Electron Density Errors and Density-Driven Exchange-Correlation Energy Errors in Approximate Density Functional Calculations

Amine adducts of triallylborane as highly reactive allylborating agents for Cu(I)-catalyzed allylation of chiral sulfinylimines

The implementation of selective catalytic processes with highly active reagents is an attractive strategy that meets the modern principles of sustainable development of chemistry. In the current study, we for the first time describe the method and general principles of Cu(I)-catalyzed allylation of imines with amine adducts of allylic triorganoboranes. Triallylborane is an extremely reactive compound and cannot be used for the catalytic allylation of imines, whereas its amine adducts are ideal substrates for catalysis. The structure of the amine fragment successfully balances the safety, selectivity and stability of the allylboron reagent, allowing it to demonstrate high activity in catalytic allylation reactions, exceeding many times any known allylboranes. The obtained results are supported by quantitative kinetics data and DFT calculations. The catalytic efficacy of the system was demonstrated on model sulfinylimines (23 examples). High diastereoselectivity up to >99% was achieved, including for the gram-scale synthesis of 2-hydroxyphenyl-derivatives. Taking into account the high reactivity and unsurpassed atom-economy of amine adducts of triallylborane (AAT), they can be considered as prospective allylation reagents with Cu(I) and other appropriate metallocatalysts.

Toward a correct treatment of core properties with local hybrid functionals

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.

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

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

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

The crucial step in density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and, hence, should be replaced by, in this case, the HF density. We introduce an indicator, based on the difference in noninteracting kinetic energies between DFT and HF calculations, to determine when the HF density is the better option. Our kinetic energy indicator directly compares the self-consistent density of the analyzed functional with the HF density, is size-intensive, reliable, and most importantly highly efficient. Moreover, we present a procedure that makes best use of the computed quantities necessary for DC(HF)-DFT by additionally evaluating a related hybrid functional and, in that way, not only "corrects" the density but also the functional itself; we call that procedure corrected Hartree-Fock density functional theory (C(HF)-DFT).

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.

Testing of Exchange-Correlation Functionals of DFT for a Reliable Description of the Electron Density Distribution in Organic Molecules

Researchers carrying out calculations using the DFT method face the problem of the correct choice of the exchange-correlation functional to describe the quantities they are interested in. This article deals with benchmark calculations aimed at testing various exchange-correlation functionals in terms of a reliable description of the electron density distribution in molecules. For this purpose, 30 functionals representing all rungs of Jacob's Ladder are selected and then the values of some QTAIM-based parameters are compared with their reference equivalents obtained at the CCSD/aug-cc-pVTZ level of theory. The presented results show that the DFT method undoubtedly has the greatest problems with a reliable description of the electron density distribution in multiple strongly polar bonds, such as C=O, and bonds associated with large electron charge delocalization. The performance of the tested functionals turned out to be unsystematic. Nevertheless, in terms of a reliable general description of QTAIM-based parameters, the M11, SVWN, BHHLYP, M06-HF, and, to a slightly lesser extent, also BLYP, B3LYP, and X3LYP functionals turned out to be the worst. It is alarming to find the most popular B3LYP functional in this group. On the other hand, in the case of the electron density at the bond critical point, being the most important QTAIM-based parameter, the M06-HF functional is especially discouraged due to the very poor description of the C=O bond. On the contrary, the VSXC, M06-L, SOGGA11-X, M06-2X, MN12-SX, and, to a slightly lesser extent, also TPSS, TPSSh, and B1B95 perform well in this respect. Particularly noteworthy is the overwhelming performance of double hybrids in terms of reliable values of bond delocalization indices. The results show that there is no clear improvement in the reliability of describing the electron density distribution with climbing Jacob's Ladder, as top-ranked double hybrids are also, in some cases, able to produce poor values compared to CCSD.

Lewis Acid-Catalyzed Chemodivergent and Regiospecific Reaction of Phenols with Quaternary Peroxyoxindoles

The indium-catalyzed regiospecific coupling of substituted phenol derivatives and quaternary peroxyoxindoles for the synthesis of C2 or C4 benzoxazin-3-one-substituted phenols via skeletal rearrangement is described. This reaction is demonstrated with 17 examples with good yields and diverse aryl substituents. In contrast to the indium-catalyzed reaction, the Cu(OTf)₂-catalyzed reaction of the phenol with quaternary peroxyoxindoles afforded C2 or C4 2-oxindole-substituted phenol derivatives. This diverse catalytic reaction generated various biologically important phenol-substituted 2-oxindole derivatives directly without any skeleton rearrangement and was demonstrated with 19 examples in high yield. The regiospecificity and the reaction pathways were explained with the support of density functional theory (DFT).

