Status and Challenges of Density Functional Theory

Density functional theory investigation of ozone gas uptake by a BeO nanoflake

Due to importance of the gas uptake topic in environment and energy issues, this work was performed for investigating ozone (Oz) gas uptake by means of a beryllium oxide (BeO) nanoflake. To this aim, density functional theory (DFT) calculations and the quantum theory of atoms in molecules (QTAIM) analysis were performed. The monolayer BeO nanoflake was decorated by a HEME-like N4Fe region to prepare an interacting region towards the Oz uptake. Accordingly, three models were optimized based on configurations of Oz molecule relaxation at the BeO surface, in which two types of O ... Fe and O ... N interactions were observed. In this case, Oz3@BeO model was involved with two mentioned types of interactions and three occurred interaction between Oz and BeO making it as the strongest bimolecular formation model of Oz@BeO. Moreover, electronic molecular orbital features indicated that the models formations could be also related to sensor functions by variations of electric conductivity because of Oz gas uptake. As a consequence, the investigated BeO nanoflake of this work was proposed for employing in Oz gas uptake for different purposes.

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH₂NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

Synthesis and photophysical properties of nitrated aza-BODIPYs

A series of nitrated aza-BODIPYs on the 2- and 6-positions were regioselectively synthesized and their photophysical properties were examined.

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

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

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

Surface modeling of photocatalytic materials for water splitting

The photocatalyst surface is central to photocatalytic reactions. However, it has been a challenge to explicitly understand both the surface configuration and the structure-dependent photocatalytic properties at the atomic level. First-principles density functional theory (DFT) calculations provide a versatile method that makes up for the lack of experimental surface studies. In DFT calculations, the initial surface model greatly affects the accuracy of the calculation results. Consequently, establishing a more realistic and more reliable material surface models is undoubtedly the first step and the most important link in theoretical calculations. The aim of this Perspective is to provide a general understanding of the methods for the surface modeling of photocatalytic materials in recent years. We begin with a discussion of the basic theories applied in photocatalytic surface research, followed by an explanation of the importance of surface modeling in photocatalysis. We then elaborate on the advantages and disadvantages of the basic surface model and briefly describe the latest surface modeling methods. Finally, we evaluate the rationality of current surface modeling methods. We summarize this Perspective by prospecting the developing directions of photocatalytic surface research in the future. It is believed that a reasonable surface model should be verified by both experimental characterization and theoretical computation with negative feedback.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

Inq, a Modern GPU-Accelerated Computational Framework for (Time-Dependent) Density Functional Theory

We present inq, a new implementation of density functional theory (DFT) and time-dependent DFT (TDDFT) written from scratch to work on graphic processing units (GPUs). Besides GPU support, inq makes use of modern code design features and takes advantage of newly available hardware. By designing the code around algorithms, rather than against specific implementations and numerical libraries, we aim to provide a concise and modular code. The result is a fairly complete DFT/TDDFT implementation in roughly 12 000 lines of open-source C++ code representing a modular platform for community-driven application development on emerging high-performance computing architectures.

Machine Learning Prediction of the Exfoliation Energies of Two-Dimension Materials via Data-Driven Approach

Exfoliation energy is one of the fundamental parameters in the science and engineering of two-dimensional (2D) materials. Traditionally, it was obtained via indirect experimental measurement or first-principles calculations, which are very time- and resource-consuming. Herein, we provide an efficient machine learning (ML) method to accurately predict the exfoliation energies for 2D materials. Toward this end, a series of simple descriptors with explicit physical meanings are defined. Regression trees (RT), support vector machines (SVM), multiple linear regression (MLR), and ensemble trees (ET) are compared to develop the most suitable model for the prediction of exfoliation energies. It is shown that the ET model can efficiently predict the exfoliation energies through extensive validations and stability analysis. The influence of the defined features on the exfoliation energies is analyzed by sensitivity analysis to provide novel physical insight into the affecting factors of the exfoliation energies.

Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.

