Density functional theory is straying from the path toward the exact functional

Systematic improvement of empirical energy functions in the era of machine learning

The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (CH  2 Cl  2 ), and solvated K  + and Cl  - ions. For the electrostatic interactions, point charges (PCs) and machine learning (ML)-based minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second-order terms is investigated by adding a fragment molecular orbital (FMO)-derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.4 kcal/mol), CH  2 Cl  2 (by 0.8 kcal/mol) and for solvated Cl  - clusters (by 0.4 kcal/mol). An additional polarization term can be neglected for CH  2 Cl  2 but further improves the models for pure water (by ∼ 1.0 kcal/mol) and hydrated Cl  - (by 0.4 kcal/mol), and is key for solvated K  + , reducing the RMSE by 2.3 kcal/mol. A 12-6 Lennard-Jones functional form performs satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many-body contributions is assessed by comparing a strictly 2-body approach with self-consistent reference data. Two-body interactions suffice for CH  2 Cl  2 whereas water and solvated K  + and Cl  - ions require explicit many-body corrections. Finally, a many-body-corrected dimer potential energy surface exceeds the accuracy attained using a conventional empirical force field, potentially reaching that of an FMO calculation. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems.

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Combining rigid and deformable groups to construct a robust birefringent crystal for compact polarization components

There is a pressing demand for the development of novel birefringent crystals tailored for compact optical components, especially for crystals exhibiting large birefringence across a range of temperatures. This has commonly been achieved by introducing various deformable groups with high polarizability anisotropy. In this study, we combined both rigid and deformable groups to synthesise a new birefringent crystal, Al2Te2MoO10, which demonstrates an exceptional birefringence value of 0.29@550 nm at room temperature. Not only is this higher birefringence than that of commercial crystals, but Al2Te2MoO10 exhibits excellent birefringence stability over a wide temperature range, from 123 to 503 K. In addition, the first-principles theory calculations and structural analyses suggest that although the rigid AlO6 groups do not make much contribution to the prominent birefringence, they nonetheless played a role in maintaining the structural anisotropy at elevated temperatures. Based on these findings, this paper proposes a novel structural design strategy to complement conventional approaches for developing optimal birefringent crystals under various environmental conditions.

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

Assessing Exchange-Correlation Functionals for Heterogeneous Catalysis of Nitrogen Species

Increasing interest in the sustainable synthesis of ammonia, nitrates, and urea has led to an increase in studies of catalytic conversion between nitrogen-containing compounds using heterogeneous catalysts. Density functional theory (DFT) is commonly employed to obtain molecular-scale insight into these reactions, but there have been relatively few assessments of the exchange-correlation functionals that are best suited for heterogeneous catalysis of nitrogen compounds. Here, we assess a range of functionals ranging from the generalized gradient approximation (GGA) to the random phase approximation (RPA) for the formation energies of gas-phase nitrogen species, the lattice constants of representative solids from several common classes of catalysts (metals, oxides, and metal-organic frameworks (MOFs)), and the adsorption energies of a range of nitrogen-containing intermediates on these materials. The results reveal that the choice of exchange-correlation functional and van der Waals correction can have a surprisingly large effect and that increasing the level of theory does not always improve the accuracy for nitrogen-containing compounds. This suggests that the selection of functionals should be carefully evaluated on the basis of the specific reaction and material being studied.

Optimal Transport Distances to Characterize Electronic Excitations

Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very useful in a plethora of classification problems and, therefore, seem a natural tool to try to tackle this challenge. We propose and investigate a new diagnostic Θ based on the Sinkhorn divergence from optimal transport. We evaluate a k-NN classification algorithm on Θ, the popular Λ diagnostic, and their combination, and assess their performance in labeling excitations, finding that (i) the combination only slightly improves the classification, (ii) Rydberg excitations are not separated well in any setting, and (iii) Θ breaks down for charge transfer in small molecules. We then define a length-scale-normalized version of Θ and show that the result correlates closely with Λ for results obtained with Gaussian basis functions. Finally, we discuss the orbital dependence of our approach and explore an orbital-independent version. Using an optimized combination of the optimal transport and overlap diagnostics together with a different metric is in our opinion the most promising for future classification studies.

