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.

Small Representative Databases for Testing and Validating Density Functionals and Other Electronic Structure Methods

Broad and diverse sets of accurate data provide useful metrics for assessing the performance of new theoretical methods. However, assessing methods against large databases can be an arduous task. Here, we present 17 representative energetic databases, defined as small databases whose errors and error spreads are representative of larger databases and which therefore can serve as efficient benchmarks for developing and testing electronic structure methods and density functionals. In 15 cases, the representative databases have 6 entries while being representative of larger databases with 14-107 entries, and in the other two cases, they have 14 entries while being representative of larger databases with 418-455 entries. The mean unsigned error (MUE) of 100 electronic structure methods on a given representative database is typically within about 8% of the MUE on its parent database, and the root-mean-square error (RMSE) is typically within about 11% of the RMSE on the parent database. Thus, the representative databases are quite successful in indicating accuracy while maintaining good diversity. The databases include both main-group and transition-metal compounds and reactions, and they include bond energies, reaction energies, barrier heights, noncovalent interactions, ionization potentials, and absolute energies.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Insight into the activation mechanism of carbonic anhydrase(II) through 2-(2-aminoethyl)-pyridine: a promising pathway for enhanced enzymatic activity

Activation of human carbonic anhydrase II (hCA II) holds great promise for treating memory loss symptoms associated with Alzheimer's disease. Despite its importance, the activation mechanism of hCA II has been largely overlooked in favor of the well-studied inhibition mechanism. To address this unexplored realm, we use first-principles calculations to tease out the activation mechanism of hCA II using 2-(2-aminoethyl)-pyridine (2-2AEPy), a promising in vitro activator. We explored both stepwise and concerted mechanisms via both available nitrogen sites of 2-2AEPy: (i) aminoethyl group (Nα) and (ii) pyridine ring (Nβ). Our results show that a concerted mechanism via Nα holds the key to hCA II activation. The activation process of the concerted mechanism exhibits the characteristics of an exergonic reaction, wherein the transition state resembles the reactant with a notably low imaginary frequency of 452.4i cm-1 and barrier height of 5.2 kcal mol-1. Such meager transition barriers propel the activation of hCA II at in vivo temperatures. These findings initiate future research into hCA II activation mechanisms and the development of efficient activators, which may lead to promising therapeutic interventions for Alzheimer's disease.

M11pz: A Nonlocal Meta Functional with Zero Hartree-Fock Exchange and with Broad Accuracy for Chemical Energies and Structures

The accuracy of Kohn-Sham density functional theory depends strongly on the approximation to the exchange-correlation functional. In this work, we present a new exchange-correlation functional called M11pz (M11 plus rung-3.5 terms with zero Hartree-Fock exchange) that is built on the M11plus functional with the goal of using its rung-3.5 terms without a Hartree-Fock exchange term, especially to improve the accuracy for strongly correlated systems. The M11pz functional is optimized with the same local and rung-3.5 ingredients that are used in M11plus but without any percentage of Hartree-Fock exchange. The performance of M11pz is compared with eight local functionals, and M11pz is found to be in top three when the errors or ranks are averaged over eight grouped and partially overlapping databases: AME418/22, atomic and molecular energies; MGBE172, main-group bond energies; TMBE40, transition-metal bond energies; SR309, single-reference systems; MR54, multireference systems; BH192, barrier heights; NC579, noncovalent interaction energies; and MS20, molecular structures. For calculations of band gaps of solids, M11pz is the second best of the nine tested functionals that have zero Hartree-Fock exchange.

The FP-LAPW/GAM-MPW1K approach: a reliable abinitio method for calculating the band gap of II-VI semiconductors monochalcogenides

CONTEXT

The bandgap of metal monochalcogenides (MMCs) is a key property that governs their physical and chemical properties. Accurate measurement of the bandgap is essential for a range of applications, including optoelectronics and photovoltaics. However, many theoretical approximations fail to accurately calculate the bandgap for MMCs, making it difficult to obtain precise values. This study investigated the suitability of the FP-LAPW/GAM-MPW1K scheme for determining the bandgap of MMCs. The investigation included lattice parameters, bandgap, band structure, and density of states, which were compared against both previous theoretical calculations and available experimental data. The findings of the study indicate that the FP-LAPW/GAM-MPW1K approach accurately calculates the bandgap value of MMCs by efficiently treating d-state electrons. The results are consistent with prior studies, confirming the method's reliability in determining the bandgap of these semiconductors.