Mechanistic Insight into Metal Ion-Catalyzed Transamination

Several classes of biological reactions that are mediated by an enzyme and a co-factor can occur, to a slower extent, not only without the enzyme but even without the co-factor, under catalysis by metal ions. This observation has led to the proposal that metabolic pathways progressively evolved from using inorganic catalysts to using organocatalysts of increasing complexity. Transamination, the biological process by which ammonia is transferred between amino acids and α-keto acids, has a mechanism that has been well studied under enzyme/co-factor catalysis and under co-factor catalysis, but the metal ion-catalyzed variant was generally studied mostly at high temperatures (70-100 °C), and the details of its mechanism remained unclear. Here, we investigate which metal ions catalyze transamination under conditions relevant to biology (pH 7, 20-50 °C) and study the mechanism in detail. Cu²⁺, Ni²⁺, Co²⁺, and V⁵⁺ were identified as the most active metal ions under these constraints. Kinetic, stereochemical, and computational studies illuminate the mechanism of the reaction. Cu²⁺ and Co²⁺ are found to predominantly speed up the reaction by stabilizing a key imine intermediate. V⁵⁺ is found to accelerate the reaction by increasing the acidity of the bound imine. Ni²⁺ is found to do both to a limited extent. These results show that direct metal ion-catalyzed amino group transfer is highly favored even in the absence of co-factors or protein catalysts under biologically compatible reaction conditions.

On the inclusion of one double within CIS and TDDFT

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

Ligand-to-Metal Charge-Transfer Photophysics and Photochemistry of Emissive d0 Titanocenes: A Spectroscopic and Computational Investigation

Complexes with ligand-to-metal charge-transfer (LMCT) excited states involving d⁰ metals represent a new design for photocatalysts. Herein, the photochemistry and photophysics of d⁰ titanocenes of the type Cp₂Ti(C₂R)₂, where C₂R = ethynylphenyl (C₂Ph), 4-ethynyldimethylaniline (C₂DMA), or 4-ethynyltriphenylamine (C₂TPA), have been investigated. Cp₂Ti(C₂Ph)₂ and Cp₂Ti(C₂DMA)₂ have also been characterized by single-crystal X-ray diffraction. The two aryl rings in Cp₂Ti(C₂DMA)₂ are nearly face-to-face in the solid state, whereas they are mutually perpendicular for Cp₂Ti(C₂Ph)₂. All three complexes are brightly emissive at 77 K but photodecompose at room temperature when irradiated into their lowest-energy absorption band. The emission wavelengths and photodecomposition quantum yields are as follows: Cp₂Ti(C₂Ph)₂, 575 nm and 0.65; Cp₂Ti(C₂TPA)₂, 642 nm and 0.42; Cp₂Ti(C₂DMA)₂, 672 nm and 0.25. Extensive benchmarking of the density functional theory (DFT) model against the structural data and of the time-dependent DFT (TDDFT) model against the absorption and emission data was performed using combinations of 13 different functionals and 4 basis sets. The model that predicted the absorption and emission data with the greatest fidelity utilized MN15/LANL2DZ for both the DFT optimization and the TDDFT. Computational analysis shows that absorption involves a transition to a ¹LMCT state. Whereas the spectroscopic data for Cp₂Ti(C₂TPA)₂ and Cp₂Ti(C₂DMA)₂ are well modeled using the optimized structure of these complexes, Cp₂Ti(C₂Ph)₂ required averaging of the spectra from multiple rotamers involving rotation of the Ph rings. Consistent with this finding, an energy scan of all rotamers showed a very flat energetic surface, with less than 1.3 kcal/mol separating the minimum and maximum. The computational data suggest that emission occurs from a ³LMCT state. Optimization of the ³LMCT state demonstrates compression of the C-Ti-C bond angle, consistent with the known products of photodecomposition.

Exploring vibronic coupling in the benzene radical cation and anion with different levels of the GW approximation

The linear vibronic coupling constants of the benzene radical cation and anion have been obtained with different levels of the GW approximation, including G₀W₀, eigenvalue self-consistent GW, and quasiparticle self-consistent GW, as well as DFT with the following exchange-correlation functionals: BLYP, B3LYP, CAM-B3LYP, tuned CAM-B3LYP, and an IP-tuned CAM-B3LYP functional. The vibronic coupling constants were calculated numerically using the gradients of the eigenvalues of the degenerate HOMOs and LUMOs of the neutral benzene molecule for DFT, while the numerical gradients of the quasiparticle energies were used in the case of GW. The results were evaluated against those of high level wave function methods in the literature, and the approximate self-consistent GW methods and G₀W₀ with long-range corrected functionals were found to yield the best results on the whole.

