Perspective: Fifty years of density-functional theory in chemical physics

A comparison of three DFT exchange-correlation functionals and two basis sets for the prediction of the conformation distribution of hydrated polyglycine

The performance of three density functional theory (DFT) exchange-correlation functionals, namely, Perdew-Burke-Ernzerhof (PBE), BP86, and B3LYP, in predicting conformational distributions of a hydrated glycine peptide is tested with two different basis sets in the framework of adaptive force matching (AFM). The conformational distributions yielded the free energy profiles of the DFT functional and basis set combinations. Unlike traditional validations of potential energy and structural parameters, our approach allows the free energy of DFT to be validated. When compared to experimental distributions, the def2-TZVP basis set provides better agreement than a slightly trimmed aug-cc-pVDZ basis set. B3LYP is shown to be better than BP86 and PBE. The glycine model fitted against B3LYP-D3(BJ) with the def2-TZVP basis set is the most accurate and named the AFM2021 model for glycine. The AFM2021 glycine model provides better agreement with experimental J-coupling constants than C36m and ff14SB, although the margin is very small when compared to C36m. Our previously published alanine model is also refitted with the slightly simplified AFM2021 energy expression. This work shows good promise of AFM for developing force fields for a range of proteinogenic peptides using only DFT as reference.

Interaction of glyphosate in matrices of cellulose and diethylaminoethyl cellulose biopolymers: theoretical viewpoint of the adsorption process

Glyphosate is an herbicide widely used in agricultural activities causing contamination of soils and bodies of water and damage to the biodiversity of ecosystems. In this context, the present study aimed to theoretically study the adsorption potential of the biopolymer cellulose (CE) and its diethylaminoethyl cellulose derivative (DEAEC) with the herbicide glyphosate (GLY). Theoretical calculations were performed using the density functional theory. Molecular electrostatic potential and frontier molecular orbital analyses were performed, which allowed identifying the possible sites of interaction of biopolymers that were in the functional groups -OH and O- of cellulose and in the groups -O- and -NH+(CH2CH3)2 of the DEAEC. Reactivity indices chemical softness and hardness showed that both adsorbents could interact with adsorbate. Simulated IR indicated that the interactions could be evinced in experimental measurements by changes in the bands of glyphosate (ν(P = O), δ(P-O-H), δ(C-N-H)) or in the bands of CE and DEAEC (ν(C-O), ν(C-H), ν(N-H)). The binding energies showed that the GLY interacts more effectively with CE than DEAEC. The ΔH prove that all processes are exothermic and the CE-GLY1 interaction showed value of ΔG < 0. The topological results showed a greater number of interactions with electrostatic nature. The results found in the study show that the theoretical data provides useful information to support the use of biopolymers as matrices for glyphosate adsorption or other contaminants.

Multi-configurational short-range density functional theory can describe spin-spin coupling constants of transition metal complexes

The multi-configurational short-range (sr) density functional theory has been extended to the calculation of indirect spin-spin coupling constants (SSCCs) for nuclear magnetic resonance spectroscopy. The performance of the new method is compared to Kohn-Sham density functional theory and the ab initio complete active space self-consistent field for a selected set of molecules with good reference values. Two density functionals have been considered, the local density approximation srLDA and srPBE from the GGA class of functionals. All srDFT calculations are of Hartree-Fock-type HF-srDFT or complete active space-type CAS-srDFT. In all cases, the calculated SSCC values are of the same quality for srLDA and srPBE functionals, suggesting that one should use the computationally cost-effective srLDA functionals in applications. For all the calculated SSCCs in organic compounds, the best choice is HF-srDFT; the more expensive CAS-srDFT does not provide better values for these single-reference molecules. Fluorine is a challenge; in particular, the FF, FC, and FO couplings have much higher statistical errors than the rest. For SSCCs involving fluorine and a metal atom CAS-srDFT with singlet, generalized Tamm-Dancoff approximation is needed to get good SSCC values although the reference ground state is not a multi-reference case. For VF₆ ^-1, all other considered models fail blatantly.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

