“Mindless” DFT Benchmarking

Substituting density functional theory in reaction barrier calculations for hydrogen atom transfer in proteins

Hydrogen atom transfer (HAT) reactions are important in many biological systems. As these reactions are hard to observe experimentally, it is of high interest to shed light on them using simulations. Here, we present a machine learning model based on graph neural networks for the prediction of energy barriers of HAT reactions in proteins. As input, the model uses exclusively non-optimized structures as obtained from classical simulations. It was trained on more than 17 000 energy barriers calculated using hybrid density functional theory. We built and evaluated the model in the context of HAT in collagen, but we show that the same workflow can easily be applied to HAT reactions in other biological or synthetic polymers. We obtain for relevant reactions (small reaction distances) a model with good predictive power (R2 ∼ 0.9 and mean absolute error of <3 kcal mol-1). As the inference speed is high, this model enables evaluations of dozens of chemical situations within seconds. When combined with molecular dynamics in a kinetic Monte-Carlo scheme, the model paves the way toward reactive simulations.

Benchmarking Basis Sets for Density Functional Theory Thermochemistry Calculations: Why Unpolarized Basis Sets and the Polarized 6-311G Family Should Be Avoided

Basis sets are a crucial but often largely overlooked choice in setting up quantum chemistry calculations. The choice of the basis set can be critical in determining the accuracy and calculation time of your quantum chemistry calculations. Clear recommendations based on thorough benchmarking are essential but not readily available currently. This study investigates the relative quality of basis sets for general properties by benchmarking basis set performance for a diverse set of 139 reactions (from the diet-150-GMTKN55 data set). In our analysis, we find the distributions of errors are often significantly non-Gaussian, meaning that the joint consideration of median errors, mean absolute errors, and outlier statistics is helpful to provide a holistic understanding of basis set performance. Our direct comparison of performance between most modern basis sets provides quantitative evidence for basis set recommendations that broadly align with the established understanding of basis set experts and is evident in the design of modern basis sets. For example, while zeta is a good measure of quality, it is not the only determining factor for an accurate calculation with unpolarized double- and triple-ζ basis sets (like 6-31G and 6-311G) having very poor performance. Appropriate use of polarization functions (e.g., 6-31G*) is essential to obtain the accuracy offered by double- or triple-ζ basis sets. In our study, the best performances for double- and triple-ζ basis sets are 6-31++G** and pcseg-2, respectively. However, the performances of singly polarized double-ζ and doubly polarized triple-ζ basis sets are quite similar with one key exception: the polarized 6-311G basis set family has poor parametrization, which means its performance is more like a double-ζ than a triple-ζ basis set. All versions of the 6-311G basis set family should be avoided entirely for valence chemistry calculations moving forward.

The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory

Exact conditions have long been used to guide the construction of density functional approximations. However, hundreds of empirical-based approximations tailored for chemistry are in use, of which many neglect these conditions in their design. We analyze well-known conditions and revive several obscure ones. Two crucial distinctions are drawn: that between necessary and sufficient conditions and that between all electronic densities and the subset of realistic Coulombic ground states. Simple search algorithms find that many empirical approximations satisfy many exact conditions for realistic densities and non-empirical approximations satisfy even more conditions than those enforced in their construction. The role of exact conditions in developing approximations is revisited.

Mehrere Triplett-Metall-zentrierte Jahn-Teller-Isomere bestimmen die temperaturabhängigen Lumineszenzlebensdauern in [Ru(bpy)3]2

Ein genaues Verständnis der Faktoren, welche die Lumineszenzlebensdauer von Übergangsmetallverbindungen bestimmen, ist für Anwendungen in der Photokatalyse und der photodynamischen Therapie von entscheidender Bedeutung. Die im Falle von [Ru(bpy)3]2+ (bpy=2,2’‐Bipyridin) allgemein akzeptierte Theorie besagt, dass die Emissionslebensdauer durch Optimierung der Energiebarriere zwischen dem emittierenden Triplett‐Zustand des Metall‐Liganden‐Ladungstransfers (3MLCT) und dem thermisch aktivierten Triplett‐Zustand des Metall‐Zentrums (3MC), oder der Energielücke zwischen beiden Zuständen gesteuert werden kann. Hier zeigen wir, dass dies nicht allgemeingültig ist. Darüber hinaus demonstrieren wir, dass die Betrachtung eines einzelnen Relaxationspfades, der vom energetisch niedrigsten Minimum aus bestimmt wird, zu falschen Vorhersagen der temperaturabhängigen Emissionslebensdauer führt. Stattdessen erhalten wir eine ausgezeichnete Übereinstimmung mit den experimentellen temperaturabhängigen Lebensdauern, wenn ein erweitertes kinetisches Modell herangezogen wird, welches alle Pfade im Zusammenhang mit mehreren Jahn–Teller‐Isomeren und ihren effektiven Reaktionsbarrieren beinhaltet. Diese Konzepte sind für das Design weiterer lumineszierender Übergangsmetallkomplexe mit individuell angepassten Emissionslebensdauern auf der Grundlage theoretischer Vorhersagen unerlässlich.

