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Uncertainties in Scaling Factors for ab Initio Vibrational Frequencies



Karl K. Irikura, Russell D. Johnson III, Raghu N. Kacker


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 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 realized; consequently, the scaling factors generally have only two significant digits. 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 upon 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.
Journal of Physical Chemistry A
No. 37


ab initio, computational chemistry, density functional theory, quantum chemistry, uncertainty, vibrational frequencies, virtual measurement


Irikura, K. , Johnson, R. and Kacker, R. (2005), Uncertainties in Scaling Factors for ab Initio Vibrational Frequencies, Journal of Physical Chemistry A (Accessed July 14, 2024)


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Created September 1, 2005, Updated February 17, 2017