Enhancing the kinetics of vanadium oxides via conducting polymer and metal ions co-intercalation for high-performance aqueous zinc-ions batteries

Aqueous zinc-ions batteries with low cost, reliable safety, high theoretical specific capacity and eco-friendliness have captured conspicuous attention in large-scale energy storage. However, the developed cathodes often suffer from low electrical conductivity and sluggish Zn²⁺ diffusion kinetics, which severely hampers the development of aqueous zinc-ions batteries. Herein, we successfully prepare Mg/PANI/V₂O₅•nH₂O (MPVO) nanosheets through conducting polymers (polyaniline) and metal ions (Mg²⁺) co-intercalated strategy and systematically explore its electrochemical performance as cathode materials for aqueous zinc-ion batteries. Benefitting from the synergistic effect of polyaniline and Mg²⁺ co-intercalated, the MPVO exhibits larger interlayer spacing and higher electrical conductivity than the single guest intercalation, which significantly enhances the electrochemical kinetics. As a consequence, the MPVO cathodes deliver superior specific capacity, rate capability and long-term cycling performance. Moreover, multiple characterizations and theoretical calculations are executed to expound the relevant mechanism.Therefore, this work provides a novel thought for the design of high-performance cathode materials for aqueous ZIBs.

Electronic Energy and Local Property Errors at QTAIM Critical Points while Climbing Perdew's Ladder of Density-Functional Approximations

We investigate the relationships between electron-density and electronic-energy errors produced by modern exchange-correlation density-functional approximations belonging to all of the rungs of Perdew's ladder. To this aim, a panel of relevant (semi)local properties evaluated at critical points of the electron-density field (as defined within the framework of Bader's atoms-in-molecules theory) are computed on a large selection of molecular systems involved in thermodynamic, kinetic, and noncovalent interaction chemical databases using density functionals developed in a nonempirical and minimally and highly parametrized fashion. The comparison of their density- and energy-based performance, also discussed in terms of density-driven errors, casts light on the strengths and weaknesses of the most recent and efficient density-functional approximations.

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

In the past years, there has been a discussion about how the errors in density functional theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics. In this study, we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.

Marriage of Peroxides and Nitrogen Heterocycles: Selective Three-Component Assembly, Peroxide-Preserving Rearrangement, and Stereoelectronic Source of Unusual Stability of Bridged Azaozonides

Stable bridged azaozonides can be selectively assembled via a catalyst-free three-component condensation of 1,5-diketones, hydrogen peroxide, and an NH-group source such as aqueous ammonia or ammonium salts. This procedure is scalable and can produce gram quantities of bicyclic stereochemically rich heterocycles. The new azaozonides are thermally stable and can be stored at room temperature for several months without decomposition and for at least 1 year at -10 °C. The chemical stability of azaozonides was explored for their subsequent selective transformations including the first example of an aminoperoxide rearrangement that preserves the peroxide group. The amino group in aminoperoxides has remarkably low nucleophilicity and does not participate in the usual amine alkylation and acylation reactions. These observations and the 15 pK_a units decrease in basicity in comparison with a typical dialkyl amine are attributed to the strong hyperconjugative n_N→σ*_C-O interaction with the two antiperiplanar C-O bonds. Due to the weakness of the complementary n_O→σ*_C-N donation from the peroxide oxygens (a consequence of "inverse α-effect"), this interaction depletes electron density from the NH moiety, protects it from oxidation, and makes it similar in properties to an amide.

Explaining and Fixing DFT Failures for Torsional Barriers

Most torsional barriers are predicted with high accuracies (about 1 kJ/mol) by standard semilocal functionals, but a small subset was found to have much larger errors. We created a database of almost 300 carbon-carbon torsional barriers, including 12 poorly behaved barriers, that stem from the Y═C-X group, where Y is O or S and X is a halide. Functionals with enhanced exchange mixing (about 50%) worked well for all barriers. We found that poor actors have delocalization errors caused by hyperconjugation. These problematic calculations are density-sensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HF-DFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchange-enhanced functionals if the HF density is used. For long-chain conjugated molecules, HF-DFT can be much better than exchange-enhanced functionals. We suggest that HF-PBE0 has the best overall performance.