Multi-Ion Bridged Pathway of N-Oxides to 1,3-Dipole Dilithium Oxide Complexes

Roussi's landmark work on the generation of 1,3-dipoles from tertiary amine N-oxides has not reached its full potential since its underlying mechanism is neither well explored nor understood. Two competing mechanisms were previously proposed to explain the transformation involving either an iminium ion or a diradical intermediate. Our investigation has revealed an alternative mechanistic pathway that explains experimental results and provides significant insights to guide the creation of new N-oxide reagents beyond tertiary alkylamines for direct synthetic transformations. Truhlar's M06-2x functional and Møller-Plesset second-order perturbation theory with Dunning's [jul,aug]-cc-pv[D,T]z basis sets and discrete-continuum solvation models were employed to determine activation enthalpies and structures. During these mechanistic explorations, we discovered a unique multi-ion bridged pathway resulting from the rate-determining step, which was energetically more favorable than other alternate mechanisms. This newly proposed mechanism contains no electrophilic intermediates, strengthening the reaction potential by broadening the reagent scope and limiting the possible side reactions. This thoroughly defined general mechanism supports a more direct route for improving the use of N-oxides in generating azomethine ylide-dilithium oxide complexes with expanded functional group tolerance and breadth of chemistry.

Benchmark calculations for bond dissociation energies and enthalpy of formation of chlorinated and brominated polycyclic aromatic hydrocarbons

Thermodynamic properties, i.e., bond dissociation energies and enthalpy of formation, of chlorinated and brominated polycyclic aromatic hydrocarbons play a fundamental role in understanding their formation mechanisms and reactivity. Computational electronic structure calculations routinely used to predict thermodynamic properties of various species are limited for these compounds due to large computational cost to obtain accurate results by employing high-level wave function theory methods. In this work, a number of composite model chemistry methods (CBS-QB3, G3MP2, G3, and G4) are used to compute bond dissociation energies and enthalpies of formation of small to medium-size chlorinated and brominated polycyclic aromatic hydrocarbon compounds. The enthalpy of formation is derived via the atomization method and compared against the recommended values. Statistical analysis indicates that G4 is the best method. For comparison, three commonly used density functional theory (DFT) methods (M06-2X, ωB97X-D and B2PLYP-D3) with various basis sets including 6-311++G(d, p), cc-pVTZ, and cc-pVQZ in the prediction of bond dissociation energies and enthalpies of formation have been tested using the optimized geometries at the same M06-2X/6-311++G(d, p) level of theory. It is found that ωB97X-D/6-311++G(d, p) shows the best performance in computing the bond dissociation energies, while ωB97X-D/cc-pVTZ exhibits the best prediction in enthalpy of formation of the studied reaction systems. The structural effect on the bond dissociation energies and enthalpy of formation of chlorinated and brominated polycyclic aromatic hydrocarbons are then systematically analyzed. Based on comparisons of the various methods, reliable DFT methods are recommended for future theoretical studies on large chlorinated and brominated polycyclic aromatic hydrocarbons considering both accuracy and computational cost. This work, to the authors' knowledge, is the first to systematically benchmark theoretical methods for the accurate prediction of thermodynamic properties for chlorinated and brominated polycyclic aromatic hydrocarbons.

Benchmark calculations using state-of-the-art DFT functionals and composite methods for bond dissociation energy and enthalpy of formation of halogenated polycyclic aromatic hydrocarbons are performed.

Towards Quantum-Chemical Modeling of the Activity of Anesthetic Compounds

The modeling of the activity of anesthetics is a real challenge because of their unique electronic and structural characteristics. Microscopic approaches relevant to the typical features of these systems have been developed based on the advancements in the theory of intermolecular interactions. By stressing the quantum chemical point of view, here, we review the advances in the field highlighting differences and similarities among the chemicals within this group. The binding of the anesthetics to their partners has been analyzed by Symmetry-Adapted Perturbation Theory to provide insight into the nature of the interaction and the modeling of the adducts/complexes allows us to rationalize their anesthetic properties. A new approach in the frame of microtubule concept and the importance of lipid rafts and channels in membranes is also discussed.

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.