Na6MCl8 rock-salt compounds with M = Mg, Ca, Ba, Zn, Sr as components for solid-state sodium ion batteries

We investigate a new series of rock-salt type structures, Na6MCl8 with M = Mg, Ca, Ba, Zn and Sr using advanced atomistic simulations. Calculated results show a direct relationship between the size of the M2+ cation and lattice parameters as well as the defect formation energy variation. The NaCl Schottky defect type is highly favourable, and the Na6BaCl8 structure possesses the lowest values of defect formation energies. These structures are predicted to be mechanically stable and ductile, implying their compatibility with possible use as electrodes/electrolytes. The Na6MCl8 structures exhibit semiconductor characteristics with an energy gap ranging between 4.1-4.6 eV, which differs from the previous value of Na6MgCl8. A 3D migration pathway is identified in each rock-salt structure. Despite the small variation of the Na diffusivity and conductivity at 250 K within the structures considered, the Na6BaCl8 is characterized by the highest conductivity at 250 K, while the Na6MgCl8 structure has the highest conductivity and diffusivity values. The outstanding properties predicted for a Na ion battery suggest future development of synthetic strategies for their actual preparation.

Polydopamine coating for enhanced electrostatic adsorption of methylene blue by multiwalled carbon nanotubes in alkaline environments

The removal of dye molecules in alkaline environments is an issue that should receive increased attention. In this study, the interaction mechanism between polydopamine-modified multiwalled carbon nanotubes (P-MWCNTs) and multiwalled carbon nanotubes (MWCNTs) with the cationic dye methylene blue (MB) in alkaline environments was explained in depth by adsorption, spectroscopy, and density functional theory (DFT). The mechanism of action and dominant forces between the adsorbent and adsorbate were analyzed graphically by introducing energy decomposition analysis (EDA) and an independent gradient model (IGM) into the DFT calculations. In addition, the force distribution was investigated through an isosurface. Moreover, batch adsorption studies were conducted to evaluate the performance of MWCNTs and P-MWCNTs for MB removal in alkaline environments. The maximum MB adsorption capacities of the MWCNTs and P-MWCNTs in solution were 113.3 mg‧g-1 and 230.4 mg‧g-1, respectively, at pH 9. The IGM and EDA showed that the better adsorption capacity of the P-MWCNTs originated from the enhancement of the electrostatic effect by the proton dissociation of polydopamine. Moreover, the adsorption of MB by MWCNTs and P-MWCNTs in alkaline environments was governed by dispersion and electrostatic effects, respectively. Through this study, it is hoped that progress will be made in the use of DFT to explore the mechanism of adsorbent-adsorbate interactions.

How Much Electron Donation Is There In Transition Metal Complexes? A Computational Study

The "dative" covalent interactions between metals and ligands in coordination compounds, i.e., metal-to-ligand and ligand-to-metal donation, are manifestations of electron delocalization and subject to errors in approximate calculations. This work addresses the extent of dative bonding/donation in a series of closed-shell transition metal complexes. Several Kohn-Sham density functionals, representing different "rungs" of approximations, along with post-Hartree-Fock methods are assessed in comparison to CCSD(T). Two widely used nonhybrid and global hybrid density functionals (B3LYP, PBE0) tend to produce notably too strong donation. Global hybrids with elevated fractions of exact exchange (40 to 50%) and the range-separated exchange functional CAM-B3LYP tend to perform better for the description of the donation. The performance of a double-hybrid functional is found to be quite satisfactory, correcting errors seen in MP2 calculations. A fast approximate coupled-cluster model (DLPNO-CCSD) also gives a reasonable description of the donation, with a tendency to underestimate its extent.

First Examples of s-Metal Complexes with Subporphyrazine and Its Phenylene-Annulated Derivatives: DFT Calculations

Using quantum chemical calculation data obtained by the DFT method with the B3PW91/TZVP and M062X/def2TZVP theory levels, the possibility of the existence of four Be(II) coordination compounds, each of which contains in the inner coordination sphere and the double deprotonated forms of subporphyrazine (H2SP), mono[benzo]subporphyrazine (H2MBSP), di[benzo]subporphyrazine (H2DBSP), and tri[benzo]subporphyrazine (subphthalocyanine) (H2TBSP) with a ratio Be(II) ion/ligand = 1:1, were examined Selected geometric parameters of the molecular structures of these (666)macrotricyclic complexes with closed contours are given; it was noted that BeN3 chelate nodes have a trigonal-pyramidal structure and exhibit a very significant (almost 30°) deviation from coplanarity; however, all three 6-membered metal-chelate and three 5-membered non-chelate rings in each of these compounds are practically planar and deviate from coplanarity by no more than 2.5°. The bond angles between two nitrogen atoms and a Be atom are equal to 60° (in the [BeSP] and [BeTBSP]) or less by no more than 0.5° (in the [BeMBSP] and [BeDBSP]). The presence of annulated benzo groups has little effect on the parameters of the molecular structures of these complexes. Good agreement between the structural data obtained using the above two versions of the DFT method was noticed. NBO analysis data for these complexes are presented; it was noted that, according to both DFT methods used, the ground state of the each of complexes under study is a spin singlet. Standard thermodynamic parameters of formation (standard enthalpy ΔfH0, entropy S0, and Gibbs free energy ΔfG0) for the above-mentioned macrocyclic compounds were calculated.

