Quadratic Corrections to Harmonic Vibrational Frequencies Outperform Linear Models

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 nonvariational 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.