A review on the use of DFT for the prediction of the properties of nanomaterials

Nanostructured materials have gained immense attraction because of their extraordinary properties compared to the bulk materials to be used in a plethora of applications in myriad fields. In this review article, we have discussed how the Density Functional Theory (DFT) calculation can be used to explain some of the properties of nanomaterials. With some specific examples here, it has been shown that how closely the different properties of nanomaterials (such as optical, optoelectronics, catalytic and magnetic) predicted by DFT calculations match well with the experimentally determined values. Some examples were discussed in detail to inspire the experimental scientists to conduct DFT-based calculations along with the experiments to derive a better understanding of the experimentally obtained results as well as to predict the properties of the nanomaterial. We have pointed out the challenges associated with DFT, and potential future perspectives of this new exciting field.

Accurate acid dissociation constant (pKa) calculation for the sulfachloropyridazine and similar molecules

Accurate calculation of the acid dissociation constant (pK_a) has fundamental importance for the description of molecular systems with pharmacological activities. The search for a more appropriate procedure for its determination is always welcome and has aroused increasing interest from the scientific community. In this sense, this work presents a computational study involving the combination of ten DFT functionals (M062X, M06L, B3LYP, BLYP, PBEPBE, BP86, LC-BLYP, SPBE, CAM-B3LYP, LC-PBEPBE) and HF method, eight basis set functions (6-311G, 6-311 + G, 6-311G(d,p), 6-311 + G(d,p), 6-311+ +G(d,p), 6-311(2d,2p), 6-311+ +G(2d,2p), and aug-cc-pVDZ), and three solvation models (SMD, PCM, and CPCM) for an accurate sulfachloropyridazine (SCR) pK_a determination. It was found that the smallest deviation (0.02 unit of pK_a) between the current study and experimental result was achieved with the BLYP/6-311 + G(d,p)/PCM combination. Therefore, this combination was extended to calculate the pK_a of six SCR similar molecules selected through the eletroshape similarity method. For all these molecules, the difference between the obtained results and experimental data ranged between 0.14 and 0.69 units of pK_a. This feature suggests that the obtained combination can determine pK_a with experimental precision for complexes that are formed by sulfonamide functional group (SO₂NHR). Graphical Abstract A computational study involving the combination of different levels of theory, basis sets and solvation models for an accurate sulfanamide pK_a determination.

How Accurate Are Approximate Density Functionals for Noncovalent Interaction of Very Large Molecular Systems?

Noncovalent intermolecular interactions are very important in many research areas. Therefore, it is vital to understand the extent to which approximate density functionals give a proper description of noncovalent interactions. Previous research has demonstrated that some approximate density functionals can predict usefully accurate interaction energies for many noncovalent systems; however, most of that work is limited to small and moderate-sized molecules. Very recently though, accurate benchmarks have become available for some very large molecules. The present work applies 21 approximate density functionals to compute the binding energies of seven large molecular systems that have a number of atoms ranging from 200 to 910. The results are judged by comparison to the recently published CIM-DLPNO-CCSD(T) results, which are assumed to provide a reliable benchmark. The five most accurate methods among those tested are found to be PW6B95-D4, PW6B95-D3(BJ), revM11, M06-L, and MN15.

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.

Structure prediction of neutral physiological copper(II) compounds with l-cysteine and l-histidine

Bis(aminoacidato)copper(II) [Cu^II(aa)₂] coordination compounds are the physiological species of copper(II) amino acid compounds in blood plasma. Since there are no experimental data in the literature about the geometries that physiological Cu^II(aa)₂ could form with l-cysteine (Cys), that is, for bis(l-cysteinato)copper(II) [Cu(Cys)₂] and the ternary (l-histidinato)(l-cysteinato)copper(II) [Cu(His)(Cys)], this paper computationally examines the possible conformations that the two compounds could form with the Cys ligand having a protonated sulfur, as in the conventional zwitterion, which was determined to be prevailing in aqueous solution. These two amino acids can bind metals in a tridentate fashion and thus form many possible coordination patterns. Density functional calculations were performed for the conformational analyses in the gas phase and in implicitly modeled aqueous solution using a polarizable continuum model. Additionally, we examine which coordination mode, with thiol or thiolate group, is more stable. The Cys coordination via the amino N and carboxylato O atoms (a glycinato mode) is obtained as the most stable one in aqueous Cu(Cys)₂, and also in Cu(His)(Cys) when the His glycinato or histaminato mode combines with the intact thiol group. Whereas the conformers with N and thiol S as the copper(II) donor atoms are predicted to be the least stable, those with the Cu-N and Cu-S(thiolate) bonding (and protonated carboxylato group) are the most stable. The differences are explained by different covalent and ionic contributions of Cu-S(thiol) vs. Cu-S(thiolate). The study can contribute to the insight into formation and reactivity of the copper(II) cysteinato complexes in solution.