METHODS

our study used the GAM-MPW1K functional and the full potential linearized augmented plane wave method (FP-LAPW) in the ELK code to calculate the lattice parameters, electronic band structure, and bandgap of ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe compounds in the wurtzite structure. The crystallographic data were obtained from the COD database and the inputs were prepared by CIF2CELL code. The results were visualized using Xmgrace and VESTA software.

Comparison of the Performance of Density Functional Methods for the Description of Spin States and Binding Energies of Porphyrins

This work analyzes the performance of 250 electronic structure theory methods (including 240 density functional approximations) for the description of spin states and the binding properties of iron, manganese, and cobalt porphyrins. The assessment employs the Por21 database of high-level computational data (CASPT2 reference energies taken from the literature). Results show that current approximations fail to achieve the "chemical accuracy" target of 1.0 kcal/mol by a long margin. The best-performing methods achieve a mean unsigned error (MUE) <15.0 kcal/mol, but the errors are at least twice as large for most methods. Semilocal functionals and global hybrid functionals with a low percentage of exact exchange are found to be the least problematic for spin states and binding energies, in agreement with the general knowledge in transition metal computational chemistry. Approximations with high percentages of exact exchange (including range-separated and double-hybrid functionals) can lead to catastrophic failures. More modern approximations usually perform better than older functionals. An accurate statistical analysis of the results also casts doubts on some of the reference energies calculated using multireference methods. Suggestions and general guidelines for users are provided in the conclusions. These results hopefully stimulate advances for both the wave function and the density functional side of electronic structure calculations.

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.

Uniting Nonempirical and Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) data-driven optimization. The proposed method employs B-splines, bell-shaped spline functions with compact support, to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn–Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment (μ), static dipole polarizability (α), and first hyperpolarizability (β), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of “adiabatic connection theorem” and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems.

Recommendation of Orbitals for G0W0 Calculations on Molecules and Crystals

The many-body GW approximation, especially the G₀W₀ method, has been widely used for condensed matter and molecules to calculate quasiparticle energies for ionization, electron attachment, and band gaps. Because G₀W₀ calculations are well-known to have a strong dependence on the orbitals, the goal of the present work is to provide guidance on the choice of density functional used to generate orbitals and to recommend a choice that gives the most broadly accurate results. We have systematically investigated the dependence of G₀W₀ calculations on the orbitals for 100 molecules and 8 crystals by considering orbitals obtained with a diverse set of Kohn-Sham (KS) and generalized KS (GKS) functionals (63 functionals plus Hartree-Fock). The percentage of Hartree-Fock exchange employed in density functionals has been found to have strong influence on the predicted molecular ionization energy and crystal fundamental band gaps (with optimum values between 40 and 56%), but to have less effect on predicting molecular electron affinities. The low cost of the Gaussian implementation, even with hybrid functionals in periodic calculations, the better performance of global hybrids as compared to range-separated hybrids of either than screened exchange or long-range-corrected type, and the relatively low cost of global-hybrid-functional periodic calculations using Gaussians means that one can employ global-hybrid functionals at a very reasonable cost and obtain more accurate band gaps of semiconductors than are obtained by the methods currently widely employed, namely local gradient approximations. We single out three global-hybrid functionals that give especially good results for both molecules (100 in the test set) and crystals (8 in the test set, for all of which our benchmark data are the proper band gap rather than an optical band gap uncorrected for exciton effects).

