Quadratic Corrections to Harmonic Vibrational Frequencies Outperform Linear Models

Abstract

Simulating accurate infrared spectra is a longstanding problem in computational quantum chemistry. Linearly scaling harmonic frequencies to better match experimental data is a popular way of approximating anharmonic effects while simultaneously attempting to account for deficiencies in ab initio method and/or basis set. As this approach is empirical, it is also non-variational and unbounded, so it is important to separate and quantify errors as robustly as possible. Eliminating the confounding factor of methodological incompleteness enables us to explore the intrinsic accuracy of the scaling approach alone. We find that single-coefficient linear scaling methods systematically overcorrect low frequencies, while generally undercorrecting higher frequencies. A two-parameter polynomial model gives significantly better predictions without systematic bias in any spectral region, while a single-parameter quadratic scaling model is parameterized to minimize overcorrection errors while only slightly decreasing predictive power.

Predicting OH stretching fundamental wavenumbers of alcohols for conformational assignment: different correction patterns for density functional and wave-function-based methods

“…A universal value for l was often derived from transitions over the full fundamental region (ñ E 0-4200 cm À1 ), 63,64 but this universality comes at the expense of accuracy, with a MAE not better than 20 cm À1 . 64,65 More refined models optimize separate values for low and high wavenumber modes, 63,[66][67][68] introduce a quadratic term 65,69 or target modes of specific functional groups. 22,70,71 Multiplicative scaling according to eqn (3) corresponds to the assumption that the to be corrected sum of anharmonic contributions to eqn (2) is proportional to the harmonic wavenumber.…”

A Series of Discrete Dichloride Dihydrates: Characterisation and Symmetry Effects

“…[a] B3LYP/6‐31+G* for C 2v symmetric complex, with empirical anharmonic scaling correction applied [b] Bending overtones estimated as double the bending fundamentals.…”

“…[a] B3LYP/6‐31+G* for C 2v symmetric complex, with empirical anharmonic scaling correction applied [b] Each complex forms 4 symmetry‐distinct isotopomers, but symmetry splittings are very small. Therefore, averaged predicted band centres are reported.…”

“…A partial hessian calculation was carried out on the dichloride dihydrate and all resultant harmonic frequencies were real, confirming that it represents a minimum on the potential energy surface subject to the applied constraints on surrounding carbon atom positions. An empirical quadratic correction model was applied to obtain predicted anharmonic vibrational frequencies . We have previously shown that errors incurred by correcting harmonic frequencies to approximately account for anharmonicity are much larger than errors due to differences in choice of electronic structure model .…”

“…An empirical quadratic correction model was applied to obtain predicted anharmonic vibrational frequencies . We have previously shown that errors incurred by correcting harmonic frequencies to approximately account for anharmonicity are much larger than errors due to differences in choice of electronic structure model . Full details of the correction procedure are provided in the Supporting Information.…”