Redirecting a Diels-Alder Reaction toward (2 + 2)-Cycloaddition

Recently, reactions of allylidenhydrazones with tetracyanoethylene were found to lead to cyclobutanes-products of usually unfavorable (2 + 2) cycloaddition. Herein we computationally demonstrate that the (4 + 2) product of this reaction is severely destabilized by incomplete C-N bond formation, arising from a complex interplay of substituent electronic effects. We show how destabilization of a single bond in the front-runner product averts its formation and redirects chemical reaction toward an uncharacteristic pathway.

Representing Exact Electron Densities by a Single Slater Determinant in Finite Basis Sets

The premise for Kohn-Sham density functional theory is that the exact electron density can be generated by a set of orbitals in a single Slater determinant. While this is ensured in a complete basis set, it has been shown that it cannot hold in small basis sets. The present work probes how accurately a reference electron density of the full-CI type can be reproduced by a set of orbitals in a single Slater determinant, as a function of the basis set used for the fitting electron density. The key finding is that the fitting error may be significant for basis sets of double- or triple-ζ quality. It is also shown that it is important that the fitting basis set includes the same basis functions as used for generating the reference electron density. The main limitation in a given basis set is the lack of higher order polarization functions. The error for practical purposes becomes insignificant for basis sets of quadruple-ζ or better quality, and this should be the choice when assessing the accuracy of exchange-correlation functionals by comparing electron densities to accurate reference results generated by wave function methods. The methodology in the present work can be used to transform an electron density from a multideterminant wave function into a set of orbitals in a single Slater determinant, and this may be useful for developing and testing new exchange-correlation functionals.

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms

Connections between the Görling-Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew-Burke-Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.

Dynamical properties of enzyme-substrate complexes disclose substrate specificity of the SARS-CoV-2 main protease as characterized by the electron density descriptors

A dynamical approach is proposed to discriminate between reactive (rES) and nonreactive (nES) enzyme-substrate complexes taking the SARS-CoV-2 main protease (Mpro) as an important example. Molecular dynamics simulations with the quantum mechanics/molecular mechanics potentials (QM(DFT)/MM-MD) followed by the electron density analysis are employed to evaluate geometry and electronic properties of the enzyme with different substrates along MD trajectories. We demonstrate that mapping the Laplacian of the electron density and the electron localization function provides easily visible images of the substrate activation that allow one to distinguish rES and nES. The computed fractions of reactive enzyme-substrate complexes along MD trajectories well correlate with the findings of recent experimental studies on the substrate specificity of Mpro. The results of our simulations demonstrate the role of the theory level used in QM subsystems for a proper description of the nucleophilic attack of the catalytic cysteine residue in Mpro. The activation of the carbonyl group of a substrate is correctly characterized with the hybrid DFT functional PBE0, whereas the use of a GGA-type PBE functional, that lacks the admixture of the Hartree-Fock exchange fails to describe activation.

How to Build Rigid Oxygen-Rich Tricyclic Heterocycles from Triketones and Hydrogen Peroxide: Control of Dynamic Covalent Chemistry with Inverse α-Effect

We describe an efficient one-pot procedure that "folds" acyclic triketones into structurally complex, pharmaceutically relevant tricyclic systems that combine high oxygen content with unusual stability. In particular, β,γ'-triketones are converted into three-dimensional polycyclic peroxides in the presence of H₂O₂ under acid catalysis. These transformations are fueled by stereoelectronic frustration of H₂O₂, the parent peroxide, where the lone pairs of oxygen are not involved in strongly stabilizing orbital interactions. Computational analysis reveals how this frustration is relieved in the tricyclic peroxide products, where strongly stabilizing anomeric n_O→σ_C-O^* interactions are activated. The calculated potential energy surfaces for these transformations combine labile, dynamically formed cationic species with deeply stabilized intermediate structures that correspond to the introduction of one, two, or three peroxide moieties. Paradoxically, as the thermodynamic stability of the peroxide products increases along this reaction cascade, the kinetic barriers for their formation increase as well. This feature of the reaction potential energy surface, which allows separation of mono- and bis-peroxide tricyclic products, also explains why formation of the most stable tris-peroxide is the least kinetically viable and is not observed experimentally. Such unique behavior can be explained through the "inverse α-effect", a new stereoelectronic phenomenon with many conceptual implications for the development of organic functional group chemistry.