A Systematic and Comparative Analysis of Four Major Classes of DFT Functionals to Compute Linear and Nonlinear Optical Properties of Benchmark Molecules

This study spotlights the fundamental insights about the systematic and comparative analysis of four famous hybrid classes of density functional theory (DFT) methods and their efficacy to calculate the linear and nonlinear optical (NLO) polarizabilities. For this study, urea and para-nitroaniline ([Formula: see text]-NA) molecular geometries are used as prototypes to calculate their linear and NLO properties. For comparative purposes, these molecules are often used as reference organic molecules for determination of NLO response properties and there is a dire need for such a benchmark database to be utilized by the researchers. We report systematically a range of functionals including hybrid (B3LYP, PBE1PBE, BH and HLYP), meta-hybrid (M06, M06-2X, M06-HF, M06-L), long-range corrected (CAM-B3LYP, LC-BLYP, LC-B97D, LC-B97D3) and functional with dispersion correction ([Formula: see text]B97, [Formula: see text]B97X, [Formula: see text]B97XD, HSEH1PBE). These groups are evaluated and their efficiency to calculate linear and NLO properties is graphically compared with each other. Overall, there are less deviations among different functionals for calculating dipole moments of [Formula: see text]-NA and urea while these deviations enhance as one moves from dipole moment to linear polarizability and nonlinear hyperpolarizabilities. In general, if we look at the trends, the polarizability values of B3LYP, M06-L, CAM-B3LYP and HSEH1PBE are relatively large and can be compared with each other. The dispersion corrected and long-range corrected functionals show more systematic deviations. For instance, among dispersion corrected functionals, the amplitudes of dipole moments, linear polarizability and NLO polarizabilities show an increasing trend as [Formula: see text]. It is also important to note that LC-B97D and LC-B97D3 of long-range corrected functional have observed exactly the same values of all the calculated parameters. A good agreement is being observed in static first and second hyperpolarizabilities of urea (B3LYP, M06-L, M06 and HSEH1PBE) and [Formula: see text]-NA (B3LYP, M06, M06-L, CAM-B3LYP and HSEH1PBE). Thus, we believe that the current investigation will provide the benchmark data of reference NLO molecules at different methods for theoretical community and molecular level insights for experimental community to design better NLO materials for hi-tech NLO applications.

Machine-Learned Energy Functionals for Multiconfigurational Wave Functions

We introduce multiconfiguration data-driven functional methods (MC-DDFMs), a group of methods which aim to correct the total or classical energy of a qualitatively accurate multiconfigurational wave function using a machine-learned functional of some featurization of the wave function such as its density, on-top density, or both. On a data set of carbene singlet-triplet energy splittings, we show that MC-DDFMs are able to achieve near-benchmark performance on systems not used for training with a robust degree of active-space independence. Beyond demonstrating that the density and on-top density hold the information necessary to correct the singlet-triplet energy splittings of multiconfigurational wave functions, this approach shows great promise for the development of functionals for MC-PDFT because corrections to the classical energy appear to be more transferable to types of molecules not included in the training data than corrections to total energies such as those yielded by CASSCF or NEVPT2.

High-Throughput Non-targeted Chemical Structure Identification Using Gas-Phase Infrared Spectra

The high-throughput identification of unknown metabolites in biological samples remains challenging. Most current non-targeted metabolomics studies rely on mass spectrometry, followed by computational methods that rank thousands of candidate structures based on how closely their predicted mass spectra match the experimental mass spectrum of an unknown. We reasoned that the infrared (IR) spectra could be used in an analogous manner and could add orthologous structure discrimination; however, this has never been evaluated on large data sets. Here, we present results of a high-throughput computational method for predicting IR spectra of candidate compounds obtained from the PubChem database. Predicted spectra were ranked based on their similarity to gas-phase experimental IR spectra of test compounds obtained from the NIST. Our computational workflow (IRdentify) consists of a fast semiempirical quantum mechanical method for initial IR spectra prediction, ranking, and triaging, followed by a final IR spectra prediction and ranking using density functional theory. This approach resulted in the correct identification of 47% of 258 test compounds. On average, there were 2152 candidate structures evaluated for each test compound, giving a total of approximately 555,200 candidate structures evaluated. We discuss several variables that influenced the identification accuracy and then demonstrate the potential application of this approach in three areas: (1) combining IR and mass spectra rankings into a single composite rank score, (2) identifying the precursor and fragment ions using cryogenic ion vibrational spectroscopy, and (3) the incorporation of a trimethylsilyl derivatization step to extend the method compatibility to less-volatile compounds. Overall, our results suggest that matching computational with experimental IR spectra is a potentially powerful orthogonal option for adding significant high-throughput chemical structure discrimination when used with other non-targeted chemical structure identification methods.