CateCom: A Practical Data-Centric Approach to Categorization of Computational Models

The advent of data-driven science in the 21st century brought about the need for well-organized structured data and associated infrastructure able to facilitate the applications of artificial intelligence and machine learning. We present an effort aimed at organizing the diverse landscape of physics-based and data-driven computational models in order to facilitate the storage of associated information as structured data. We apply object-oriented design concepts and outline the foundations of an open-source collaborative framework that is (1) capable of uniquely describing the approaches in structured data, (2) flexible enough to cover the majority of widely used models, and (3) utilizes collective intelligence through community contributions. We present example database schemas and corresponding data structures and explain how these are deployed in software at the time of this writing.

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.

Optical Configuration Effect on the Structure and Reactivity of Diastereomers Revealed by Spin Effects and Molecular Dynamics Calculations

The peculiarities of spin effects in photoinduced electron transfer (ET) in diastereomers of donor-acceptor dyads are considered in order to study the influence of chirality on reactivity. Thus, the spin selectivity—the difference between the enhancement coefficients of chemically induced dynamic nuclear polarization (CIDNP)—of the dyad’s diastereomers reflects the difference in the spin density distribution in its paramagnetic precursors that appears upon UV irradiation. In addition, the CIDNP coefficient itself has demonstrated a high sensitivity to the change of chiral centers: when one center is changed, the hyperpolarization of all polarized nuclei of the molecule is affected. The article analyzes the experimental values of spin selectivity based on CIDNP calculations and molecular dynamic modeling data in order to reveal the effect of optical configuration on the structure and reactivity of diastereomers. In this way, we succeeded in tracing the differences in dyads with L- and D-tryptophan as an electron donor. Since the replacement of L-amino acid with D-analog in specific proteins is believed to be the cause of Alzheimer’s and Parkinson’s diseases, spin effects and molecular dynamic simulation in model dyads can be a useful tool for investigating the nature of this phenomenon.

BH9, a New Comprehensive Benchmark Data Set for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. To assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as a benchmark for density functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness errors. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date and a useful tool for the development and assessment of computational methods.

Structural and Energetic Properties of Amino Acids and Peptides Benchmarked by Accurate Theoretical and Experimental Data

Structural, energetic, and spectroscopic data derived in this work aim at the setup of an "experimentally validated" database for amino acids and polypeptides conformers. First, the "cheap" composite scheme (ChS, CCSD(T)/(CBS+CV)^MP2) is tested for evaluation of conformational energies of all eight stable conformers of glycine, by comparing to the more accurate CCSD(T)/CBS+CV computations (Phys. Chem. Chem. Phys. 2013, 15, 10094-10111 and J Mol. Model. 2020, 26, 129). The recently proposed jun-ChS (J. Chem. Theory and Comput. 2020, 16, 988-1006), employing the jun-cc-pVnZ basis set family for CCSD(T) computations and CBS extrapolation, yields conformational energies accurate to 0.2 kJ·mol^-1, at reduced computational cost with respect to aug-ChS employing aug-cc-pVnZ basis sets. The jun-ChS composite scheme is further applied to derive conformational energies for three dipeptide analogues Ac-Gly-NH₂, Ac-Ala-NH₂, and Gly-Gly. Finally, dipeptide conformational energies and semiexperimental equilibrium rotational constants along with the CCSD(T)/(CBS+CV)^MP2 structural parameters (J. Phys. Chem. Lett. 2014, 5, 534-540) stand as the reference for benchmarking of selected density functional methodologies. The double-hybrid functionals B2-PLYP-D3(BJ) and DSD-PBEP86, perform best for structural and energetic characterization of all dipeptide analogues. From hybrid functionals CAM-B3LYP-D3(BJ) and ωB97X-D3(BJ) represent promising methods applicable for larger peptide-based systems for which computations with double-hybrid functionals are not feasible.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Replacing hybrid density functional theory: motivation and recent advances

Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.