TDDFT and the x-ray absorption spectrum of liquid water: Finding the "best" functional

We investigate the performance of time-dependent density functional theory (TDDFT) for reproducing high-level reference x-ray absorption spectra of liquid water and water clusters. For this, we apply the integrated absolute difference (IAD) metric, previously used for x-ray emission spectra of liquid water [T. Fransson and L. G. M. Pettersson, J. Chem. Theory Comput. 19, 7333-7342 (2023)], in order to investigate which exchange-correlation (xc) functionals yield TDDFT spectra in best agreement to reference, as well as to investigate the suitability of IAD for x-ray absorption spectroscopy spectrum calculations. Considering highly asymmetric and symmetric six-molecule clusters, it is seen that long-range corrected xc-functionals are required to yield good agreement with the reference coupled cluster (CC) and algebraic-diagrammatic construction spectra, with 100% asymptotic Hartree-Fock exchange resulting in the lowest IADs. The xc-functionals with best agreement to reference have been adopted for larger water clusters, yielding results in line with recently published CC theory, but which still show some discrepancies in the relative intensity of the features compared to experiment.

Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations

The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.

The first-principles study of interfacial bonding strength and segregation behavior of alloyed elements at the η(MgZn2)/Al interface

For precipitation-strengthened Al alloys, the interfacial segregation behavior of alloying elements plays an important role in controlling the effectiveness of precipitation strengthening. In this work, the adhesion work (Wad) and interfacial energy (γ) of the η(0001)/Al(111) interface were studied to gain an insight into the interface properties between the precipitate η and the Al matrix. Additionally, we examined the impact of the segregation behavior of alloyed elements on the bonding strength of the interface. The computed values for Wad and interfacial energies indicated that the T6S3 terminated configuration represents the interfacial structure with the highest stability across all models analyzed. Focusing on the T6S3 interface, the assessed segregated energies (Eseg) disclose that the segregation ability of elements from strong to weak exhibits the order of Ti > Sc > Zr > Y > Ta > Nb > Lu > Hf > Mo > V > W, while Cr and Mn elements are not easy to segregate at the interface. Sc, Ti, V, Cr, Mn, Zr, Nb, Mo, Hf, and Ta preferentially occupy Al atoms, whereas Y and Lu predominantly inhabit Mg atoms. Relative to the clean interface, the electron cloud enrichment at the interface after alloying element X (Zr, Sc, Ti, W, Hf, Mn, Y, Lu and V) doping is weakened, and the ion interaction among interface atoms is enhanced. After doping alloying element X (Nb, Mo, Ta, and Cr), the degree of electron cloud enrichment at the interface is obviously enhanced, and the covalent interaction among interface atoms is enhanced. This suggests that the introduction of alloyed elements through doping can augment the bond strength at the interface between the precipitated phase and matrix, thereby reinforcing the strength and toughness of 7xxx series alloys.

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

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

Exploration of the Existence Forms and Patterns of Dissolved Oxygen Molecules in Water

The structure of liquid water is primarily composed of three-dimensional networks of water clusters formed by hydrogen bonds, and dissolved oxygen is one of the most important indicators for assessing water quality. In this work, distilled water with different concentration of dissolved oxygen were prepared, and a clear negative correlation between the size of water clusters and dissolved oxygen concentration was observed. Besides, a phenomenon of rapid absorption and release of oxygen at the water interfaces was unveiled, suggesting that oxygen molecules predominantly exist at the interfaces of water clusters. Oxygen molecules can move rapidly through the interfaces among water clusters, allowing dissolved oxygen to quickly reach a saturation level at certain partial pressure of oxygen and temperature. Further exploration into the mechanism by molecular dynamics simulations of oxygen and water clusters found that oxygen molecules can only exist stably at the interfaces among water clusters. A semi-empirical formula relating the average number of water molecules in a cluster (n) to 17O NMR half-peak width (W) was summarized: n = 0.1 W + 0.85. These findings provide a foundation for exploring the structure and properties of water.

Self-Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as "Jacob's ladder." This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBE α ${\alpha }$ framework with α ${\alpha }$ being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

Adsorption and Sensing Mechanism of a nTiO2 Particle (n = 1-3)-Doped MoTe2 Monolayer to Faulty and Hazardous Gases in the Underground Cableway

With the rapid growth of the economy and industrial technology, vigoroso and stable power distribution networks have gradually been established worldwide. Among these networks, underground cables play a crucial role in the distribution process, determining the overall electrical stability of entire cities. Based on density functional theory, this paper first proposes a TiO2 particle-doped MoTe2 monolayer to detect and eliminate these faults and hazardous gases within the underground cableway. The band structure, total density of states, projected density of states, and differential charge density are analyzed. The results demonstrate that the presence of TiO2 particles significantly enhances the adsorption capacity of MoTe2, diminishes the electrical conductivity of the doping system, and heightens electron activity in the doping reaction zone. The best adsorption performance is achieved in the case of two-particle doping. Furthermore, the modified MoTe2 exhibits an enhanced capability for capturing SO2 and SOF2, with the adsorption mechanism classified as physical-chemical adsorption. This work not only introduces a novel surface modification method for a MoTe2 monolayer but also provides a substantial data set to support the design and production of efficient sensors used in the underground cableway. These contributions further enhance the safety and stability of power systems and ensure human health.

