| Abstract
| - Vibrational frequencies determined from ab initio calculations are often scaled by empirical factors. Anempirical scaling factor partially compensates for the errors arising from vibrational anharmonicity andincomplete treatment of electron correlation. These errors are not random but are systematic biases. We reportscaling factors for 40 combinations of theory and basis set, intended for predicting the fundamental frequenciesfrom 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 generallyacknowledged; 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 tocorresponding uncertainties in predicted vibrational frequencies. The proposed method for quantifying theuncertainties associated with scaling factors is based on the Guide to the Expression of Uncertainty inMeasurement, published by the International Organization for Standardization (ISO). The data used are fromthe Computational Chemistry Comparison and Benchmark Database (CCCBDB), maintained by the NationalInstitute of Standards and Technology, which includes more than 3939 independent vibrations for 358molecules.
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