When a "Dimroth Rearrangement" Is Not a Dimroth Rearrangement

In the Dimroth rearrangement of heterocycles, often pyrimidines, an exocyclic and a ring substituent are interchanged. However, the term Dimroth rearrangement is frequently used even when there is no knowledge of the reaction mechanism and alternatives are likely. Here, we have employed density functional theory (DFT) calculations at the M06-2X/6-311+G(d,p) level to determine the most plausible rearrangement pathways of 3-aminothiocarbonylquinazoline 5, tetrahydrofuranylpyrimidine 21, and 5-allyltriazocine 30. For the rearrangement of quinazoline 5 to 9, the [1,3]-sigmatropic shift of the thioamido group with an activation barrier of 26.7 kcal/mol is much preferred over the Dimroth rearrangement (∼46 kcal/mol). An even lower barrier of 21.6 kcal/mol applies to a stepwise [1,3]-shift. The migration of the tetrahydrofuranyl unit in pyrimidines like 21 → 23 can take place by means of a [1,3]-sigmatropic shift with a low barrier (≤17.5 kcal/mol) rather than a Dimroth rearrangement under acidic conditions and most likely also under neutral conditions (∼30 kcal/mol). In the rearrangement of 5-allyl-6-iminotriazocine 30 to 32, the [3,3]-sigmatropic shift (aza-Cope rearrangement) is preferred over the Dimroth mechanism under neutral conditions, but in the presence of acid, the azonia-Cope rearrangement of an allyl group and the true Dimroth rearrangement have comparable activation energies.

Theoretical study on charge distribution in cetylpyridinium cationic surfactant

Here, we report the electrostatic potential maxima and partial atomic charges evaluated on cetylpyridinium cation. The Hartree-Fock method and six DFT functionals (namely, PBE, TPSS, B3LYP, PBE0, M06, and wB97) were used to calculate partial atomic charges via CHELPG, Mulliken, Löwdin, Hirshfeld, and natural population schemes. Calculations were performed for the gas phase and for the CPCM water solvated cation, resulting in a set of 70 types of partial atomic charges. The main tendencies in charge deviations were discussed. In comparison with the electrostatic potential-based CHELPG partial charges, Hirshfeld, Mulliken, Löwdin, and NPA partitioning schema lead to an almost steady decrease in the partial charges in the cetyl chain. This agreed closely with the redistribution of electrostatic potential mapped onto the 0.002 e/Bohr³ isodensity surface.

Inverse Kohn-Sham Density Functional Theory: Progress and Challenges

Inverse Kohn-Sham (iKS) methods are needed to fully understand the one-to-one mapping between densities and potentials on which density functional theory is based. They can contribute to the construction of empirical exchange-correlation functionals and to the development of techniques for density-based embedding. Unlike the forward Kohn-Sham problems, numerical iKS problems are ill-posed and can be unstable. We discuss some of the fundamental and practical difficulties of iKS problems with constrained-optimization methods on finite basis sets. Various factors that affect the performance are systematically compared and discussed, both analytically and numerically, with a focus on two of the most practical methods: the Wu-Yang method (WY) and the partial differential equation constrained optimization (PDE-CO). Our analysis of the WY and PDE-CO highlights the limitation of finite basis sets. We introduce new ideas to make iKS problems more tractable, provide an overall strategy for performing numerical density-to-potential inversions, and discuss challenges and future directions.

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.