Unveiling the antioxidant superiority of α-tocopherol: Implications for vitamin E nomenclature and classification

Since the discovery of tocopherols a century ago, α-tocopherol has been distinguished for its unique biological functions. In this study, we aim to elucidate the unique characteristics of α-tocopherol from a chemical perspective. Utilizing density functional theory (DFT) calculations, we evaluated the thermodynamic and kinetic properties of tocopherols, tocotrienols and their oxidation products. Our findings highlight the superior thermodynamic and kinetic properties of α-tocopherol. Although tocopherol substrates generally exhibit similar reactivities, α-tocopherol is distinguished by a larger gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) in intermediates, indicating a potential for greater energy release and favoring reaction progression. Moreover, α-tocopherol shows enhanced efficiency in quenching radical intermediates, especially when combined with vitamin C. All these dates provide valuable support for the naming of vitamin E.

Building an ab initio solvated DNA model using Euclidean neural networks

Accurately modeling large biomolecules such as DNA from first principles is fundamentally challenging due to the steep computational scaling of ab initio quantum chemistry methods. This limitation becomes even more prominent when modeling biomolecules in solution due to the need to include large numbers of solvent molecules. We present a machine-learned electron density model based on a Euclidean neural network framework that includes a built-in understanding of equivariance to model explicitly solvated double-stranded DNA. By training the machine learning model using molecular fragments that sample the key DNA and solvent interactions, we show that the model predicts electron densities of arbitrary systems of solvated DNA accurately, resolves polarization effects that are neglected by classical force fields, and captures the physics of the DNA-solvent interaction at the ab initio level.

Mo-based MXenes: Synthesis, properties, and applications

Ti-MXene allows a range of possibilities to tune their compositional stoichiometry due to their electronic and electrochemical properties. Other than conventionally explored Ti-MXene, there have been ample opportunities for the non-Ti-based MXenes, especially the emerging Mo-based MXenes. Mo-MXenes are established to be remarkable with optoelectronic and electrochemical properties, tuned energy, catalysis, and sensing applications. In this timely review, we systematically discuss the various organized synthesis procedures, associated experimental tunning parameters, physiochemical properties, structural evaluation, stability challenges, key findings, and a wide range of applications of emerging Mo-MXene over Ti-MXenes. We also critically examined the precise control of Mo-MXenes to cater to advanced applications by comprehensively evaluating the summary of recent studies using artificial intelligence and machine learning tools. The critical future perspectives, significant challenges, and possible outlooks for successfully developing and using Mo-MXenes for various practical applications are highlighted.

Molecular insight into endosulfan degradation by Ese protein from Arthrobacter: Evidence-based structural bioinformatics and quantum mechanical calculations

Endosulfan is an organochlorine insecticide widely used for agricultural pest control. Many nations worldwide have restricted or completely banned it due to its extreme toxicity to fish and aquatic invertebrates. Arthrobacter sp. strain KW has the ability to degrade α, β endosulfan and its intermediate metabolite endosulfate; this degradation is associated with Ese protein, a two-component flavin-dependent monooxygenase (TC-FDM). Employing in silico tools, we obtained the 3D model of Ese protein, and our results suggest that it belongs to the Luciferase Like Monooxygenase family (LLM). Docking studies showed that the residues V59, V315, D316, and T335 interact with α-endosulfan. The residues: V59, T60, V315, D316, and T335 are implicated in the interacting site with β-endosulfan, and the residues: H17, V315, D316, T335, N364, and Q363 participate in the interaction with endosulfate. Topological analysis of the electron density by means of the Quantum Theory of Atoms in Molecules (QTAIM) and the Non-Covalent Interaction (NCI) index reveals that the Ese-ligands complexes are formed mainly by dispersive forces, where Cl atoms have a predominant role. As Ese is a monooxygenase member, we predict the homodimer formation. However, enzymatic studies must be developed to investigate the Ese protein's enzymatic and catalytic activity.

