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

Abstract

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 modelchemistry-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 doublehybrid 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.

Accurate Structures and Spectroscopic Parameters of Phenylalanine and Tyrosine in the Gas Phase: A Joint Venture of DFT and Composite Wave-Function Methods

“…In the following this computational model is referred to simply as B3 and is used also for the computation of anharmonic contributions. The geometries and harmonic force fields of conformers lying within a predefined energy range are then refined by the revDSD-PBEP86-D3BJ/jun-cc-pv­(T+d)­Z model − (hereafter rDSD), which provides excellent conformational landscapes, ,, geometries, dipole moments, and spectroscopic parameters. , In the present context, we will analyze in detail only conformers not involved in fast relaxation processes and with a relative free energy below 620 cm –1 at room temperature (i.e., a relative population of about 5% when only the considered conformer and the absolute free energy minimum are taken into account, since kT / hc = 207 cm –1 ).…”

DFT Meets Wave-Function Composite Methods for Characterizing Cytosine Tautomers in the Gas Phase

“…Several studies have shown that neglect of diffuse f functions on non-hydrogen atoms (which leads from the jul-cc-pVTZ to the jun-cc-pvTZ basis set) reduces the computational cost without any significant accuracy loss for geometries, 32 dipole moments, 51 and spectroscopic parameters. 39,52 The typical error of rDSD/j3 bond lengths and valence angles (0.3%) 32 is sufficient to obtain accurate relative electronic energies and vibrational spectra of different tautomers, but the situation is different for the leading terms of MW spectra, namely rotational constants of the vibrational ground-state (B i 0 , where i refers to the inertial axes a, b, c). These parameters include vibrational corrections (ΔB i vib ) in addition to equilibrium rotational constants (B i eq ).…”

“…Next, the geometries and harmonic force fields of the most stable species have been refined at the revDSD-PBEP86-D3BJ/jun-cc-pvTZ level − (hereafter rDSD/j3). Several studies have shown that neglect of diffuse f functions on non-hydrogen atoms (which leads from the jul-cc-pVTZ to the jun-cc-pvTZ basis set) reduces the computational cost without any significant accuracy loss for geometries, dipole moments, and spectroscopic parameters. , …”

Towards a reliable prediction of the infrared spectra of cosmic fullerenes and their derivatives in the JWST era

“…To evaluate the accuracy of the fitted scaling factors, we calculated the median errors as a more robust evaluation compared to RMSE, which can be significantly influenced by outliers (Zapata Trujillo & McKemmish 2022, Zapata Trujillo & McKemmish 2023. Specifically, median errors refer to the median of the differences between the and .…”

“…The prediction can either base on harmonic approximation, or use the more accurate but also more expensive anharmonic method. To achieve a reliable prediction using the much cheaper harmonic calculations, scaling factors have been developed for correcting the computed frequencies (Pople et al 1993, Scott & Radom 1996, Zapata Trujillo & McKemmish 2023.…”