Evaluating Power-LawScaling Factors for HarmonicVibrational 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.