Assessment of Performance of Density Functionals for Predicting Potential Energy Curves in Hydrogen Storage Applications

The availability of accurate computational tools for modeling and simulation is vital to accelerate the discovery of materials capable of storing hydrogen (H₂) under given parameters of pressure swing and temperature. Previously, we compiled the H2Bind275 data set consisting of equilibrium geometries and assessed the performance of 55 density functionals over this data set (Veccham, S. P.; Head-Gordon, M. J. Chem. Theory Comput. 2020, 16, 4963-4982). As it is crucial for computational tools to accurately model the entire potential energy curve (PEC), in addition to the equilibrium geometry, we extended this data set with 389 new data points to include two compressed and three elongated geometries along 78 PECs for H₂ binding, forming the H2Bind78 × 7 data set. By assessing the performance of 55 density functionals on this significantly larger and more comprehensive H2Bind78 × 7 data set, we identified the best performing density functionals for H₂ binding applications: PBE0-DH, ωB97X-V, ωB97M-V, and DSD-PBEPBE-D3(BJ). The addition of Hartree-Fock exchange improves the performance of density functionals, albeit not uniformly throughout the PEC. We recommend the usage of ωB97X-V and ωB97M-V density functionals as they offer good performance for both geometries and energies. In addition, we also identified B97M-V and B97M-rV as the best semilocal density functionals for predicting H₂ binding energy at its equilibrium geometry.

Accurate prediction of the properties of materials using the CAM-B3LYP density functional

Density functionals with asymptotic corrections to the long-range potential provide entry-level methods for calculations on molecules that can sustain charge transfer, but similar applications in materials science are rare. We describe an implementation of the CAM-B3LYP range-separated functional within the Vienna Ab-initio Simulation Package (VASP) framework, together with its analytical functional derivatives. Results obtained for eight representative materials: aluminum, diamond, graphene, silicon, NaCl, MgO, 2D h-BN, and 3D h-BN, indicate that CAM-B3LYP predictions embody mean-absolute deviations (MAD) compared to HSE06 that are reduced by a factor of six for lattice parameters, four for quasiparticle band gaps, three for the lowest optical excitation energies, and six for exciton binding energies. Further, CAM-B3LYP appears competitive compared to ab initio G₀ W₀ and Bethe-Salpeter equation approaches. The CAM-B3LYP implementation in VASP was verified by comparison of optimized geometries and reaction energies for isolated molecules taken from the ACCDB database, evaluated in large periodic unit cells, to analogous results obtained using Gaussian basis sets. Using standard GW pseudopotentials and energy cutoffs for the plane-wave calculations and the aug-cc-pV5Z basis set for the atomic-basis ones, the MAD in energy for 1738 chemical reactions was 0.34 kcal mol^-1 , while for 480 unique bond lengths this was 0.0036 Å; these values reduced to 0.28 kcal mol^-1 (largest error 0.94 kcal mol^-1 ) and 0.0009 Å by increasing the plane-wave cutoff energy to 850 eV.

Quantum Mechanical Methods Predict Accurate Thermodynamics of Biochemical Reactions

Thermodynamics plays a crucial role in regulating the metabolic processes in all living organisms. Accurate determination of biochemical and biophysical properties is important to understand, analyze, and synthetically design such metabolic processes for engineered systems. In this work, we extensively performed first-principles quantum mechanical calculations to assess its accuracy in estimating free energy of biochemical reactions and developed automated quantum-chemistry (QC) pipeline (https://appdev.kbase.us/narrative/45710) for the prediction of thermodynamics parameters of biochemical reactions. We benchmark the QC methods based on density functional theory (DFT) against different basis sets, solvation models, pH, and exchange-correlation functionals using the known thermodynamic properties from the NIST database. Our results show that QC calculations when combined with simple calibration yield a mean absolute error in the range of 1.60-2.27 kcal/mol for different exchange-correlation functionals, which is comparable to the error in the experimental measurements. This accuracy over a diverse set of metabolic reactions is unprecedented and near the benchmark chemical accuracy of 1 kcal/mol that is usually desired from DFT calculations.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Spin-Orbit Coupling Changes the Identity of the Hyper-Open-Shell Ground State of Ce+, and the Bond Dissociation Energy of CeH+ Proves to Be Challenging for Theory

