Evaluating Power-Law Scaling Factors for Harmonic Vibrational Frequencies across Model Chemistries

Scaling factors are derived for fundamental harmonic vibrational frequencies and molecular thermodynamic corrections using the recently developed wavenumber power scaling (WPS) method [Spectrochim. Acta, Part A2026, 359, 127967.]. WPS enables a simple two-parameter scaling of vibrational frequencies that improves on uniform scaling errors by up to ca. 64% for the best methods tested. Power law and uniform scaling factors are calculated using over 500 model chemistries, including wave function theories (HF, MP2, CCSD) and density functional theories with a range of atom-centered basis sets. Experimental comparisons are performed using a set of 894 vibrations with C≡C and C≡N triple bond bending modes removed. The B97, B97-1, and τ-HCTHh density functional methods match the experimental fundamentals closely and are recommended for general use. WPS frequencies converge more quickly with respect to basis-set size than uniformly scaled frequencies, making them both more accurate and computationally efficient to calculate. Power law scaling describes fundamental vibrations, enthalpies, and entropies using a unified set of scaling factors, and can improve generalized gradient approximation frequencies that are resistant to uniform scaling.