Binding interaction of protoberberine alkaloids against acetylcholinesterase (AChE) using molecular dynamics simulations and QM/MM calculations

Acetylcholinesterase (AChE) plays a vital role in Alzheimer's disease (AD), which is one of the most common causes of dementia. Discovering new effective inhibitors against AChE activity is seen to be one of the effective approaches to reduce the suffering from AD. Protoberberine alkaloids isolated from natural resources have previously been reported as potent AChE inhibitors. In order to gain insights into how these alkaloids could inhibit AChE, berberine, palmatine, and cyclanoline were selected to investigate in terms of binding orientation and their key interactions with AChE using molecular docking and molecular dynamics simulations and quantum chemical calculations. The results revealed that the molecular dynamics structures of palmatine and berberine indicated that their equilibrated structures did not occupy the gorge but they slightly moved away from the catalytic site (CAS). For cyclanoline, the binding mode was quite different from those of donepezil and the other protoberberine alkaloids: it preferred to stay deeper in the CAS site. Interaction energies and residual interaction energies confirmed that the key interactions for palmatine and berberine were π-π interactions with Trp286 and Tyr341 and H-bond interactions with Tyr124. Cyclanoline formed π-π interactions with Trp86 and H-bonds to the amino acids in the CAS site. The results suggested the importance of aromaticity in the core structure and the flexibility of the core structure or the substituents in order to fit into the narrow gorge. The HOMO, LUMO, bioavailability, drug-likeness and pharmacokinetics were also predicted. The results obtained will be useful for further AD drug development.

Multiconfiguration Pair-Density Functional Theory

Kohn-Sham density functional theory with the available exchange-correlation functionals is less accurate for strongly correlated systems, which require a multiconfigurational description as a zero-order function, than for weakly correlated systems, and available functionals of the spin densities do not accurately predict energies for many strongly correlated systems when one uses multiconfigurational wave functions with spin symmetry. Furthermore, adding a correlation functional to a multiconfigurational reference energy can lead to double counting of electron correlation. Multiconfiguration pair-density functional theory (MC-PDFT) overcomes both obstacles, the second by calculating the quantum mechanical part of the electronic energy entirely by a functional, and the first by using a functional of the total density and the on-top pair density rather than the spin densities. This allows one to calculate the energy of strongly correlated systems efficiently with a pair-density functional and a suitable multiconfigurational reference function. This article reviews MC-PDFT and related background information.

iSPECTRON: A simulation interface for linear and nonlinear spectra with ab-initio quantum chemistry software

We introduce iSPECTRON, a program that parses data from common quantum chemistry software (NWChem, OpenMolcas, Gaussian, Cobramm, etc.), produces the input files for the simulation of linear and nonlinear spectroscopy of molecules with the Spectron code, and analyzes the spectra with a broad range of tools. Vibronic spectra are expressed in term of the electronic eigenstates, obtained from quantum chemistry computations, and vibrational/bath effects are incorporated in the framework of the displaced harmonic oscillator model, where all required quantities are computed at the Franck-Condon point. The program capabilities are illustrated by simulating linear absorption, transient absorption and two dimensional electronic spectra of the pyrene molecule. Calculations at two levels of electronic structure theory, time-dependent density functional theory (with NWChem) and RASSCF/RASPT2 (with OpenMolcas) are presented and compared where possible. The iSPECTRON program is available online at https://github.com/ispectrongit/iSPECTRON/ and distributed open source under the terms of the Educational Community License version 2.0 (ECL 2.0).

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.

Lewis Acidic Boranes, Lewis Bases, and Equilibrium Constants: A Reliable Scaffold for a Quantitative Lewis Acidity/Basicity Scale

A quantitative Lewis acidity/basicity scale toward boron-centered Lewis acids has been developed based on a set of 90 experimental equilibrium constants for the reactions of triarylboranes with various O-, N-, S-, and P-centered Lewis bases in dichloromethane at 20 °C. Analysis with the linear free energy relationship log KB =LAB +LBB allows equilibrium constants, KB , to be calculated for any type of borane/Lewis base combination through the sum of two descriptors, one for Lewis acidity (LAB ) and one for Lewis basicity (LBB ). The resulting Lewis acidity/basicity scale is independent of fixed reference acids/bases and valid for various types of trivalent boron-centered Lewis acids. It is demonstrated that the newly developed Lewis acidity/basicity scale is easily extendable through linear relationships with quantum-chemically calculated or common physical-organic descriptors and known thermodynamic data (ΔHBF 3 ). Furthermore, this experimental platform can be utilized for the rational development of borane-catalyzed reactions.

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.