Cerium (Ce) plays important roles in catalysis. Its position in the sixth period of the periodic table leads to spin-orbit coupling (SOC) and other open-shell effects that make the quantum mechanical calculation of cerium compounds challenging. In this work, we investigated the low-lying spin states of Ce⁺ and the bond energy of CeH⁺, both by multiconfigurational methods, in particular, SA-CASSCF, MC-PDFT, CASPT2, XMS-PDFT, and XMS-CASPT2, and by single-configurational methods, namely, Hartree-Fock theory and unrestricted Kohn-Sham density functional theory with 34 choices of the exchange-correlation functional. We found that only CASPT2, XMS-CASPT2, and SA-CASSCF (among the five multiconfigurational methods) and GAM, HCTH, SOGGA11, and OreLYP (among the 35 single-configuration methods) successfully predict that the SOC-free ground spin state of Ce⁺ is a doublet state, and CASPT2 and GAM give the most accurate multireference and single-reference calculations, respectively, of the excitation energy of the first SOC-free excited state for Ce⁺. We calculated that the ground doublet state of Ce⁺ is an intra-atomic hyper-open-shell state. We calculated the spin-orbit energy (E^SO) of Ce⁺ by the five multiconfigurational methods and found that E^SO calculated by CASPT2 is the closest to the experimental value. Taking advantage of the availability of an experimental D₀ for CeH⁺ as a way to provide a unique test of theory, we showed that all the multiconfigurational methods overestimate D₀ by at least 246 meV (5.7 kcal/mol), and only three functionals, namely, SOGGA, MN15, and GAM, have an error of D₀ that is less than 200 meV (5 kcal/mol).

Hydride Affinities for Main-Group Hydride Reductants: Assessment of Density Functionals and Trends in Reactivities

In the present study, we have examined hydride affinities relevant to a range of group 13 and group 14 reductants. We use the high-level W1X-G0, G4(MP2)-XK, and DSD-PBEP86 methods to obtain the RHA42 set of accurate reductant hydride affinities. Assessment of DFT methods with the RHA42 set shows that all functionals that we have examined are fairly accurate. Overall, we find ωB97X-V to be the most accurate. The MN12-SX screened-exchange functional and the nonhybrid B97-D3BJ method also perform well, and they may provide a lower-cost means for obtaining hydride affinities. The trend in the hydride affinities suggests an increased reducing power when one moves down the periodic table, e.g., with TlH₃ being a stronger reductant than BH₃. We also find that group 13 hydrides are stronger reductants than the group 13 analogues. In general, substitution of a hydrogen, e.g., BH₂⁺ → BHMe⁺, and the formation of dimer, e.g., BH₂⁺ → B₂H₅⁺, also lead to stronger reductants. A notable observation is the small hydride affinities for silyl cations, which are indicative of the potential of silanes as strong reducing agents. In particular, poly(methylhydrosiloxane) (PMHS) cations are associated with especially small hydride affinities owing to the presence of intramolecular oxygen atoms that can stabilize the cation center. We have further found the germanium analogues of the silanes to be more reactive, and they may further widen the scope of main-group hydride reducing agents.

Reactivity of arsenoplatin complex versus water and thiocyanate: a DFT benchmark study

Seven different density functionals, including GGAs, meta-GGAs, hybrids and range-separated hybrids, and considering Grimme’s empirical dispersion correction (M06-L, M06-2X, PBE0, B3LYP, B3LYP-D3, CAM-B3LYP, ωB97X) have been tested for their performance in the prediction of molecular structures, energies and energy barriers for a class of newly developed antitumor platinum complexes involving main group heavy elements such as arsenic. The calculated structural parameters, energies and energy barriers have been compared to the available experimental data. The results show that range-separated hybrid functionals CAM-B3LYP and ωB97X give good results in predicting both geometrical parameters and isomerization energies and barrier heights and are promising new tools for the theoretical study of novel platinum(II) arsenic compounds.