Localizing electron density errors in density functional theory

The accuracy of different density functional approximations is assessed through the use of quantum chemical topology on molecular electron densities. In particular, three simple yet ever-important systems are studied: N₂, CO and ethane. Our results exemplify how real-space descriptors can help understand the sources of errors in density functional theory, avoiding unwanted error compensation present in simplified statistical metrics. Errors in "well-built" functionals are shown to be concentrated in chemically meaningful regions of space, and hence they are predictable. Conversely, strongly parametrized functionals show isotropic errors that cannot be traced back to chemically transferable units. Moreover, we will show that energetic corrections are mapped back into improvements in the density in chemically meaningful regions. These results point at the relevance of real-space perspectives when parametrizing or relating energy and density errors.

Exploring Nature and Predicting Strength of Hydrogen Bonds: A Correlation Analysis Between Atoms-in-Molecules Descriptors, Binding Energies, and Energy Components of Symmetry-Adapted Perturbation Theory

This work studies the underlying nature of H-bonds (HBs) of different types and strengths and tries to predict binding energies (BEs) based on the properties derived from wave function analysis. A total of 42 HB complexes constructed from 28 neutral and 14 charged monomers were considered. This set was designed to sample a wide range of HB strengths to obtain a complete view about HBs. BEs were derived with the accurate coupled cluster singles and doubles with perturbative triples correction (CCSD(T))(T) method and the physical components of the BE were investigated by symmetry-adapted perturbation theory (SAPT). Quantum theory of atoms-in-molecules (QTAIM) descriptors and other HB indices were calculated based on high-quality density functional theory wave functions. We propose a new and rigorous classification of H-bonds (HBs) based on the SAPT decomposition. Neutral complexes are either classified as "very weak" HBs with a BE ≥ -2.5 kcal/mol that are mainly dominated by both dispersion and electrostatic interactions or as "weak-to-medium" HBs with a BE varying between -2.5 and -14.0 kcal/mol that are only dominated by electrostatic interactions. On the other hand, charged complexes are divided into "medium" HBs with a BE in the range of -11.0 to -15.0 kcal/mol, which are mainly dominated by electrostatic interactions, or into "strong" HBs whose BE is more negative than -15.0 kcal/mol, which are mainly dominated by electrostatic together with induction interactions. Among various explored correlations between BEs and wave function-based HB descriptors, a fairly satisfactory correlation was found for the electron density at the bond critical point (BCP; ρ_BCP ) of HBs. The fitted equation for neutral complexes is BE/kcal/mol =  - 223.08 × ρ_BCP /a. u. + 0.7423 with a mean absolute percentage error (MAPE) of 14.7%, while that for charged complexes is BE/kcal/mol =  - 332.34 × ρ_BCP /a. u. - 1.0661 with a MAPE of 10.0%. In practice, these equations may be used for a quick estimation of HB BEs, for example, for intramolecular HBs or large HB networks in biomolecules. © 2019 Wiley Periodicals, Inc.

Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT

Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.

The maximum occupancy condition for the localized property-optimized orbitals

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation

We have studied the correlation potentials produced by various adiabatic connection models (ACMs) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-interaction limit potentials have also been investigated and discussed.

Kinetic-energy-based error quantification in Kohn–Sham density functional theory

We present a basis-independent metric to assess the quality of the electron density obtained from Kohn–Sham (KS) density functional theory (DFT).

Understanding the Molecular Structure of the Sialic Acid-Phenylboronic Acid Complex by using a Combined NMR Spectroscopy and DFT Study: Toward Sialic Acid Detection at Cell Membranes

The origin of the unusually high stability of the sialic acid (SA) and phenylboronic acid (PBA) complex was investigated by a combined nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) study. SA is a glycan-terminating monosaccharide, and its importance as a clinical target has long been recognized. Inspired by the fact that the binding properties of SA-PBA complexation are anomalously high relative to those of typical monosaccharides, great effort has been made to build a clinical platform with the use of PBA as a SA-selective receptor. Although a number of applications have been reported in recent years, the ability of PBA to recognize SA-terminating surface glycans selectively is still unclear, because high-affinity SA-PBA complexation might not occur in a physiological environment. In particular, different forms of SA (α- and β-pyranose) were not considered in detail. To answer this question, the combined NMR spectroscopy/DFT study revealed that the advantageous binding properties of the SA-PBA complex arise from ester bonding involving the α-carboxylate moieties (C1 and C2) of β-SA but not α-SA. Moreover, the facts that the C2 atom is blocked by a glycoside bond in a physiological environment and that α-SA basically exists on membrane-bound glycans in a physiological environment lead to the conclusion that PBA cannot selectively recognize the SA unit to discriminate specific types of cells. Our results have a significant impact on the field of SA-based cell recognition.