The origin of the regiospecificity of acrolein dimerization

Acrolein dimerization is a intriguing case since the reaction does not occur to form the electronically preferred regioisomeric adduct. Various explanations have been suggested to rationalize this experimental regioselectivity, however, none of these arguments had been convincing enough. In this work, the hetero Diels-Alder acrolein dimerization was theoretically investigated using DFT and MP2 methods. The influence of nucleophilic/electrophilic interactions and non-covalent interactions (NCI) in the regiospecificity of the reaction were analyzed. Our results show that the NCI at the transition state are the key factor controlling the regiospecificity in this reaction. Besides, we found that the choice of calculation method can have an effect on the prediction of the mechanism in the reaction, as all DFT methods forecast a one-step hetero Diels-Alder acrolein dimerization, while MP2 predicts a stepwise description for the lower energy reaction channel.

Data-driven machine learning model for the prediction of oxygen vacancy formation energy of metal oxide materials

Metal oxides are widely used in the fields of chemistry, physics and materials science. Oxygen vacancy formation energy is a key parameter to describe the chemical, mechanical, and thermodynamic properties of metal oxides. How to acquire quickly and accurately oxygen vacancy formation energy remains a challenge for both experimental and theoretical researchers. Herein, we propose a machine learning model for the prediction of oxygen vacancy formation energy via data-driven analysis and the definition of simple descriptors. Starting with the database containing oxygen vacancy formation energies for 1750 metal oxides with enough structural diversity, new descriptors that effectively avoid the defects of molecular fingerprints, molecular graphic descriptors and site descriptors are defined. The descriptors have obvious physical meanings and wide practicability. Multiple linear regression analysis is then used to screen important features for machine learning model development, and two strongly associated features are obtained. The selected descriptors are used as input for the training of 21 machine learning models to select and develop the most accurate machine learning model. Finally, it is shown that the least squares support vector regression method exhibits the best performance for accurate prediction of the targeted oxygen vacancy formation energy through systematic error analysis, and the prediction accuracy is also verified by the external dataset. Our work establishes a novel and simple computational approach for accurate prediction of the oxygen vacancy formation energy of metal oxides and highlights the availability of data-driven analysis for metal oxide material research.

Lewis acid-catalyzed domino generation/[2,3]-sigmatropic rearrangement of ammonium ylides to access chiral azabicycles

[2,3]-Sigmatropic rearrangement of ammonium ylides represents a fundamental reaction for stereoselective synthesis of nitrogenous compounds. However, its applicability is limited by the scarcity of efficient, catalytic, and mild methods for generating ammonium ylides. Here, we report silver-catalyzed domino generation/[2,3]-sigmatropic rearrangement of ammonium ylides, furnishing chiral azabicycles with bridgehead quaternary stereogenic centers in high enantiomeric purity (up to 99% ee). A combination of density functional theory calculations and experimental studies revealed that residual water in the reaction system is crucial for the mild reaction conditions by functioning as a proton shuttle to assist carbon-silver bond protonation and C2─H deprotonation to generate the ammonium ylide. This reaction has a broad application scope. Besides the diverse substituents, N-fused azabicycles of various ring sizes are also easily accessed. In addition to silver salts, this strategy has also been successfully implemented by using a stoichiometric amount of nonmetallic I2.

Accurate and rapid prediction of pKa of transition metal complexes: semiempirical quantum chemistry with a data-augmented approach

Data-augmented high-throughput QM approach to compute pK_a of transition metal hydride complexes with hDFT accuracy and low cost.

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.

Improvement of d-d interactions in density functional tight binding for transition metal ions with a ligand field model: assessment of a DFTB3+U model on nickel coordination compounds

To improve the description of interactions among the localized d, f electrons in transition metals, we have introduced a ligand-field motivated contribution into the Density Functional Tight Binding (DFTB) model. Referred to as DFTB3+U, the approach treats the d, f electron repulsions with rotationally invariant orbital-orbital interactions and a Hartree-Fock model; this represents a major conceptual improvement over the original DFTB3 approach, which treats the d, f-shell interactions in a highly averaged fashion without orbital level of description. The DFTB3+U approach is tested using a series of nickel compounds that feature Ni(ii) and Ni(iii) oxidation states. By using parameters developed with the original DFTB3 Hamiltonian and empirical +U parameters (F0/2/4 Slater integrals), we observe that the DFTB3+U model indeed provides substantial improvements over the original DFTB3 model for a number of properties of the nickel compounds, including the population and spin polarization of the d-shell, nature of the frontier orbitals, ligand field splitting and the energy different between low and high spin states at OPBE optimized structures. This proof-of-concept study suggests that with self-consistent parameterization of the electronic and +U parameters, the DFTB3+U model can develop into a promising model that can be used to efficiently study reactive events involving transition metals ion condensed phase systems. The methodology can be integrated with other approximate QM methods as well, such as the extended tight binding (xTB) approach.