Multiple Triplet Metal-Centered Jahn-Teller Isomers Determine Temperature-Dependent Luminescence Lifetimes in [Ru(bpy)3 ]2

Understanding the factors that determine the luminescence lifetime of transition metal compounds is key for applications in photocatalysis and photodynamic therapy. Here we show that for[ Ru ( bpy ) 3 ] 2 + ${[{\rm{Ru}}({\rm{bpy}})_{\rm{3}} ]^{{\rm{2 + }}} }$ (bpy = 2,2'-bipyridine), the generally accepted idea that emission lifetimes can be controlled optimizing the energy barrier from the emissive triplet metal-to-ligand charge-transfer (3 MLCT) state to the thermally-activated triplet metal-centered (3 MC) state or the energy gap between both states is a misconception. Further, we demonstrate that considering a single relaxation pathway determined from the minimum that is lowest in energy leads to wrong temperature-dependent emission lifetimes predictions. Instead, we obtain excellent agreement with experimental temperature-dependent lifetimes when an extended kinetic model that includes all the pathways related to multiple Jahn-Teller isomers and their effective reaction barriers is employed. These concepts are essential to correctly design other luminescent transition metal complexes with tailored emission lifetimes based on theoretical predictions.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

Benchmarking First-Principles Reaction Equilibrium Composition Prediction

The availability of thermochemical properties allows for the prediction of the equilibrium compositions of chemical reactions. The accurate prediction of these can be crucial for the design of new chemical synthesis routes. However, for new processes, these data are generally not completely available. A solution is the use of thermochemistry calculated from first-principles methods such as Density Functional Theory (DFT). Before this can be used reliably, it needs to be systematically benchmarked. Although various studies have examined the accuracy of DFT from an energetic point of view, few studies have considered its accuracy in predicting the temperature-dependent equilibrium composition. In this work, we collected 117 molecules for which experimental thermochemical data were available. From these, we constructed 2648 reactions. These experimentally constructed reactions were then benchmarked against DFT for 6 exchange-correlation functionals and 3 quality of basis sets. We show that, in reactions that do not show temperature dependence in the equilibrium composition below 1000 K, over 90% are predicted correctly. Temperature-dependent equilibrium compositions typically demonstrate correct qualitative behavior. Lastly, we show that the errors are equally caused by errors in the vibrational spectrum and the DFT electronic ground state energy.

Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry

Multicomponent methods are a conceptually simple way to include nuclear quantum effects into quantum chemistry calculations. In multicomponent methods, the electronic molecular orbitals are described using the linear combination of atomic orbitals approximation. This requires the selection of a one-particle electronic basis set which, in practice, is commonly a correlation-consistent basis set. In multicomponent method studies, it has been demonstrated that large electronic basis sets are required for quantum hydrogen nuclei to accurately describe electron-nuclear correlation. However, as we show in this study, much of the need for large electronic basis sets is due to the correlation-consistent electronic basis sets not being optimized to describe nuclear properties and electron-nuclear correlation. Herein, we introduce a series of correlation-consistent electronic basis sets for hydrogen atoms called cc-pVnZ-mc with additional basis functions optimized to reproduce multicomponent density functional theory protonic densities. These new electronic basis sets are shown to yield better protonic densities with fewer electronic basis functions than the standard correlation-consistent basis sets and reproduce other protonic properties such as proton affinities and protonic excitation energies, even though they were not optimized for these purposes. The cc-pVnZ-mc basis sets should enable multicomponent many-body calculations on larger systems due to the improved computational efficiency they provide for a given level of accuracy.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Supervised learning of a chemistry functional with damped dispersion