Quantifying and Understanding Errors in Molecular Geometries

Electronic structure calculations are ubiquitous in most branches of chemistry, but all have errors in both energies and equilibrium geometries. Quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. A single natural measure of geometric error is introduced, the geometry energy offset (GEO). GEO links many disparate aspects of geometry errors: a new ranking of different methods, quantitative insight into errors in specific geometric parameters, and insight into trends with different methods. GEO can also reduce the cost of high-level geometry optimizations and shows when geometric errors distort the overall error of a method. Results, including some surprises, are given for both covalent and weak interactions.

An insight into the electro-chemical properties of halogen (F, Cl and Br) doped BP and BN nanocages as anodes in metal-ion batteries

Here, electro-chemical properties of BN and BP nanocages as anodes in metal-ion batteries are examined. The effect of halogens adoption of BN and BP-NCs on electro-chemical properties of M-IBs are investigated. Results showed that the BP nanocages as anode electrode in M-IBs has higher efficiency than BN nanocages and the K-IB has higher cell voltage than N-IBs. Results indicated that the halogens adoption of BN and BP-NCs are improved the cell voltage of M-IBs. Results proved that the F-doped M-IBs have higher cell voltage than M-IBs. Finally, F-B17P18 as anodes in K-IB is proposed as suitable electrodes.

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium-Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D_e and bond length r_e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15-0.19. For the single-reference methods, Kohn-Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D_e and r_e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core-valence terms; this results in highly accurate dissociation energies and good bond lengths. Averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

Density Functionals for Hydrogen Storage: Defining the H2Bind275 Test Set with Ab Initio Benchmarks and Assessment of 55 Functionals

Efficient and high-capacity storage materials are indispensable for a hydrogen-based economy. In silico tools can accelerate the process of discovery of new adsorbent materials with optimal hydrogen adsorption enthalpies. Density functional theory is well-poised to become a very useful tool for enabling high-throughput screening of potential materials. In this work, we have identified density functional approximations that provide good performance for hydrogen binding applications following a two-pronged approach. First, we have compiled a data set (H2Bind275) that comprehensively represents the hydrogen binding problem capturing the chemical and mechanistic diversity in the binding sites encountered in hydrogen storage materials. We have also computed reference interaction energies for this data set using coupled-cluster theory. Second, we have assessed the performance of 55 density functional approximations for predicting H₂ interaction energies and have identified two hybrid density functionals (ωB97X-V and ωB97M-V), two double hybrid density functionals (DSD-PBEPBE-D3(BJ) and PBE0-DH), and one semilocal density functional (B97M-V) as the best performing ones. We have recommended the addition of empirical dispersion corrections to systematically underbinding density functionals such as revPBE, BLYP, and B3LYP for improvements in performance at negligible additional cost. We have also recommended the usage of the def2-TZVPP basis set as it represents a good compromise between accuracy and cost, limiting the finite basis set errors to less than 1 kJ/mol.

Relationships between Orbital Energies, Optical and Fundamental Gaps, and Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory

The relationships between Kohn-Sham (KS) and generalized KS (GKS) density functional orbital energies and fundamental gaps or optical gaps raise many interesting questions including the physical meanings of KS and GKS orbital energies when computed with currently available approximate density functionals (ADFs). In this work, by examining three diverse databases with various ADFs, we examine such relations from the point of view of the exciton shift of quasiparticle theory. We start by calculating a large number of excitation energies by time-dependent density functional theory (TDDFT) with a large number of ADFs. To relate the exciton shift implicit in TDDFT to the exciton shift that is explicit in Green's function theory, we define the exciton shift in TDDFT as the difference of the response shift and the quasiparticle shift. We found a strong correlation between the response shift and the amount of Hartree-Fock exchange included in the density functional, with the response shift varying between -1 and 5 eV. This range is an order of magnitude larger than the mean errors of the TDDFT excitation energies. This result suggests that, with currently available functionals, the KS or GKS orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe²⁺, Fe³⁺, and Co³⁺, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF₂, FeCl₂, and CoF₂. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

M06-SX screened-exchange density functional for chemistry and solid-state physics

Screened-exchange hybrid density functionals are especially recommended for solid-state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree-Fock exchange at long range. We present a screened-exchange hybrid functional, M06-SX, that combines the functional form of the local revM06-L functional with a percentage of short-range nonlocal Hartree-Fock exchange. The M06-SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06-SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened-exchange hybrid functionals tested in this work. The M06-SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long-range charge transfer excitations. For the LC18 lattice constants database, the M06-SX functional gives an MUE of only 0.034 Å. Therefore, the M06-SX functional is well suited for studying molecular chemistry as well as solid-state physics.

