The transferability limits of static benchmarks

Galván I, Lindh R. A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

A step toward density benchmarking-The energy-relevant "mean field error"

Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that are precise enough to be predictive in many instances, as validated by large- and small-scale benchmarking efforts. However, assessing the quality of densities has been the subject of far less attention, in part because reliable error measures are difficult to define. To this end, this work introduces the mean-field error, which directly assesses the quality of densities from approximations. The mean-field error is contextualized within existing frameworks of density functional error analysis and understanding and shown to be part of the density-driven error. It is demonstrated in several illustrative examples. Its potential use in future benchmarking protocols is discussed, and some conclusions are drawn.

The first HyDRA challenge for computational vibrational spectroscopy

Vibrational spectroscopy in supersonic jet expansions is a powerful tool to assess molecular aggregates in close to ideal conditions for the benchmarking of quantum chemical approaches. The low temperatures achieved as well as the absence of environment effects allow for a direct comparison between computed and experimental spectra. This provides potential benchmarking data which can be revisited to hone different computational techniques, and it allows for the critical analysis of procedures under the setting of a blind challenge. In the latter case, the final result is unknown to modellers, providing an unbiased testing opportunity for quantum chemical models. In this work, we present the spectroscopic and computational results for the first HyDRA blind challenge. The latter deals with the prediction of water donor stretching vibrations in monohydrates of organic molecules. This edition features a test set of 10 systems. Experimental water donor OH vibrational wavenumbers for the vacuum-isolated monohydrates of formaldehyde, tetrahydrofuran, pyridine, tetrahydrothiophene, trifluoroethanol, methyl lactate, dimethylimidazolidinone, cyclooctanone, trifluoroacetophenone and 1-phenylcyclohexane-cis-1,2-diol are provided. The results of the challenge show promising predictive properties in both purely quantum mechanical approaches as well as regression and other machine learning strategies.

Statistical Equivalence of Quantum Chemical Methods for Energy Distribution in Water Clusters

Methods of quantum chemistry are instrumental in understanding molecular structures and properties. However, the results demonstrate significant variability, which is difficult to predict and rationalize. The fundamental question is whether some molecular systems exhibit properties invariant with respect to the computational method. The idea explored here is that collective properties of statistical ensembles should be more robust than characteristics of individual molecules and their arbitrary sets. This effect is demonstrated for the complete set of hydrogen-bond topologies of the dodecahedral water cluster (H₂ O)₂₀ . Non-Gaussian energy distributions produced by various methods have the same functional form despite strong differences in mean values and standard deviations. The conclusion is tested on methods of different complexity and origin employing a number of criteria. A linear mapping between the energies produced by different methods is discussed. The significance of the results is in establishing a collective equivalence property of quantum chemical methods.

Redox-active ligands as a challenge for electronic structure methods

To improve the catalytic activity of 3d transition metal catalysts, redox-active ligands are a promising tool. These ligands influence the oxidation state of the metal center as well as the ground spin-state and make the experimental determination of both properties challenging. Therefore, first-principles calculations, in particular employing density functional theory with a proper choice of exchange-correlation (xc) functional, are crucial. Common xc functionals were tested on a simple class of metal complexes: homoleptic, octahedral tris(diimine) iron(II) complexes. The spin-state energy splittings for most of these complexes showed the expected linear dependence on the amount of exact exchange included in the xc functionals. Even though varying redox-activity affects the electronic structure of the complexes considerably, the sensitivity of the spin-state energetics to the exact exchange admixture is surprisingly small. For iron(II) complexes with highly redox-active ligands and for a broad range of ligands in the reduced tris(diimine) iron(I) complexes, self-consistent field convergence to local minima was observed, which differ from the global minimum in the redox state of the ligand. This may also result in convergence to a molecular structure that corresponds to an energetically higher-lying local minimum. One criterion to detect such behavior is a change in the sign of the slope for the dependence of the spin-state energy splittings on the amount of exact exchange. We discuss possible protocols for dealing with such artifacts in cases in which a large number of calculations makes checking by hand unfeasible.