Kohn-Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol^-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol^-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

Keto-enol tautomerism from the electron delocalization perspective

The equilibrium between keto and enol forms in acetylacetone and its derivatives is studied using electron delocalization indices and delocalization tensor density. We demonstrate how electron delocalization governs the equilibrium between keto and enol forms. The less stable enols have more distinct double and single bond character in the CCC fragment, while electron delocalization in this fragment is more pronounced in more stable enols. Looking for the origin of such behavior, we considered the one-electron potentials entering the Euler equation for the electron density. We found that electron delocalization is mainly governed by the static exchange potential, which depends on the three-dimensional atomic structure. It, however, does not distinguish differences in electron delocalization in more and less stable enols, the effect arising from the kinetic exchange contribution, which reflects spin-dependent effects in the electron motion. The local depletion of kinetic exchange in the conjugated fragment yields the enhanced electron delocalization along the CCC bonds in more stable enols. Thus, a combination of considered descriptors allowed us to reveal the influence of electron delocalization on the equilibrium between keto and enol forms and showed the significant features of this phenomenon.

Poisoning density functional theory with benchmark sets of difficult systems

Large benchmark sets like GMTKN55 [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] let us analyse the performance of density functional theory over a diverse range of systems and bonding types. However, assessing over a large and diverse set can miss cases where approaches fail badly, and can give a misleading sense of security. To this end we introduce a series of 'poison' benchmark sets, P30-5, P30-10 and P30-20, comprising systems with up to 5, 10 and 20 atoms, respectively. These sets represent the most difficult-to-model systems in GMTKN55. We expect them to be useful in developing new approximations, identifying weak points in existing ones, and to aid in selecting appropriate DFAs for computational studies involving difficult physics, e.g. catalysis.

Electronic structure analysis of electrochemical CO2 reduction by iron-porphyrins reveals basic requirements to design catalysts bearing non-innocent ligands

Electrocatalytic CO2 reduction is a possible solution to the increasing CO2 concentration in the earth atmosphere, because it enables storage of energy while using the harmful CO2 feedstock as starting...

Pushing the frontiers of density functionals by solving the fractional electron problem

[Figure: see text].

Molecular Modeling Strategies of Cancer Multidrug Resistance

Cancer remains a leading cause of morbidity and mortality worldwide. Hence, the increase in cancer cases observed in the elderly population, as well as in children and adolescents, makes human malignancies a prime target for anticancer drug development. Although highly effective chemotherapeutic agents are continuously developed and approved for clinical treatment, the major impediment towards curative cancer therapy remains multidrug resistance (MDR). In recent years, intensive studies have been carried out on the identification of new therapeutic molecules to reverse MDR efflux transporters of the ATP-binding cassette (ABC) superfamily. Although a great deal of progress has been made in the development of specific inhibitors for certain MDR efflux pumps in experimental studies, advanced computational studies can accelerate this drug development process. In the literature, there are many experimental studies on the impact of natural products and synthetic small molecules on the reversal of cancer MDR. Molecular modeling methods provide an opportunity to explain the activity of these molecules on the ABC-transporter family with non-covalent interactions as well as it is possible to carry out studies for the discovery of new anticancer drugs specific to MDR with these methods. The coordinate file of the 3-dimensional (3D) structure of the target protein is indispensable for molecular modeling studies. In some cases where a 3D structure cannot be obtained by experimental methods, the homology modeling method can be applied to obtain the file containing the target protein's information including atomic coordinates, secondary structure assignments, and atomic connectivity. Homology modeling studies are of great importance for efflux transporter proteins that still lack 3D structures due to crystallization problems with multiple hydrophobic transmembrane domains. Quantum mechanics, molecular docking and molecular dynamics simulation applications are the most frequently used molecular modeling methods in the literature to investigate non-covalent interactions between the drug-ABC transporter superfamily. The quantitative structure-activity relationship (QSAR) model provides a relationship between the chemical properties of a compound and its biological activity. Determining the pharmacophore region for a new drug molecule by superpositioning a series of molecules according to their physicochemical properties using QSAR models is another method in which molecular modeling is used in computational drug development studies with ABC transporter proteins. There are also in silico absorption, distribution, metabolism, excretion, and toxicity (ADME/Tox) studies conducted to make a prediction about the pharmacokinetic properties, and drug-likeness of new molecules. Drug repurposing studies, which have become a trending topic in recent years, involve identifying possible new targets for an already approved drug molecule. There are few studies in the literature in which drug repurposing performed by molecular modelling methods has been applied on ABC transporter proteins. The aim of the current paper is to create a complete review of drug development studies including aforementioned molecular modeling methods carried out between the years 2019-2021. Furthermore, an intensive investigation is also conducted on licensed applications and free web servers used in in silico studies. The current review is an up-to-date guide for researchers who plan to conduct computational studies with MDR transporter proteins.