Aqueous-Phase Conformations of Lactose, Maltose, and Sucrose and the Assessment of Low-Cost DFT Methods with the DSCONF Set of Conformers for the Three Disaccharides

In the present study, we have examined a range of quantum chemistry methods for the calculation of conformers for lactose, maltose, and sucrose. We find that the DSD-PBE-P86/aug'-cc-pVTZ//B3-LYP-D3BJ/6-311+G(2d,p) protocol yields good relative energies in comparison with reference CCSD(T)/CBS//B3-LYP-D3BJ/maug-cc-pVTZ values. We have surveyed a total of ∼550 conformers for the three disaccharides with the chosen DSD-PBE-P86 method in conjunction with continuum aqueous solvation. In each case, the lowest free energy conformer is characterized by hydrogen bond(s) between the two rings. Another finding is that the major contributors to the overall variations in aqueous free energies are the electronic energies and the solvation energies. To facilitate investigations of larger systems, we have compiled the DSCONF set of conformers for the three disaccharides, and we have assessed lower cost methods with this set. We find MS1-D3/6-31+G(2d,p) to be cost-effective and accurate for both geometry optimization and the calculation of relative energies for disaccharides. In addition, we note that MS1-D3 has previously been found to yield good relative energies for the WATER27 set of water clusters. We thus deem this method to be appropriate for the study of saccharide conformations in both gas phase and aqueous solution.

The CUAGAU Set of Coupled-Cluster Reference Data for Small Copper, Silver, and Gold Compounds and Assessment of DFT Methods

We have obtained benchmark data for a set of small molecular systems of Cu, Ag, and Au using coupled-cluster methods. Using this collection of reference data (that we termed the CUAGAU set) for assessing DFT-type methods, we find the MN15-L nonhybrid DFT to be cost-effective for geometry optimization [mean absolute deviation (MAD) in bond length = 0.20 Å], with an accuracy that is comparable to that for the double-hybrid (DH) DFT method DSD-PBEP86 (MAD = 0.19 Å). For the computation of thermochemical properties, among "conventional" (non-MP2-based) DFT methods, the best performance is found for the global-hybrid meta-GGA functional MN15, with an MAD of 11.4 kJ mol^-1. We also find the nonhybrid method B97M-rV to have a reasonable performance (MAD = 14.4 kJ mol^-1), and it may serve as a cost-effective means for qualitative study. If we look beyond conventional functionals, we find DSD-PBEP86 (MAD = 7.3 kJ mol^-1) to be more accurate than even MN15. Nonetheless, this level of accuracy is still not sufficient for quantitative studies. In this regard, high-level wave function methods such as composite procedures that are based on coupled cluster are still indispensable for obtaining reliable reference data for transition-metal species.

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).

Simultaneous Attenuation of Both Self-Interaction Error and Nondynamic Correlation Error in Density Functional Theory: A Spin-Pair Distinctive Adiabatic-Connection Approximation

We present a spin-pair distinctive algorithm in the context of adiabatic-connection fluctuation-dissipation (ACFD) theorem, which enables to quantify the self-interaction error (SIE) and the nondynamic/strong correlation error (NCE) in the direct random-phase approximation (dRPA). Using this knowledge, we propose a spin-component scaled dRPA (scsRPA) correlation model with simultaneous attenuation of both the SIE and the NCE. Along with the exact exchange, scsRPA is shown to present a comprehensive improvement over dRPA, as well as the well-established PBE and PBE0 functionals, for bonding energies of pronounced multireference characters and transition-metal complexes of strongly correlated systems, while consistently providing an accurate description for reaction energies, reaction barriers, and noncovalent bond interactions of weakly correlated systems.