Natural determinant reference functional theory

The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an N-electron state of interest. Unlike the Kohn-Sham (KS) determinant, which yields the exact ground-state density, the NDR only yields the best idempotent approximation to the interacting one-particle reduced density matrix, but it is well-defined in common atom-centered basis sets and is representation-invariant. We show that the under-determination problem of prior attempts to define a ground-state energy functional of the NDR is overcome in a grand-canonical ensemble framework at the zero-temperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an "exactification" of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KS-inversion or optimized effective potentials.

Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, which has been known for ∼30 years. The conventional explanation is that the Hartree-Fock theory yields the more accurate density. This work presents a benchmark Kohn-Sham inversion of accurate coupled-cluster densities for the reaction H2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree-Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532-543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.

Design of Two New Sulfur Derivatives of Perezone: In Silico Study Simulation Targeting PARP-1 and In Vitro Study Validation Using Cancer Cell Lines

Poly-ADP-Ribose Polymerase (PARP-1) is an overexpressed enzyme in several carcinomas; consequently, the design of PARP-1 inhibitors has acquired special attention. Hence, in the present study, three compounds (8-10) were produced through a Michael addition protocol, using phenylmethanethiol, 5-fluoro-2-mercaptobenzyl alcohol, and 4-mercaptophenylacetic acid, respectively, as nucleophiles and perezone as the substrate, expecting them to be convenient candidates that inhibit PARP-1. It is convenient to note that in the first stage of the whole study, the molecular dynamics (MD) simulations and the quantum chemistry studies of four secondary metabolites, i.e., perezone (1), perezone angelate (2), hydroxyperezone (3), and hydroxyperezone monoangelate (4), were performed, to investigate their interactions in the active site of PARP-1. Complementarily, a docking study of a set of eleven sulfur derivatives of perezone (5-15) was projected to explore novel compounds, with remarkable affinity to PARP-1. The molecules 8-10 provided the most adequate results; therefore, they were evaluated in vitro to determine their activity towards PARP-1, with 9 having the best IC50 (0.317 µM) value. Additionally, theoretical calculations were carried out using the density functional theory (DFT) with the hybrid method B3LYP with a set of base functions 6-311++G(d,p), and the reactivity properties were compared between the natural derivatives of perezone and the three synthesized compounds, and the obtained results exhibited that 9 has the best properties to bind with PARP-1. Finally, it is important to mention that 9 displays significant inhibitory activity against MDA-MB-231 and MCF-7 cells, i.e., 145.01 and 83.17 µM, respectively.

Structure of Tris[2-(4-pyridyl)ethyl]phosphine, Tris[2-(2-pyridyl)ethyl]phosphine, and Their Chalcogenides in Solution: Dipole Moments, IR Spectroscopy, and DFT Study

Tris(hetaryl)substituted phosphines and their chalcogenides are promising polydentate ligands for the design of metal complexes. An experimental and theoretical conformational analysis of tris[2-(4-pyridyl)ethyl]phosphine, tris[2-(2-pyridyl)ethyl]phosphine, and their chalcogenides was carried out by the methods of dipole moments, IR spectroscopy and DFT B3PW91/6-311++G(df,p) calculations. In solution, these compounds exist as an equilibrium of mainly non-eclipsed (synclinal or antiperiplanar) forms with a predominance of a symmetrical conformer having a gauche-orientation of the Csp3-Csp3 bonds of pyridylethyl substituents relative to the P=X bond (X = lone pair, O, S, Se) and a gauche-orientation of the pyridyl rings relative to the zigzag ethylene bridges. Regardless of the presence and nature of the chalcogen atom (oxygen, sulfur, or selenium) in the studied molecules with many axes of internal rotation, steric factors-the different position of the nitrogen atoms in the pyridyl rings and the configuration of ethylene bridges-determine the realization and spatial structure of preferred conformers.

Toward a correct treatment of core properties with local hybrid functionals

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

Universal Generalization of Density Functional Theory for Static Correlation

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

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

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

Total and orbital density-based analyses of molecules revealing long-range interaction regions

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO - 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

Quantifying the Accuracy of Density Functionals on Transition Metal Bulk and Surface Properties

Density functional theory would be exact when the exact exchange-correlation (xc) functional would be known, but since it is regretfully not known, dozens of xc functionals have been developed in the past decades, with some of them better suited for describing certain systems and/or properties. For transition metals (TMs), recent systematic studies assessing bulk properties─shortest interatomic bond distance, δ, cohesive energy, Ecoh, and bulk modulus, B0─and surface features─surface energy, γ, work function, ϕ, and interlayer distances, δij─of 27 TM bulks and 81 TM surfaces, highlighted that generalized gradient approximation (GGA) based xc functionals are, overall, better suited than other types of xc functionals for the TMs bulk and surfaces description, such as Perdew-Burke-Ernzerhof (PBE) or Vega-Viñes (VV). Still, some basic local density approximation xc functionals were not assessed, such as the Hedin-Lundqvist (HL) and Perdew-Zunger (PZ), or GGAs such as the revised Perdew-Burke-Ernzerhof (revPBE) or the Armiento-Mattsson (AM05). Here, we expand the analysis by not only including them but also the recent meta-GGA strongly constrained appropriately normed (SCAN) xc functional, characterized by fulfilling all 17 mathematical conditions an xc must comply, plus the Bayesian error estimation functional (BEEF) xc, a functional parametrized over a large and diverse set of experimental results using machine learning. The present results reveal that none of the xc studied excel neither PBE nor VV, yet AM05 and SCAN performance is quite acceptable, while BEEF xc probably needs more shells of parametrization to reach competitive accuracy levels.