Accurate density functional made more versatile

We propose a one-electron self-interaction-free correlation energy functional compatible with the order-of-limit problem-free Tao-Mo (TM) semilocal functional (regTM) [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016) and Patra et al., J. Chem. Phys. 153, 184112 (2020)] to be used for general purpose condensed matter physics and quantum chemistry. The assessment of the proposed functional for large classes of condensed matter and chemical systems shows its improvement in most cases compared to the TM functional, e.g., when applied to the relative energy difference of MnO₂ polymorphs. In this respect, the present exchange-correction functional, which incorporates the TM technique of the exchange hole model combined with the slowly varying density correction, can achieve broad applicability, being able to solve difficult solid-state problems.

Strategies for the construction of machine-learning potentials for accurate and efficient atomic-scale simulations

Recent advances in machine-learning interatomic potentials have enabled the efficient modeling of complex atomistic systems with an accuracy that is comparable to that of conventional quantum-mechanics based methods. At the same time, the construction of new machine-learning potentials can seem a daunting task, as it involves data-science techniques that are not yet common in chemistry and materials science. Here, we provide a tutorial-style overview of strategies and best practices for the construction of artificial neural network (ANN) potentials. We illustrate the most important aspects of (a) data collection, (b) model selection, (c) training and validation, and (d) testing and refinement of ANN potentials on the basis of practical examples. Current research in the areas of active learning and delta learning are also discussed in the context of ANN potentials. This tutorial review aims at equipping computational chemists and materials scientists with the required background knowledge for ANN potential construction and application, with the intention to accelerate the adoption of the method, so that it can facilitate exciting research that would otherwise be challenging with conventional strategies.

Spin-Opposite-Scaled Range-Separated Exchange Double-Hybrid Models (SOS-RSX-DHs): Marriage Between DH and RSX/SOS-RSX Is Not Always a Happy Match

The range-separated version of double-hybrid density functional theory (DH-DFT) with a remarkable efficiency for both ground-state and excited-state characteristics has recently come into spotlight. In this work, based on theoretical arguments, several variants of spin-opposite-scaled range-separated exchange double-hybrid models (SOS-RSX-DHs) have been proposed and validated. More specifically, we first extend the RSX-DHs to design some other related models. Next, the SOS version of the resulting approximations is constructed and thoroughly evaluated using standard benchmark compilations of various properties. It is shown that although there are properties for which the RSX-DH and SOS-RSX-DH frameworks are rival, there are still some problems particularly prone to the self-interaction error issues where our proposed models seem to be beneficial. Furthermore, some of the presented models devoid of any additional corrections can also surpass the recently proposed approximations from different rungs of "Jacob's Ladder". Nonetheless, perusing the results of different methods and detailed comparisons with the predecessors discloses that all things may not necessarily be well with the RSX and SOS-RSX schemes, where the parent DHs as well as their SOS counterparts can still come into play.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

From Electronegativity towards Reactivity-Searching for a Measure of Atomic Reactivity

