VIBFREQ1295: A New Database for Vibrational 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.

Approximating large-basis coupled-cluster theory vibrational frequencies using focal-point approximations

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller-Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm-1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.

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.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.