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

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

Variational principle to regularize machine-learned density functionals: The non-interacting kinetic-energy functional

Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange-correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work, we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange-correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.

Consistent density functional theory-based description of ion hydration through density-corrected many-body representations

Delocalization error constrains the accuracy of density functional theory in describing molecular interactions in ion-water systems. Using Na+ and Cl- in water as model systems, we calculate the effects of delocalization error in the SCAN functional for describing ion-water and water-water interactions in hydrated ions, and demonstrate that density-corrected SCAN (DC-SCAN) predicts n-body and interaction energies with an accuracy approaching coupled cluster theory. The performance of DC-SCAN is size-consistent, maintaining an accurate description of molecular interactions well beyond the first solvation shell. Molecular dynamics simulations at ambient conditions with many-body MB-SCAN(DC) potentials, derived from the many-body expansion, predict the solvation structure of Na+ and Cl- in quantitative agreement with reference data, while simultaneously reproducing the structure of liquid water. Beyond rationalizing the accuracy of density-corrected models of ion hydration, our findings suggest that our unified density-corrected MB formalism holds great promise for efficient DFT-based simulations of condensed-phase systems with chemical accuracy.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Learning from the 4-(dimethylamino)benzonitrile twist: Two-parameter range-separated local hybrid functional with high accuracy for triplet and charge-transfer excitations

The recent ωLH22t range-separated local hybrid (RSLH) is shown to provide outstanding accuracy for the notorious benchmark problem of the two lowest excited-state potential energy curves for the amino group twist in 4-(dimethylamino)benzonitrile (DMABN). However, the design of ωLH22t as a general-purpose functional resulted in less convincing performance for triplet excitations, which is an important advantage of previous LHs. Furthermore, ωLH22t uses 8 empirical parameters to achieve broad accuracy. In this work, the RSLH ωLH23ct-sir is constructed with minimal empiricism by optimizing its local mixing function prefactor and range-separation parameter for only 8 excitation energies. ωLH23ct-sir maintains the excellent performance of ωLH22t for the DMABN twist and charge-transfer benchmarks but significantly improves the errors for triplet excitation energies (0.17 vs 0.24 eV). Additional test calculations for the AE6BH6 thermochemistry test set and large dipole moment and static polarizability test sets confirm that the focus on excitation energies in the optimization of ωLH23ct-sir has not caused any dramatic errors for ground-state properties. Although ωLH23ct-sir cannot replace ωLH22t as a general-purpose functional, it is preferable for problems requiring a universally good description of localized and charge-transfer excitations of both singlet and triplet multiplicity. Current limitations on the application of ωLH23ct-sir and other RSLHs to the study of singlet-triplet gaps of emitters for thermally activated delayed fluorescence are discussed. This work also includes the first systematic analysis of the influence of the local mixing function prefactor and the range-separation parameter in an RSLH on different types of excitations.

Machine Learning Density Functionals from the Random-Phase Approximation

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.

Synthesis, Cytotoxic Activity and In Silico Study of Novel Dihydropyridine Carboxylic Acids Derivatives

To aid the possible prevention of multidrug resistance in tumors and cause lower toxicity, a set of sixteen novel dihydropyridine carboxylic acids derivatives 3a-p were produced; thus, the activation of various ynones with triflic anhydride was performed, involving a nucleophilic addition of several bis(trimethylsilyl) ketene acetals, achieving good yields requiring easy workup. The target molecules were unequivocally characterized by common spectroscopic methods. In addition, two of the tested compounds (3a, and 3b) were selected to perform in silico studies due to the highest cytotoxic activity towards the HCT-15 cell line (7.94 ± 1.6 μM and 9.24 ± 0.9 μM, respectively). Employing theoretical calculations with density functional theory (DFT) using the B3LYP/6-311++G(d,p) showed that the molecular parameters correlate adequately with the experimental results. In contrast, predictions employing Osiris Property Explorer showed that compounds 3a and 3b present physicochemical characteristics that would likely make it an orally active drug. Moreover, the performance of Docking studies with proteins related to the apoptosis pathway allowed a proposal of which compounds could interact with PARP-1 protein. Pondering the obtained results (synthesis, in silico, and cytotoxic activity) of the target compounds, they can be judged as suitable antineoplastic agent candidates.