Pauling introduced the concept of electronegativity of an atom which has played an important role in understanding the polarity and ionic character of bonds between atoms. We set out to define a related concept of atomic reactivity in such a way that it can be quantified and used to predict the stability of covalent bonds in molecules. Guided by the early definition of electronegativity by Mulliken in terms of first ionization energies and Pauling in terms of bond energies, we propose corresponding definitions of atomic reactivity. The main goal of clearly distinguishing the inert gas atoms as nonreactive is fulfilled by three different proposed measures of atomic reactivity. The measure likely to be found most useful is based on the bond energies in atomic hydrides, which are related to atomic reactivities by a geometric average. The origin of the atomic reactivity is found in the symmetry of the atomic environment and related conservation laws which are also the origin of the shell structure of atoms and the periodic table. The reactive atoms are characterized by degenerate or nearly degenerate (several states of the same or nearly the same energy) ground states, while the inert atoms have nondegenerate ground states and no near-degeneracies. We show how to extend the use of the Aufbau model of atomic structure to qualitatively describe atomic reactivity in terms of ground state degeneracy. The symmetry and related conservation laws of atomic electron structures produce a strain (energy increase) in the structure, which we estimate by use of the Thomas-Fermi form of DFT implemented approximately with and without the symmetry and conservation constraints. This simplified and approximate analysis indicates that the total strain energy of an atom correlates strongly with the corresponding atomic reactivity measures but antibonding mechanisms prevent full conversion of strain relaxation to bonding.

Assessing locally range-separated hybrid functionals from a gradient expansion of the exchange energy density

Locally range-separated hybrid (LRSH) functionals feature a real-space-dependent range separation function (RSF) instead of a system-independent range-separation parameter, which thus enables a more flexible admixture of exact exchange than conventional range-separated hybrid functionals. In particular, the development of suitable RSF models and exploring the capabilities of the LRSH approach, in general, are tasks that require further investigations and will be addressed in this work. We propose a non-empirical scheme based on a detailed scaling analysis with respect to a uniform coordinate scaling and on a short-range expansion of the range-separated exchange energy density to derive new RSF models from a gradient expansion of the exchange energy density. After optimizing a small set of empirical parameters introduced to enhance their flexibility, the resulting second- and fourth-order RSFs are evaluated with respect to atomic exchange energies, atomization energies, and transition barrier heights.

Cyclopentadienyl radical formation from the reaction of excited nitrogen atoms with benzene: a theoretical study

Ab initio CCSD(T)/CBS//ωB97X-D/6-311+G(d,p) calculations of the C6H6N potential energy surface were performed to investigate the reaction mechanism underlying the reaction of atomic nitrogen (2D) with benzene. Thereafter, Rice-Ramsperger-Kassel-Marcus (RRKM) calculations of reaction rate constants and product branching ratios were performed under single-collision conditions. The results revealed that the N(2D) + C6H6 reaction in the case of statistical behavior is expected to produce hydrogen cyanide plus a cyclopentadienyl radical (91.5-88.9%), acetylene plus a pyrrole radical (5.8-7.5%), 1-cyano-2,4-cyclopentadiene + H (2.3-3.0%) and 1-ethynyl-pyrrole + H (0.4-0.6%), with the most favorable pathways being the initial adduct i1 leading to the formation of a seven-membered cyclic intermediate i12 through an exothermic ring expansion process and a multistep route i12 → i15 → i16 → C5H5 + HCN featuring an intramolecular ring-shrinking process involving a C-C bond fusion elimination channel to yield the bicyclic intermediate i15, followed by hydrogen cyanide elimination, thus forming a cyclopentadienyl radical. The calculated product branching ratios were consistent with the available experimental data; however, some quantitative deviations from the experimental results and the possible reasons are also discussed. The possible effects of the title reaction on the upper atmosphere of Titan, with critical implications for the rapid degradation of nitrogen-bearing polycyclic aromatic hydrocarbons, were compared with the mass growth processes of their polycyclic aromatic hydrocarbon counterparts produced through ring expansion.

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.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

Modelling biocompatible ionic liquids based on organic acids and amino acids: challenges for computational models and future perspectives

In this short review I shall highlight the basic principle and the difficulties that arise in attempting the computational modeling of seemingly simple systems which hide an unexpected complexity. Biocompatible ionic liquids which are based on the coupling of organic or amino acid anions with metabolic cations such as cholinium are the target of this review. These substances have been the subject of intense research activities in the last few years and have attracted the attention of computational chemists. I shall show that the computational description of these substances is far from trivial and requires the use of sophisticated techniques in order to account for a surprisingly rich chemistry that is due to several phenomena such as polarization, charge transfer, proton transfer equilibria and tautomerization reactions.