Exploring the OH-initiated reactions of styrene in the atmosphere and the role of van der Waals complex

Reacting with OH provides a major sink for styrene in the atmosphere, with three possible pathways including OH-addition, H-abstraction and addition-dissociation reactions. However, the total rate coefficients of styrene + OH were measured as 1.2-6.2 × 10^-11 cm³ molecule^-1 s^-1 under atmospheric conditions, varying by a maximum factor of 5. On the other hand, only one theoretical work reported this rate coefficient as 19.1 × 10^-11 cm³ molecule^-1 s^-1, which exhibits up to 16 times that measured in laboratory studies. In the present study, the reaction kinetics of styrene + OH was extensively studied with high-level quantum chemical methods combined with RRKM/master equation simulations. In particular, we carried out theoretical treatments for the formation of pre-reaction Van der Waals complexes of styrene + OH, and examined their influence on the reaction kinetics. The total rate coefficient for styrene + OH is calculated to be 1.7 × 10^-11 cm³ molecule^-1 s^-1 at 300 K, 1 atm. The main products are addβ (88.2%), add5 (6.9%), addα (1.9%) and add3 (1.7%). Using our computed rate coefficient and the global atmospheric hydroxyl radical concentration (2 × 10⁶ radicals per cm³), the lifetime of styrene in the atmosphere is estimated at 8.0 h. The degradation of styrene might be negligible for the formation of ozone in the atmosphere based upon the photochemical ozone creation potentials calculation. The computed product yields indicate that addβ via subsequent reactions could significantly produce formaldehyde and benzaldehyde that were observed in previous experimental studies on styrene oxidation, and contribute to the formation of secondary organic aerosols.

Ab Initio Machine Learning in Chemical Compound Space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.

Density functionals with full nonlocal exchange, nonlocal rung-3.5 correlation, and D3 dispersion: Combined accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions

We introduce the HF-R35-D3(BJ) functional combining full nonlocal exact (Hartree-Fock-like, HF) exchange, inexpensive rung-3.5 correlation constructed from nonlocal one-electron operators, and nonlocal D3 dispersion corrections. HF-R35-D3(BJ) is among the first full-exact-exchange functionals offering competitive accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions. HF-R35-D3(BJ) gives weighted mean absolute deviation WTMAD-2 8.5 kcal/mol across the entire GMTKN55 dataset, outperforming most dispersion-corrected semilocal functionals and approaching the accuracy of dispersion-corrected global hybrids. This requires six fitted parameters, three each in the nonlocal correlation and dispersion corrections. Full nonlocal exchange appears to help give accurate binding energies and reasonable energy orderings for water hexamers. These results motivate continued exploration of inexpensive nonlocal correlation corrections to nonlocal exchange.

Density Functional Geometries and Zero-Point Energies in Ab Initio Thermochemical Treatments of Compounds with First-Row Atoms (H, C, N, O, F)

Density functionals are often used in ab initio thermochemistry to provide optimized geometries for single-point evaluations at a high level and to supply estimates of anharmonic zero-point energies (ZPEs). Their use is motivated by relatively high accuracy at a modest computational expense, but a thorough assessment of geometry-related error seems to be lacking. We have benchmarked 53 density functionals, focusing on approximations of the first four rungs and on relatively small basis sets for computational efficiency. Optimized geometries of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy penalties relative to the best available geometries, using the composite model ATOMIC/B5 as energy probe. Only hybrid functionals provide good accuracy with root-mean-square errors around 0.1 kcal/mol and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously, first-generation hybrids with few or no empirical parameters tend to perform better than highly parameterized ones. A number of them show good accuracy already with small basis sets (6-31G(d), 6-311G(d)). As is standard practice, anharmonic ZPEs are estimated from scaled harmonic values. Statistics of the latter show less performance variation among functionals than observed for geometry-related error, but they also indicate that ZPE error will generally dominate. We have selected PBE0-D3/6-311G(d) for the next version of the ATOMIC protocol (ATOMIC-2) and studied it in more detail. Empirical expressions have been calibrated to estimate bias corrections and 95% uncertainty intervals for both geometry-related error and scaled ZPEs.

