Model Chemistry Recommendations for Scaled Harmonic Frequency Calculations: A Benchmark Study

Despite
the widespread popularity of scaled harmonic frequency
calculations to predict experimental fundamental frequencies in chemistry,
sparse benchmarking is available to guide users on the appropriate
level of theory and basis set choices (model chemistry) or deep understanding
of expected errors. An updated assessment of the best approach for
scaling to minimize errors is also overdue. Here, we assess the performance
of over 600 popular, contemporary, and robust model chemistries in
the calculation of scaled harmonic frequencies, evaluating different
scaling factor types and their implications in the scaled harmonic
frequencies and model chemistry performance. We can summarize our
results into three main findings: (1) Using model-chemistry-specific
scaling factors optimized for three different frequency regions (low
(<1,000 cm–1), mid (1,000–2,000 cm–1), and high (>2,000 cm–1)) results
in substantial improvements in the agreement between the scaled harmonic
and experimental frequencies compared to other choices. (2) Larger
basis sets and more robust levels of theory generally lead to superior
performance; however, the particular model chemistry choice matters
and poor choices lead to significantly reduced accuracies. (3) Outliers
are expected in routine calculations regardless of the model chemistry
choice. Our benchmarking results here do not consider the intensity
of vibrational transitions; however, we draw upon previous benchmarking
results for dipole moments that highlight the importance of diffuse
functions (i.e., augmented basis sets) in high-quality intensity predictions.
In terms of specific recommendations, overall, the highest accuracy
model chemistries are double-hybrid density functional approximations
with a non-Pople augmented triple-ζ basis set, which can produce
median frequency errors down to 7.6 cm–1 (DSD-PBEP86/def2-TZVPD),
which is very close to the error in the harmonic approximation, i.e.,
the anharmonicity error. Double-ζ basis sets should not be used
with double-hybrid functionals as there is no improvement compared
to hybrid functional results (unlike for double-hybrid triple-ζ
model chemistries). Note that 6-311G* and 6-311+G* basis sets perform
like a double-ζ basis set for vibrational frequencies. After
scaling, all studied hybrid functionals with non-Pople triple-ζ
basis sets will produce median errors of less than 15 cm–1, with the best result of 9.9 cm–1 with B97-1/def2-TZVPD.
Appropriate matching of double-ζ basis sets with hybrid functionals
can produce high-quality results, but the precise choice of functional
and basis set is more important. The B97-1, TPSS0-D3(BJ), or ωB97X-D
hybrid density functionals with 6-31G*, pc-1, or pcseg-1 are recommended
for fast routine calculations, all delivering median errors of 11–12
cm–1. Note that dispersion corrections are not easily
available for B97-1; given its strong performance here, we recommend
these be added to major programs in coming updates.