A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the high-throughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree-Fock exchange matrix. We call this new scheme the "approximate pair coefficient" (APC) method and we show that it performs quite well for the test systems presented.

Methane C-H Activation by [Cu2O]2+ and [Cu3O3]2+ in Copper-Exchanged Zeolites: Computational Analysis of Redox Chemistry and X-ray Absorption Spectroscopy

There is an ongoing debate regarding the role of [Cu₃O₃]²⁺ in methane-to-methanol conversion by copper-exchanged zeolites. Here, we perform electronic structure analysis and localized orbital bonding analysis to probe the redox chemistry of its Cu and μ-oxo sites. Also, the X-ray absorption near-edge structure, XANES, of methane activation in [Cu₃O₃]²⁺ is compared to that of the more ubiquitous [Cu₂O]²⁺. Methane C-H activation is associated with only the Cu²⁺/Cu⁺ redox couple in [Cu₂O]²⁺. For [Cu₃O₃]²⁺, there is no basis for the Cu³⁺/Cu²⁺ couple's participation at the density functional theory ground state. In [Cu₃O₃]²⁺, there are many possible intrazeolite intermediates for methane activation. In the nine possibilities that we examined, methane activation is driven by a combination of the Cu²⁺/Cu⁺ and oxyl/O^2- redox couples. Based on this, the Cu 1s-edge XANES spectra of [Cu₂O]²⁺ and [Cu₃O₃]²⁺ should both have energy signatures of Cu²⁺ → Cu⁺ reduction during methane activation. This is indeed what we obtained from the calculated XANES spectra. [Cu₂O]²⁺ and [Cu₃O₃]²⁺ intermediates with one Cu⁺ site are shifted by 0.9-1.7 eV, while those with two Cu⁺ sites are shifted by 3.0-4.2 eV. These are near a range of 2.5-3.2 eV observed experimentally after contacting methane with activated copper-exchanged zeolites. Thus, activation of methane by [Cu₃O₃]²⁺ will lead to formation of Cu⁺ sites. Importantly, for future quantitative XANES studies, involvement of O^- + e^- → O^2- in [Cu₃O₃]²⁺ implies a disconnect between the overall reactivity and the number of electrons used in the Cu²⁺/Cu⁺ redox couple.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.

Self-Interaction-Corrected Random Phase Approximation

The short-range correlation energy of the random phase approximation (RPA) is too negative and is often corrected by local or nonlocal methods. These beyond-RPA corrections usually lead to a mixed performance for thermodynamics and dissociation properties. RPA+ is an additive correction based on density functional approximations that often gives realistic total energies for atoms or solids. RPA+ adds a moderate correction to the ionization energies/electron affinities of RPA but does not yield an improvement beyond RPA for atomization energies of molecules. This incompleteness results in severely underestimated atomization energies just like in RPA. Exchange-correlation kernels within the Dyson equation could simultaneously improve atomization, ionization energies, and electron affinities, but their implementation is computationally less feasible in localized basis set codes. In preceding work ( Phys. Rev. A 100, 2019022515), two of the authors proposed a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities. gRPA+ was found to yield a large improvement of ionization energies and electron affinities of light atoms over RPA, and a smaller improvement over RPA+. Within this work, we investigate to what extent this improvement transfers to atomization energies, ionization energies, and electron affinities of molecules, using a modified gRPA+ (mgRPA+) method that can be applied in codes with localized basis functions. We thereby aim to understand the applicability of beyond-RPA corrections based on density functional approximations.

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.

Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

This work presents a method to move beyond the recently introduced atomic fragment approximation. Like the bare atomic fragment approach, the new method is an ab initio, parameter-free, orbital-free implementation of density functional theory based on the bifunctional formalism that treats the potential and the electron density as two separate variables, and provides access to the Kohn–Sham Pauli kinetic energy for an appropriately chosen Pauli potential. In the present ansatz, the molecular Pauli potential is approximated by the sum of the bare atomic fragment approach, and a so-called deformation potential that takes the interaction between the atoms into account. It is shown that this model can reproduce the bond-length contraction due to multiple bonding within the list of second-row homonuclear dimers. The present model only relies on the electron densities of the participating atoms, which themselves are represented by a simple monopole expansion. Thus, the bond-length contraction can be rationalized without referring to the angular quantum numbers of the participating atoms.