Decoding Chemical Bonds: Assessment of the Basis Set Effect on Overlap Electron Density Descriptors and Topological Properties in Comparison to QTAIM

Quantum chemical bonding descriptors based on the total and overlap density can provide valuable information about chemical interactions in different systems. However, these descriptors can be sensitive to the basis set used. To address this, different numerical treatments of electron density have been proposed to reduce the basis set dependency. In this work, we introduce overlap properties (OPs) obtained through numerical treatment of the electron density and present the topology of overlap density (TOP) for the first time. We compare the basis set dependency of numerical OP and TOP descriptors with their quantum theory of atoms in molecules (QTAIM) counterparts, considering the total electron density. Three single (C-C, C-O, and C-F) bonds in ethane, methanol, and fluoromethane and two double (C═C and C═O) bonds in ethene and formaldehyde were analyzed. Diatomic molecules Li-X with X = F, Cl, and Br were also analyzed. Eight parameters, including QTAIM descriptors and OP/TOP descriptors, are used to assess the basis dependency at the ωB97X-D level of theory using 28 basis sets from three classes: Pople, Ahlrichs, and Dunning. The study revealed that the topological overlap electron density properties exhibit comparatively lesser dependence on the basis set compared to their total electron density counterparts. Remarkably, these properties retain their chemical significance even with reduced basis set dependency. Similarly, numerical OP descriptors show less basis set dependency than their QTAIM counterparts. The excess of polarization functions increases charge concentration in the interatomic region and influences both QTAIM and OP descriptors. The basis sets Def2TZVP, 6-31++G(d,p), 6-311++G(d,p), cc-pVDZ, cc-pVTZ, and cc-pVQZ demonstrate reduced variability for the tested bond classes in this study, with particular emphasis on the triple-ζ quality Ahlrichs' basis set. We recommend against using basis sets with numerous polarization functions, such as augmented Dunning's and Ahlrichs' quadruple-ζ.

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling

We present a low-scaling algorithm for the random phase approximation (RPA) with k-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of k-points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.

Sm/Co Magnetic Materials: A Recycling Strategy Using Modifiable Hydrophobic Deep Eutectic Solvents Based on Trioctylphosphine Oxide

Hydrophobic deep eutectic solvents (HDES) are widely used as extractants. Usually, when preparing HDES, only the extraction ability of one component is taken into account, with the second serving as an "inert" component, whose effect on the extraction process is not taken into account. The present study demonstrates the possibility of controlling the selectivity of a hydrophobic deep eutectic solvent based on trioctylphosphine oxide (TOPO) by varying the substance that acts as a hydrogen bond donor, but which does not have an extractive ability. In the course of the work, the influence of the "inert" component on the physicochemical and extraction properties of HDES was confirmed by experimental, spectroscopic, and also calculation methods. A number of phenols with different structural features were chosen as the HDES' hydrogen bond donors to modify: phenol (Ph), para-tert-butylphenol (PTBP) and thymol (Th). Using the example of separation of the Sm/Co pair, the influence of the structure of a hydrogen bond donor on the extraction ability of a hydrophobic deep eutectic solvent was established, where the degree of extraction of Sm (III) increased in the series Th:TOPO < PTBP:TOPO < Ph:TOPO. HDES based on TOPO and phenols can potentially be used to separate Sm and Co from the process leach solutions generated during the hydrometallurgical processing of waste SmCo magnets.

Better performance of Hartree-Fock over DFT: a quantum mechanical investigation on pyridinium benzimidazolate types of zwitterions in the light of localization/delocalization issues

CONTEXT

With the advent of fast computing facilities, combined with rapid emerges of many new and intricate quantum mechanical functionals, computations with pure Hartree-Fock (HF) theory are now-a-days regarded as trivial or obsolete, or even considered as not reliable by many researchers. Consequently, current trends in computational chemistry show extensive use of post-HF theories for smaller molecular systems and various DFT methods for organic and inorganic chemistry related problems (larger molecules/systems). In this contribution, I have tried to show that sometimes, HF might be more suitable over DFT methodologies in addressing structure-property correlations. Molecules studied here were previously synthesized by Boyd in 1966 and important experimental data were produced by Alcalde and co-workers in 1987. Comparison of computed and experimental results clearly shows that HF method was more effective in reproducing the experimental data compared to especially the DFT methodologies. Reliability of HF method was further assured from the very similar results shown by the CCSD, CASSCF, CISD and QCISD methods. Current study also indicates that the localization issue associated with HF proved to be advantageous over delocalization issue of DFT based methodologies, in correctly describing the structure-property correlation for zwitterion systems.

