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