Fixation stability of glass matrix co-existent with crystal phases for heavy metals formed by high-temperature vitrification

Vitrification is an effective solidification method for heavy metal-containing wastes. However, most investigations focused on the formation of glass matrix. Seldom report discussed the influence of co-existing crystals on heavy metal stabilizations. In this work, Ca-Al-Si phase was formed in the glass matrix by adjusting the composition of feeding ingredient and melting temperature. As a result, when molar ratio of CaO/(SiO₂+Al₂O₃) was lower than 0.97 and reaction temperature was bigger than 1300 °C, small-size Ca-Al-Si phase (Ca₂Al₂SiO₇ and CaAl₂Si₂O₈) was homogeneously distributed in vitreous matrix. At the same time, Cr, Zn, and Pb leaching concentrations were the lowest, far lower than the leaching standard values. According to theoretical calculations, Zn and Pb replaced Ca atom; Cr replaced Al atom in Ca-Al-Si phase under thermal conditions. These replacements resulted in the fixation and stabilization of heavy metals. When the CaO/(SiO₂+Al₂O₃) molar ratio was bigger than 1.00, neither glass nor Ca-Al-Si was formed. Similarly, when the melting temperature was decreased, Ca-Al-Si phase formed a bigger size. Both these went against the stabilization, resulting in high leaching concentrations of heavy metals. The main of this work will help the development of high-temperature melting for the treatment of hazardous wastes.

Analysis of the kinetic energy functional in the generalized gradient approximation

A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.

Reaction mechanisms of C(3PJ) and C+(2PJ) with benzene in the interstellar medium from quantum mechanical molecular dynamics simulations

While spectroscopic data on small hydrocarbons in interstellar media in combination with crossed molecular beam (CMB) experiments have provided a wealth of information on astrochemically relevant species, much of the underlying mechanistic pathways of their formation remain elusive. Therefore, in this work, the chemical reaction mechanisms of C(3PJ) + C6H6 and C+(2P) + C6H6 systems using the quantum mechanical molecular dynamics (QMMD) technique at the PBE0-D3(BJ) level of theory is investigated, mimicking a CMB experiment. Both the dynamics of the reactions as well as the electronic structure for the purpose of the reaction network are evaluated. The method is validated for the first reaction by comparison to the available experimental data. The reaction scheme for the C(3PJ) + C6H6 system covers the literature data, e.g. the major products are the 1,2-didehydrocycloheptatrienyl radical (C7H5) and benzocyclopropenyl radical (C6H5-CH), and it reveals the existence of less common pathways for the first time. The chemistry of the C+(2PJ) + C6H6 system is found to be much richer, and we have found that this is because of more exothermic reactions in this system in comparison to those in the C(3PJ) + C6H6 system. Moreover, using the QMMD simulation, a number of reaction paths have been revealed that produce three distinct classes of reaction products with different ring sizes. All in all, at all the collision energies and orientations, the major product is the heptagon molecular ion for the ionic system. It is also revealed that the collision orientation has a dominant effect on the reaction products in both systems, while the collision energy mostly affects the charged system. These simulations both prove the applicability of this approach to simulate crossed molecular beams, and provide fundamental information on reactions relevant for the interstellar medium.

What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange–correlation (XC) functionals (PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation, HF-DFT is highly beneficial, particularly at low HF exchange percentages. This is especially true for noncovalent interactions where the electrostatic component is dominant, such as hydrogen and halogen bonds: for π-stacking, HF-DFT is detrimental. For subsets with significant nondynamical correlation (i.e., where a Hartree–Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use of HF orbitals greatly mitigates the error at 25% for barrier heights. Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree–Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorially optimized empirical range-separated hybrids ωB97X-V and ωB97M-V.