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

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

Influence of Electronic Structure Modeling and Junction Structure on First-Principles Chiral Induced Spin Selectivity

We have carried out a comprehensive study of the influence of electronic structure modeling and junction structure description on the first-principles calculation of the spin polarization in molecular junctions caused by the chiral induced spin selectivity (CISS) effect. We explore the limits and the sensitivity to modeling decisions of a Landauer/Green's function/two-component density functional theory approach to CISS. We find that although the CISS effect is entirely attributed in the literature to molecular spin filtering, spin-orbit coupling being partially inherited from the metal electrodes plays an important role in our calculations on ideal carbon helices, even though this effect cannot explain the experimental conductance results. Its magnitude depends considerably on the shape, size, and material of the metal clusters modeling the electrodes. Also, a pronounced dependence on the specific description of exchange interaction and spin-orbit coupling is manifest in our approach. This is important because the interplay between exchange effects and spin-orbit coupling may play an important role in the description of the junction magnetic response. Our calculations are relevant for the whole field of spin-polarized electron transport and electron transfer, because there is still an open discussion in the literature about the detailed underlying mechanism and the magnitude of physical parameters that need to be included to achieve a consistent description of the CISS effect: seemingly good quantitative agreement between simulation and the experiment can be caused by error compensation, because spin polarization as contained in a Landauer/Green's function/two-component density functional theory approach depends strongly on computational and structural parameters.

Nonlocal rung-3.5 correlation from the density matrix expansion: Flat-plane condition, thermochemistry, and kinetics

The rung-3.5 approach to density functional theory constructs nonlocal approximate correlation from the expectation values of nonlocal one-electron operators. This offers an inexpensive solution to hybrid functionals' imbalance between exact nonlocal exchange and local approximate correlation. Our rung-3.5 correlation functionals also include a local complement to the nonlocal ingredient, analogous to the local exchange component of a hybrid functional. Here, we use the density matrix expansion (DME) to build rung-3.5 complements. We demonstrate how these provide a measure of local fractional occupancy and use them to approximate the flat-plane condition. We also use these complements in a three-parameter nonlocal correlation functional compatible with full nonlocal exchange. This functional approaches the accuracy of widely used hybrids for molecular thermochemistry and kinetics. The DME provides a foundation for practical, minimally empirical, nonlocal correlation functionals compatible with full nonlocal local exchange.

Sodium cationization can disrupt the intramolecular hydrogen bond that mediates the sunscreen activity of oxybenzone

A key decay pathway by which organic sunscreen molecules dissipate harmful UV energy involves excited-state hydrogen atom transfer between proximal enol and keto functional groups. Structural modifications of this molecular architecture have the potential to block ultrafast decay processes, and hence promote direct excited-state molecular dissociation, profoundly affecting the efficiency of an organic sunscreen. Herein, we investigate the binding of alkali metal cations to a prototype organic sunscreen molecule, oxybenzone, using IR characterization. Mass-selective IR action spectroscopy was conducted at the free electron laser for infrared experiments, FELIX (600-1800 cm-1), on complexes of Na+, K+ and Rb+ bound to oxybenzone. The IR spectra reveal that K+ and Rb+ adopt binding positions away from the key OH intermolecular hydrogen bond, while the smaller Na+ cation binds directly between the keto and enol oxygens, thus breaking the intramolecular hydrogen bond. UV laser photodissociation spectroscopy was also performed on the series of complexes, with the Na+ complex displaying a distinctive electronic spectrum compared to those of K+ and Rb+, in line with the IR spectroscopy results. TD-DFT calculations reveal that the origin of the changes in the electronic spectra can be linked to rupture of the intramolecular bond in the sodium cationized complex. The implications of our results for the performance of sunscreens in mixtures and environments with high concentrations of metal cations are discussed.