METHODS

All computations were performed with Gaussian 09. A wide-range of quantum mechanical methodologies, HF, B3LYP, CAM-B3LYP, BMK, B3PW91, TPSSh, LC-ωPBE, M06-2X, M06-HF, ωB97xD, MP2, CASSCF, CCSD, QCISD, CISD and semi-empirical methods like, Huckel, CNDO, AM1, PM3MM and PM6, were used for investigations.

The effect of composition changes on the structure and electronic properties of jamesonite: a DFT study

Models of jamesonite with different compositions were built by different amounts of Sb or Pb substitution at Fe sites, and their structures and electronic properties were studied using the DFT method. The structure and properties of jamesonite significantly changed after Sb or Pb substitution. The lengths of the Sb-S and Pb-S bonds are larger than those of the corresponding Fe-S bonds of pure jamesonite, and the polarization of iron atoms adjacent to substitute atoms is weakened. After one Sb atom substitution, the S atoms bonded to Sb (substitution atom) gain more charges than those before Sb substitution. The Sb atom has more positive charges than the corresponding Fe atom before Sb substitution. For one Pb substitution system, the electrons transfer from the substituted Pb to adjacent S atoms, and the larger negative charge of the S atoms causes a slightly stronger Pb-S bond. With increasing Sb or Pb content, the electronic structural changes of the adjacent atoms are similar to those of one Sb or Pb substitution. However, the increase of 4-coordination Sb or 4-coordination Pb with the decrease of Fe atom changes the electronic structure of jamesonite, which will change its flotation performance.

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

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

The central role of density functional theory in the AI age

Density functional theory (DFT) plays a pivotal role in chemical and materials science because of its relatively high predictive power, applicability, versatility, and computational efficiency. We review recent progress in machine learning (ML) model developments, which have relied heavily on DFT for synthetic data generation and for the design of model architectures. The general relevance of these developments is placed in a broader context for chemical and materials sciences. DFT-based ML models have reached high efficiency, accuracy, scalability, and transferability and pave the way to the routine use of successful experimental planning software within self-driving laboratories.

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations

Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837-847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C-F and third-period elements Si-Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT's limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT's limitations for Rydberg and charge-transfer excitations.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V^xx operator), and (iii) adaptively compressed exchange (ACE, a low-rank V^xx approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank V^xx approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H₂O)₆₄ configurations (with densities spanning 0.4-1.7 g/cm³), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H₂O)₆₄ configurations. Using an out-of-sample set of (H₂O)₅₁₂ configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Realistic phase diagram of water from "first principles" data-driven quantum simulations

Since the experimental characterization of the low-pressure region of water's phase diagram in the early 1900s, scientists have been on a quest to understand the thermodynamic stability of ice polymorphs on the molecular level. In this study, we demonstrate that combining the MB-pol data-driven many-body potential for water, which was rigorously derived from "first principles" and exhibits chemical accuracy, with advanced enhanced-sampling algorithms, which correctly describe the quantum nature of molecular motion and thermodynamic equilibria, enables computer simulations of water's phase diagram with an unprecedented level of realism. Besides providing fundamental insights into how enthalpic, entropic, and nuclear quantum effects shape the free-energy landscape of water, we demonstrate that recent progress in "first principles" data-driven simulations, which rigorously encode many-body molecular interactions, has opened the door to realistic computational studies of complex molecular systems, bridging the gap between experiments and simulations.

Molecular and Electronic Structures of Macrocyclic Compounds Formed at Template Synthesis in the M(II)-Thiocarbohydrazide-Diacetyl Triple Systems: A Quantum-Chemical Analysis by DFT Methods

Using density functional theory (DFT) B3PW91/TZVP, M06/TZVP, and OPBE/TZVP chemistry models and the Gaussian09 program, a quantum-chemical calculation of geometric and thermodynamic parameters of Ni(II), Cu(II), and Zn(II) macrotetracyclic chelates, with (NNNN)-coordination of ligand donor centers arising during template synthesis between the indicated ions of 3d elements, thiocarbohydrazide H₂N-HN-C(=S)-NH-NH₂ and diacetyl Me-C(=O)-C(=O)-Me, in gelatin-immobilized matrix implants was performed. The key bond lengths and bond angles in these coordination compounds are provided, and it is noted that in all these complexes the MN₄ chelate sites, the grouping of N₄ atoms bonded to the M atom, and the five-membered and six-membered metal chelate rings are practically coplanar. NBO analysis of these compounds was carried out, on the basis of which it was shown that all these complexes, in full accordance with theoretical expectations, are low-spin complexes. The standard thermodynamic characteristics of the template reactions for the formation of the above complexes are also presented. Good agreement between the data obtained using the above DFT levels is noted.