The Devil's Triangle of Kohn-Sham density functional theory and excited states

Exchange-correlation (XC) functionals from Density Functional Theory (DFT) developed under the rigorous arguments of Correlated Orbital Theory (COT) address the Devil's Triangle of prominent errors in Kohn-Sham (KS) DFT. At the foundation of this triangle lie the incorrect one-particle spectrum, the lack of integer discontinuity, and the self-interaction error. At the top level, these failures manifest themselves in incorrect charge transfer and Rydberg excitation energies, along with poor activation barriers. Accordingly, the Quantum Theory Project (QTP) XC functionals have been created to address several of the long-term issues encountered in KS theory and its Time Dependent DFT (TDDFT) variant for electronic excitations. Recognizing that COT starts with a correct one-particle spectrum, a condition imposed on the QTP functionals by means of minimum parameterization, the question that arises is how does this affect the electronically excited states? Among up to 28 XC functionals considered, the QTP family provides one of the smallest mean absolute deviations for charge-transfer excitations while also showing excellent results for Rydberg states. However, there is some room for improvement in the case of excitation energies to valence states, which are systematically underestimated by all functionals investigated. An alternative path for better treatment of excitation energies, mainly for valence states, is offered by using orbital energies from QTP functionals, especially by CAM-QTP-02 and LC-QTP. In this case, the deviations from the reference data can be reduced approximately by half.

From Kohn-Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential

Accurately describing excited states within Kohn–Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

Meta-Local Density Functionals: A New Rung on Jacob's Ladder

The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density n_σ, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a geometric average n_σ^avg(r) = n_σ^1-x(r)ñ_σ^x(r) of the local spin density n_σ(r) and the spin density ñ_σ(r) of a HEG that has the local kinetic energy density τ_σ(r) of the inhomogeneous system. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG and which form a new rung of Jacob's ladder of density functionals [ AIP Conf. Proc. 2001, 577, 1]. The first functional of this ladder, the local τ approximation (LTA) of Ernzerhof and Scuseria [ J. Chem. Phys. 1999, 111, 911] that corresponds to x = 1 is unfortunately not stable enough to be used in self-consistent field calculations because it leads to divergent potentials, as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of x not only leads to numerical stability of the resulting functional but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional (x = 1/4) of Eich and Hellgren [ J. Chem. Phys. 2014, 141, 224107]. We choose x = 0.50, as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice x = 0.50 also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.

The Role of Range-Separated Correlation in Long-Range Corrected Hybrid Functionals

The extensive application of long-range corrected hybrid functionals highlights the importance of further improving their accuracy. Unlike common long-range corrected hybrid functionals mainly focusing on the exchange part, range-separated correlation and its role in long-range corrected hybrid functionals are the main concerns of this work. To this end, we present theory on the derivation of the range-separated correlation, whose reliability and validity are proved by the agreement with the full CI on the test of the short-range correlation energy. The tests on various properties indicate that the long-range part of the LYP functional cannot effectively capture the long-range correlation effect required in LC-BLYP, whose absence instead results in a better XC functional. This new functional significantly improves LC-BLYP on all the tests in this work, with an accuracy on par with or even greater than the widely recognized CAM-B3LYP method for some applications, while maintaining the important -1/r asymptotic behavior of the XC potential. The advances and insights gained in this work are useful for the application and development of long-range corrected hybrid functionals, while emphasizing the significance of developing effective and low-cost long-range correlation functionals.

Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming

Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems, and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the static correlation in DFT when frontier orbitals are degenerate by the means of using a semidefinite programming (SDP) approach to minimize the system energy as a function of the N-representable, non-idempotent 1-electron reduced density matrix. While showing greatly improved singlet-triplet gaps for local density approximation and generalized gradient approximation (GGA) functionals, the SDP procedure reveals flaws in modern meta and hybrid GGA functionals, which show no major improvements when provided with an accurate electron density.

Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method

We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide benchmark all-electron results with very tight convergence of the particle-number constraint, associated chemical potential, and electron density. It is demonstrated that, by preserving the saddle-point nature of the optimization and simultaneously optimizing the density and chemical potential, an order of magnitude reduction in the number of iterations required for convergence is obtained. The approach is compared and contrasted with a new implementation of the nested optimization scheme put forward by Chan, Cohen, and Handy. Our implementation allows for semilocal kinetic-energy (and exchange-correlation) functionals to be handled self-consistently in all-electron calculations. The all-electron Gaussian-basis setting for these calculations will enable direct comparison with a wide range of standard high-accuracy quantum-chemical methods as well as with Kohn-Sham density-functional theory. We expect that the present implementation will provide a useful tool for analyzing the performance of approximate kinetic-energy functionals in finite systems.

Facet-Dependent Photodegradation of Methylene Blue by Hematite Nanoplates in Visible Light

The expression of specific crystal facets in different nanostructures is known to play a vital role in determining the sensitivity toward the photodegradation of organics, which can generally be ascribed to differences in surface structure and energy. Herein, we report the synthesis of hematite nanoplates with controlled relative exposure of basal (001) and edge (012) facets, enabling us to establish direct correlation between the surface structure and the photocatalytic degradation efficiency of methylene blue (MB) in the presence of hydrogen peroxide. MB adsorption experiments showed that the capacity on (001) is about three times larger than on (012). Density functional theory calculations suggest the adsorption energy on the (001) surface is 6.28 kcal/mol lower than that on the (012) surface. However, the MB photodegradation rate on the (001) surface is around 14.5 times faster than on the (012) surface. We attribute this to a higher availability of the photoelectron accepting surface Fe³⁺ sites on the (001) facet. This facilitates more efficient iron valence cycling and the heterogeneous photo-Fenton reaction yielding MB-oxidizing hydroxyl radicals at the surface. Our findings help establish a rational basis for the design and optimization of hematite nanostructures as photocatalysts for environmental remediation.

Valence electrons in lanthanide-based single-atom magnets: a paradigm shift in 4f-magnetism modeling and design

Impact of valence electrons on the magnetic properties of lanthanide-based monatomic magnetic systems on surfaces and in molecules. And FV-magnetism - as a crucial bit in the further understanding and design of a new generation of atomic magnets.

New insights on the ESIPT process based on solid-state data and state-of-the-art computational methods

Benzothiazole derivatives were used as models to study the excited-state intramolecular proton transfer (ESIPT) from an experimental and theoretical point of view. The experimental electronic and vibrational results were compared with a comprehensive selection of state-of-the-art computational methods in a workflow approach. The latter were performed based on modern techniques, such as DLPNO-CCSD(T), which gives the reference energies and current methodologies for ESIPT analysis, such as molecular dynamics and charge density difference testing. The theoretical vibrational results were focused on the stretch vibrational-mode of the hydroxyl group, which indicated a large increase in the intramolecular hydrogen bond strength, which facilitates the ESIPT process. Theoretically, the optimization of a large number of molecules shows that π-stacking plays a fundamental role in benzothiazole stabilization, with a remarkably strong intramolecular hydrogen bond. The potential energy surface of the ESIPT reactive benzothiazole (4HBS) has a clear transition state where ESIPT is easily observed with a large difference in energy between the enol and keto tautomer. Additionally, molecular dynamics showed that the ESIPT process occurs very fast. The tautomer appears around 8.7 fs and the enolic form is regenerated in just 24 fs, closing the Förster cycle. The calculated Stokes shift could be related to the ESIPT process and the experimental solid-state emission spectrum matched almost perfectly with the theoretical one. In contrast, for the non-ESIPT benzothiazole (4HBSN), the agreement between theory and experiment was limited, probably due to intermolecular interaction effects that are not considered in these calculations.

On the role of steric and exchange–correlation effects in halogenated complexes

Density functional theory formalisms of energy partitioning schemes are utilized to find out what energetic components govern interactions in halogenated complexes.

Surface and morphological studies of LiNbO3: p-type semiconductivity on stoichiometric surfaces

The surface and morphological properties of LiNbO3 surfaces were calculated, and particular semiconductor types for crystal morphologies were found.