r2SCAN-3c: A "Swiss army knife" composite electronic-structure method

The recently proposed r²SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r²SCAN-3c. To this end, the unaltered r²SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r²SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r²SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Accurate Hybrid Density Functionals with UW12 Correlation

In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here, we further investigate hybrid functionals containing UW12 correlation and in particular look at functionals with a large fraction of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered while eliminating the need for virtual orbitals.

New theoretical insights into the reaction kinetics of toluene and hydroxyl radicals

This work provides theoretical insights into the kinetics of toluene + OH, focusing on the anharmonic effect and the accuracy of barrier heights.

Atlas of putative minima and low-lying energy networks of water clusters n = 3-25

We report a database consisting of the putative minima and ∼3.2 × 10⁶ local minima lying within 5 kcal/mol from the putative minima for water clusters of sizes n = 3-25 using an improved version of the Monte Carlo temperature basin paving (MCTBP) global optimization procedure in conjunction with the ab initio based, flexible, polarizable Thole-Type Model (TTM2.1-F, version 2.1) interaction potential for water. Several of the low-lying structures, as well as low-lying penta-coordinated water networks obtained with the TTM2.1-F potential, were further refined at the Møller-Plesset second order perturbation (MP2)/aug-cc-pVTZ level of theory. In total, we have identified 3 138 303 networks corresponding to local minima of the clusters n = 3-25, whose Cartesian coordinates and relative energies can be obtained from the webpage https://sites.uw.edu/wdbase/. Networks containing penta-coordinated water molecules start to appear at n = 11 and, quite surprisingly, are energetically close (within 1-3 kcal/mol) to the putative minima, a fact that has been confirmed from the MP2 calculations. This large database of water cluster minima spanning quite dissimilar hydrogen bonding networks is expected to influence the development and assessment of the accuracy of interaction potentials for water as well as lower scaling electronic structure methods (such as different density functionals). Furthermore, it can also be used in conjunction with data science approaches (including but not limited to neural networks and machine and deep learning) to understand the properties of water, nature's most important substance.

Tungsten-Ligand Bond Strengths for 2p Elements Including σ- and π-Bond Strength Components, A Density Functional Theory and ab Initio Study

Three W^VI crystal structures with multifarious metal-ligand bond types are used to theoretically predict homolytic metal-element bond enthalpies with 11 popular DFT functionals, MP2 wave function methods, and four common valence basis set/pseudopotentials in order to evaluate the accuracy and precision of the resultant bond enthalpy data. To our knowledge, for the first time, estimates of component metal-ligand σ- and π-bond strengths are computed. The WE (E = C, N, O) bond enthalpies have the consistent trend σ > second π > first π. In contrast, the element-element BDE trend for the 2p homologues is second π > first π > σ for nitrogen and oxygen, and σ > first π > second π for carbon. These differences may underpin the differences in stability trends and thus reactivity behavior for metal-element multiple bonds as compared to the element-element multiple bonds, and metal-element triple bonds versus their corresponding double bonded counterparts. For example, Odom et al. show that MeI nucleophilically attacks at the imide (M═N) rather than the nitride (M ≡ N) ligand; the relative π-bond strengths derived herein provide a thermodynamic rationalization for this site preference. In this study, it is deduced from the calculated thermodynamics that the W-oxo ligand is more congruous with a triple bond than a double bond, consistent with the bonding model set forth in the seminal 1961 Ballhausen-Gray paper.