Simple Modifications of the SCAN Meta-Generalized Gradient Approximation Functional

We analyzed various possibilities to improve upon the SCAN meta-generalized gradient approximation density functional obeying all known properties of the exact functional that can be satisfied at this level of approximation. We examined the necessity of locally satisfying a strongly tightened lower bound for the exchange energy density in single-orbital regions, the nature of the error cancellation between the exchange and correlation parts in two-electron regions, and the effect of the fourth-order term in the gradient expansion of the correlation energy density. We have concluded that the functional can be modified to separately reproduce the exchange and correlation energies of the helium atom by locally releasing the strongly tightened lower bound for the exchange energy density in single-orbital regions, but this leads to an unbalanced improvement in the single-orbital electron densities. Therefore, we decided to keep the F_X ≤ 1.174 exact condition for any single-orbital density, where F_X is the exchange enhancement factor. However, we observed a general improvement in the single-orbital electron densities by revising the correlation functional form to follow the second-order gradient expansion in a wider range. Our new revSCAN functional provides more-accurate atomization energies for the systems with multireference character, compared to the SCAN functional. The nonlocal VV10 dispersion-corrected revSCAN functional yields more-accurate noncovalent interaction energies than the VV10-corrected SCAN functional. Furthermore, its global hybrid version with 25% of exact exchange, called revSCAN0, generally performs better than the similar SCAN0 for reaction barrier heights. Here, we also analyzed the possibility of the construction of a local hybrid from the SCAN exchange and a specific locally bounded nonconventional exact exchange energy density. We predict compatibility problems since this nonconventional exact exchange energy density does not really obey the strongly tightened lower bound for the exchange energy density in single-orbital regions.

Doubly hybrid density functionals that correctly describe both density and energy for atoms

Recently, it was argued [Medvedev MG, et al. (2017) Science 355:49-52] that the development of density functional approximations (DFAs) is "straying from the path toward the exact functional." The exact functional should yield both exact energy and density for a system of interest; nevertheless, they found that many heavily fitted functionals for molecular energies actually lead to poor electron densities of atoms. They also observed a trend that, for the nonempirical and few-parameter functionals, densities can be improved as one climbs up the first four rungs of the Jacob's ladder of DFAs. The XYG3 type of doubly hybrid functionals (xDHs) represents a less-empirical and fewer-parameter functional on the top fifth rung, in which both the Hartree-Fock-like exchange and the second-order perturbative (MP2-like) correlation are hybridized with the low rung functionals. Here, we show that xDHs can well describe both density and energy for the same atomic set of Medvedev et al., showing that the latter trend can well be extended to the top fifth rung.

Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U

Approximate density functional theory (DFT) is widely used in chemistry and physics, despite delocalization errors that affect energetic and density properties. DFT+U (i.e., semilocal DFT augmented with a Hubbard U correction) and global hybrid functionals are two commonly employed practical methods to address delocalization error. Recent work demonstrated that in transition-metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity. In this work, we compare density localization trends with DFT+U and global hybrids on a diverse set of 34 transition-metal-containing solids with varying magnetic state, electron configuration and valence shell, and coordinating-atom orbital diffuseness (i.e., O, S, Se). We also study open-framework solids in which the metal is coordinated by molecular ligands, i.e., MCO₃, M(OH)₂, M(NCNH)₂, K₃M(CN)₆ (M = V-Ni). As in transition-metal complexes, incorporation of Hartree-Fock exchange consistently localizes density away from the metal, but DFT+U exhibits diverging behavior, localizing density (i) onto the metal in low-spin and late transition metals and (ii) away from the metal in other cases in agreement with hybrids. To isolate the effect of the crystal environment, we extract molecular analogues from open-framework transition-metal solids and observe consistent localization of the density away from the metal in all cases with both DFT+U and hybrid exchange. These observations highlight the limited applicability of trends established for functional tuning on transition-metal complexes even to equivalent coordination environments in the solid state.