Meta-analysis of uniform scaling factors for harmonic frequency calculations

Vibrational frequency calculations performed under the harmonic approximation are widespread across chemistry. However, it is well-known that the calculated harmonic frequencies tend to systematically overestimate experimental fundamental frequencies; a limitation commonly overcome with multiplicative scaling factors. In practice, multiplicative scaling factors are derived for each individual model chemistry choice (i.e., a level of theory and basis set pair), where performance is judged by, for example, the root-mean square error (RMSE) between the predicted scaled and experimental frequencies. However, despite the overwhelming number of scaling factors reported in the literature and model chemistry approximations available, there is little guidance for users on appropriate model chemistry choices for harmonic frequency calculations. Here, we compile and analyze the data for 1495 scaling factors calculated using 141 levels of theory and 109 basis sets. Our meta-analysis of this data shows that scaling factors and RMSE approach convergence with only hybrid functionals and double-zeta basis sets, with anharmonicity error already dominating model chemistry errors. Noting inconsistent data and the lack of independent testing, we can nevertheless conclude that a minimum error of 25 cm⁻¹—arising from insufficiently accurate treatment of anharmonicity—is persistent regardless of the model chemistry choice. Based on the data we compiled and cautioning the need for a future systematic benchmarking study, we recommend ωB97X-D/def2-TZVP for most applications and B2PLYP/def2-TZVPD for superior intensity predictions. With a smaller benchmark set, direct comparison prefers ωB97X-D/6-31G* to B3LYP/6-31G*.

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