First-Principles Study of the Reaction Mechanism of CHO + H on Graphene Surface

Many organic molecules observed in the interstellar medium are considered to be formed on dust grains and populated into the gas phase. We analyzed the reaction of HCO + H on a graphene surface using ab initio molecular dynamics simulations as a case study of the formation and desorption of organic molecules on interstellar dust particles. During the reactions of chemisorbed CHO (chemisorbed at the C atom) with free H, CO was generated and efficiently desorbed from the surface. These results suggest that the reactions, of which the reactant forms a covalent bond with the surface while the product does not, cause efficient desorption of the product upon reaction. In such reactions a repulsive force between the product and the surface would be generated and accelerate translation of the product in a specific direction. In addition, it was also shown that the branching ratio of the reactions between radical species on the surface would be affected by the form of the adsorption on the surface, e.g., when a free H reacted with the CHO chemisorbed at the C atom, CH₂O was not generated.

Minimally Empirical Double-Hybrid Functionals Trained against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed ωB97M(2) empirical double hybrid (with 16 adjustable parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, refits of the DSD-BLYP and DSD-PBEP86 spin-component-scaled, dispersion-corrected double hybrids can achieve WTMAD2 values as low as 2.33 with the very recent D4 dispersion correction (2.42 kcal/mol with the D3(BJ) dispersion term) using just a handful of adjustable parameters. If we use full DFT correlation in the initial orbital evaluation, the xrevDSD-PBEP86-D4 functional reaches WTMAD2 = 2.23 kcal/mol, statistically indistinguishable from ωB97M(2) but using just four nonarbitrary adjustable parameters (and three semiarbitrary ones). The changes from the original DSD parametrizations are primarily due to noncovalent interaction energies for large systems, which were undersampled in the original parametrization set. With the new parametrization, same-spin correlation can be eliminated at minimal cost in performance, which permits revDOD-PBEP86-D4 and revDOD-PBE-D4 functionals that scale as N⁴ or even N³ with the size of the system. Dependence of WTMAD2 for DSD functionals on the percentage of HF exchange is roughly quadratic; it is sufficiently weak that any reasonable value in the 64% to 72% range can be chosen semiarbitrarily. DSD-SCAN and DOD-SCAN double hybrids involving the SCAN nonempirical meta-GGA as the semilocal component have also been considered and offer a good alternative if one wishes to eliminate either the empirical dispersion correction or the same-spin correlation component. noDispSD-SCAN66 achieves WTMAD2 = 3.0 kcal/mol, compared to 2.7 kcal/mol for DOD-SCAN66-D4. However, the best performance without dispersion corrections (WTMAD2 = 2.8 kcal/mol) is reached by revωB97X-2, a slight reparametrization of the Chai–Head-Gordon range-separated double hybrid. Finally, in the context of double-hybrid functionals, the very recent D4 dispersion correction is clearly superior over D3(BJ).

Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections

We present two new semiempirical quantum-chemical methods with orthogonalization and dispersion corrections: ODM2 and ODM3 (ODM x). They employ the same electronic structure model as the OM2 and OM3 (OM x) methods, respectively. In addition, they include Grimme's dispersion correction D3 with Becke-Johnson damping and three-body corrections E ABC for Axilrod-Teller-Muto dispersion interactions as integral parts. Heats of formation are determined by adding explicitly computed zero-point vibrational energy and thermal corrections, in contrast to standard MNDO-type and OM x methods. We report ODM x parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine that are optimized with regard to a wide range of carefully chosen state-of-the-art reference data. Extensive benchmarks show that the ODM x methods generally perform better than the available MNDO-type and OM x methods for ground-state and excited-state properties, while they describe noncovalent interactions with similar accuracy as OM x methods with a posteriori dispersion corrections.

Quantum Chemical Characterization of Factors Affecting the Neutral and Radical-Cation Newman-Kwart Reactions

Details of the electronic and geometric structures of stationary points along the reaction coordinate of the Newman Kwart rearrangement, which transforms an O-arylthiocarbamate into an S-arylcarbamothioate, are examined using quantum-chemical methods for a large number of compounds considering both the thermal reactions of uncharged substrates as well as the corresponding reactions of radical-cation substrates generated under photoredox conditions. The uncharged mechanism, which has intrinsically high 298 K free energies of activation (in excess of 30 kcal mol^-1), has the character of nucleophilic aromatic substitution and is thus accelerated by electron-withdrawing substituents on the aromatic ring. The radical-cationic mechanism, by contrast, has 298 K free energies of activation that are typically below 20 kcal mol^-1 and is accelerated by electron donating substituents on the aromatic ring, which stabilize the hole character that is transferred to this fragment from the thiocarbamate fragment as the reaction proceeds. Opportunities to further accelerate the radical-cation reaction are revealed by computational assessment of alternative amino groups for the thiocarbamate functionality.