Evaluating Transition Metal Barrier Heights with the Latest Density Functional Theory Exchange-Correlation Functionals: The MOBH35 Benchmark Database

A new database of transition metal reaction barrier heights (MOBH35) is presented. Benchmark energies (forward and reverse barriers and reaction energy) are calculated using DLPNO-CCSD(T) extrapolated to the complete basis set limit using a Weizmann-1-like scheme. Using these benchmark energies, the performance of a wide selection of density functional theory (DFT) exchange-correlation functionals, including the latest from the Martin, Truhlar, and Head-Gordon groups, is evaluated. It was found, using the def2-TZVPP basis set, that the ωB97M-V (MAD 1.7 kcal/mol), ωB97M-D3BJ (MAD 1.9 kcal/mol), ωB97X-V (MAD 2.0 kcal/mol), and revTPSS0-D4 (MAD 2.2 kcal/mol) hybrid functionals are recommended. The double-hybrid functionals B2K-PLYP (MAD 1.7 kcal/mol) and revDOD-PBEP86-D4 (MAD 1.8 kcal/mol) also performed well, but this has to be balanced by their increased computational cost.

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.

Performance of density functional theory for describing hetero-metallic active-site motifs for methane-to-methanol conversion in metal-exchanged zeolites

Methane-to-methanol conversion (MMC) can be facilitated with high methanol selectivities by copper-exchanged zeolites. There are however two open questions regarding the use of these zeolites to facilitate the MMC process. The first concerns the possibility of operating the three cycles in the stepwise MMC process by these zeolites in an isothermal fashion. The second concerns the possibility of improving the methanol yields by systematic substitution of some copper centers in these active sites with other earth-abundant transition metals. Quantum-mechanical computations can be used to compare methane activation by copper oxide species and analogous mixed-metal systems. To carry out such screening, it is important that we use theoretical methods that are accurate and computationally affordable for describing the properties of the hetero-metallic catalytic species. We have examined the performance of 47 exchange-correlation density functionals for predicting the relative spin-state energies and chemical reactivities of six hetero-metallic [M-O-Cu]²⁺ and [M-O₂ -Cu]²⁺ , (where MCo, Fe, and Ni), species by comparison with coupled cluster theory including iterative single, double excitations as well as perturbative treatment of triple excitations, CCSD(T). We also performed multireference calculations on some of these systems. We considered two types of reactions (hydrogen addition and oxygen addition) that are relevant to MMC. We recommend the use of τ-HCTH and OLYP to determine the spin-state energy splittings in the hetero-metallic motifs. ωB97, ωB97X, ωB97X-D3, and MN15 performed best for predicting the energies of the hydrogen and oxygen addition reactions. In contrast, local, and semilocal functionals do poorly for chemical reactivity. Using [Fe-O-Cu]²⁺ as a test, we see that the nonlocal functionals perform well for the methane CH activation barrier. In contrast, the semilocal functionals perform rather poorly. © 2018 Wiley Periodicals, Inc.

Revised M06 density functional for main-group and transition-metal chemistry

We present a hybrid metageneralized-gradient-approximation functional, revM06, which is based on adding Hartree-Fock exchange to the revM06-L functional form. Compared with the original M06 suite of density functionals, the resulting revM06 functional has significantly improved across-the-board accuracy for both main-group and transition-metal chemistry. The revM06 functional improves on the M06-2X functional for main-group and transition-metal bond energies, atomic excitation energies, isomerization energies of large molecules, molecular structures, and both weakly and strongly correlated atomic and molecular data, and it shows a clear improvement over M06 and M06-2X for noncovalent interactions, including smoother potential curves for rare-gas dimers. The revM06 functional also predicts more accurate results than M06 and M06-2X for most of the outside-the-training-set test sets examined in this study. Therefore, the revM06 functional is well-suited for a broad range of chemical applications for both main-group and transition-metal elements.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.