factors lead to corresponding uncertainties in predicted vibrational frequencies. The proposed method for quantifying the uncertainties associated with scaling factors is based on the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization (ISO). The data used are from the Computational Chemistry Comparison and Benchmark Database (CCCBDB), maintained by the National Institute of Standards and Technology, which includes more than 3939 independent vibrations for 358 molecules.