Statistically representative databases for density functional theory via data science

Cluster analysis applied to quantum chemistry: a new broad database of chemical properties with a reasonable computational cost.

A Trip to the Density Functional Theory Zoo: Warnings and Recommendations for the User

This account is written for general users of density functional theory (DFT) methods as well as experimental researchers who are new to the field and would like to conduct such calculations. Its main emphasis lies on how to find a way through the confusing ‘zoo’ of DFT by addressing common misconceptions and highlighting those modern methods that should ideally be used in calculations of energetic properties and geometries. A particular focus is on highly popular methods and the important fact that popularity does not imply accuracy. In this context, we present a new analysis of the openly available data published in Swart and co-workers’ famous annual ‘DFT poll’ (http://www.marcelswart.eu/dft-poll/) to demonstrate the existing communication gap between the DFT user and developer communities. We show that despite considerable methodological advances in the field, the perception of some parts of the user community regarding their favourite approaches has changed little. It is hoped that this account makes a contribution towards changing this status and that users are inspired to adjust their current computational protocols to accommodate strategies that are based on proven robustness, accuracy, and efficiency rather than popularity.

Error-Controlled Exploration of Chemical Reaction Networks with Gaussian Processes

For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present in all but the simplest chemical processes, approximate quantum chemical methods are required that allow for fast evaluations of the relative energies but at the expense of accuracy. Despite the plethora of benchmark studies, the accuracy of a quantum chemical method is often difficult to assess. Moreover, a significant improvement of a method's accuracy (e.g., through reparameterization or systematic model extension) is rarely possible. Here, we present a new approach that allows for the systematic, problem-oriented, and rolling improvement of quantum chemical results through the application of Gaussian processes. Due to its Bayesian nature, reliable error estimates are provided for each prediction. A reference method of high accuracy can be employed if the uncertainty associated with a particular calculation is above a given threshold. The new data point is then added to a growing data set in order to continuously improve the model and, as a result, all subsequent predictions. Previous predictions are validated by the updated model to ensure that uncertainties remain within the given confidence bound, which we call backtracking. We demonstrate our approach with the example of a complex chemical reaction network.

Metadynamics for training neural network model chemistries: A competitive assessment

Neural network model chemistries (NNMCs) promise to facilitate the accurate exploration of chemical space and simulation of large reactive systems. One important path to improving these models is to add layers of physical detail, especially long-range forces. At short range, however, these models are data driven and data limited. Little is systematically known about how data should be sampled, and "test data" chosen randomly from some sampling techniques can provide poor information about generality. If the sampling method is narrow, "test error" can appear encouragingly tiny while the model fails catastrophically elsewhere. In this manuscript, we competitively evaluate two common sampling methods: molecular dynamics (MD), normal-mode sampling, and one uncommon alternative, Metadynamics (MetaMD), for preparing training geometries. We show that MD is an inefficient sampling method in the sense that additional samples do not improve generality. We also show that MetaMD is easily implemented in any NNMC software package with cost that scales linearly with the number of atoms in a sample molecule. MetaMD is a black-box way to ensure samples always reach out to new regions of chemical space, while remaining relevant to chemistry near k_bT. It is a cheap tool to address the issue of generalization.

Computational modelling of singlet excitation energy transfer: a DFT/TD-DFT study of the ground and excited state properties of a syn bimane dimer system using non-empirically tuned range-separated functionals

Range-tuned DFT/TD-DFT improves predicted properties for the sequence of events leading to excitation energy transfer (EET) in bimanes.

‘Diet GMTKN55’ offers accelerated benchmarking through a representative subset approach

The GMTKN55 benchmarking protocol allows comprehensive analysis and ranking of density functional approximations with diverse chemical behaviours. This work reports diet versions of GMTKN55 which reproduce key properties of the full protocol at substantially reduced numerical cost. ‘Diet GMTKN55’ can thus be used for benchmarking expensive methods, or in combination with solid state benchmarks.

Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?

Theoreticians and experimentalists should work together more closely to establish reliable rankings and benchmarks for quantum chemical methods. Comparison to carefully designed experimental benchmark data should be a priority. Guidelines to improve the situation for experiments and calculations are proposed.