Meta‐analysis of uniform scaling factors for harmonic frequency calculations

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

Fluorinated Propionic Acids Unmasked: Puzzling Fragmentation Phenomena of the Deprotonated Species

Environmental contamination by per- and polyfluorinated substances (PFAS) is an emerging concern for the public. In this study, short-chain PFAS such as deprotonated per- and polyfluorinated propionic acids are investigated using a combination of infrared multiple-photon dissociation (IRMPD) spectroscopy, collision-induced dissociation (CID), and density functional theory calculations. IRMPD and CID proceed via multiple competing pathways: (1) production of fluoroformate (FCO2-) and the associated ethylene derivative, (2) production of HF and the associated carbanion, or (3) loss of CO2 and the associated carbanion. Fluorinated propionic acids with at least one fluorine atom bound to the terminal carbon yield FCO2-, whereas loss of HF is observed in polyfluorinated species with at least one fluorine atom bound to the α-carbon. To explore the reaction pathways of the various fluorinated propionic acids, the nudged elastic band method is employed. The relative energy of the four-membered ring transition state leading to FCO2- dictates which product channel is observed in dissociation.

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

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.

VIBFREQ1295: A New Database for Vibrational Frequency Calculations

High-throughput approaches for producing approximate vibrational spectral data for molecules of astrochemistry interest rely on harmonic frequency calculations using computational quantum chemistry. However, model chemistry recommendations (i.e., a level of theory and basis set pair) for these calculations are not yet available and, thus, thorough benchmarking against comprehensive benchmark databases is needed. Here, we present a new database for vibrational frequency calculations (VIBFREQ1295) storing 1295 experimental fundamental frequencies and CCSD(T)(F12*)/cc-pVDZ-F12 ab initio harmonic frequencies from 141 molecules. VIBFREQ1295's experimental data was complied through a comprehensive review of contemporary experimental data, while the ab initio data was computed here. The chemical space spanned by the molecules chosen is considered in-depth and is shown to have good representation of common organic functional groups and vibrational modes. Scaling factors are routinely used to approximate the effect of anharmonicity and convert computed harmonic frequencies to predicted fundamental frequencies. With our experimental and high-level ab initio data, we find that a single global uniform scaling factor of 0.9617(3) results in median differences of 15.9(5) cm^-1. A far superior performance with a median difference of 7.5(5) cm^-1 can be obtained, however, by using separate scaling factors (SFs) for three regions: frequencies less than 1000 cm^-1 (SF = 0.987(1)), between 1000 and 2000 cm^-1 (SF = 0.9727(6)), and above 2000 cm^-1 (SF = 0.9564(4)). This sets a lower bound for the performance that could be reliably obtained using scaling of harmonic frequency calculations to predict experimental fundamental frequencies. VIBFREQ1295's most important purpose is to provide a robust database for benchmarking the performance of any vibrational frequency calculations. VIBFREQ1295 data could also be used to train machine-learning models for the prediction of vibrational spectra and as a reference and data starting point for more detailed spectroscopic modeling of particular molecules. The database can be found as part of the Supporting Information for this paper or in the Harvard DataVerse at https://doi.org/10.7910/DVN/VLVNU7.