Density Functional Theory Functionals Research Articles

Scalar and vectorized implementations of the density functional theory via Geant4 and GeantV project

In this paper, we present the implementation of the Density Functional Theory (DFT) method using the Geant4-DNA framework in the Single Instruction Single Data (SISD) mode. Furthermore, this implementation is improved in terms of execution time within the GeantV project with vectorization techniques such as Single Instruction Multiple Data (SIMD). Within this framework, a set of SIMD strategies in molecular calculation algorithms such as one-electron operators, two-electron operator, quadrature grids, and functionals, was implemented using the VecCore library. The applications developed in this work implement two DFT functionals, the Local Density Approximation (LDA) and the General Gradient Approximation (GGA), to approximate the molecular ground-state energies of small molecules and amino acids. To assess the performance of the implementations, a standard test simulation was performed in multiple CPU platforms. The SIMD vectorization strategy significantly accelerates DFT calculations, leading to time ratios ranging from 1.6 to 5.4 in either individual steps or entire implementations when compared with the scalar process within Geant4.

The Best DFT Functional Is the Ensemble of Functionals.

The development of better density functional theory (DFT) methods is one of the most active research areas, given the importance of DFT for ubiquitous molecular and materials simulations. However, this research primarily focuses on improving a specific exchange-correlation Kohn-Sham density functional. Here, a robust procedure is proposed for constructing transferable ensembles of density functionals that perform superior to any constituent individual density functional. It is shown that such ensembles built only with the density functionals predating the GMTKN55 benchmark of 2017 can reach a record-low weighted error of 1.62kcal mol-1 on this benchmark compared to 3.08kcal mol-1 of the best constituent density functional. The DENS24 density functional ensembles are also introduced as practical DFT methods with consistently accurate performance for various simulations at affordable cost. DENS24 ensembles are open-source and can be used for simulations online. Additionally, it is shown that the ensembles can be integrated into the SCF procedure by creating mixed DENS24 functionals, which have the same accuracy but are faster than ensembles of independent functionals.

Design, synthesis, and evaluation of a pyrazole-based corrosion inhibitor: a computational and experimental study

By employing a synergistic blend of experimental and theoretical methodologies, we investigated the corrosion inhibition efficacy of a synthesized pyrazole derivative (BM-01) in a solution of hydrochloric acid (1 M). We utilized molecular dynamics (MD) simulations, scanning electron microscopy (SEM), density functional theory (DFT), complexation, plus electrochemical impedance spectroscopy (EIS). We conducted weight loss (WL) measurements from 298 to 328 K. Inhibition efficacy reached a maximum at a BM-01 concentration of 10−3 M, achieving 90.0% (EIS), 90.40% (WL), and 90.38% (potentiodynamic polarization (PDP)). SEM unveiled the shielding of the carbon-steel surface from acid-induced damage by BM-01. The Langmuir adsorption isotherm exhibited a robust fit with a low sum of squares, standard deviation, and a high correlation coefficient. PDP findings indicated that BM-01 acted as a mixed-type inhibitor, predominantly favoring the cathodic process, suggesting potential corrosion-mitigation properties. Theoretical analyses involving DFT, MD simulations, and radial distribution function were conducted to postulate a mechanism and identify an inhibitory layer. Theoretical outcomes aligned closely with experimental data, thereby reinforcing the validity of our findings.

Evaluating the Chemical Reactivity of DFT-Simulated Liquid Water with Hydrated Electrons via the Dual Descriptor.

Modeling the various properties of liquid water, particularly its reactivity, has been a longstanding challenge for simulation methods. Recently, ab initio simulations based on density functional theory (DFT) have come to the fore as tenable methods for calculating the properties and reactivity of water, with varying degrees of success for different exchange-correlation functionals. In particular, hybrid-GGA and meta-GGA functionals have been shown to reproduce many of the structural, dynamical, and energetic properties of water to a high degree of accuracy relative to their computational cost. Here, we show that the dual descriptor (DD) measure of nucleophilicity and electrophilicity, which is sometimes used to elucidate organic chemistry reaction mechanisms, can also be used to characterize the reactivity of DFT-simulated liquid water. The DD is especially apt for understanding the reactivity of excess electrons with water as its calculation explicitly involves adding and removing an excess electron from a reference system. We use the DD to explore the reactivity of water simulated using three different DFT functionals: the LDA functional (LDA), a hybrid-GGA functional (PBE0), and a hybrid meta-GGA functional (SCAN0). Using the DD, we show that the SCAN0 functional with the standard 25% Hartree-Fock exchange produces simulated liquid water with many regions that are far more reactive than either PBE0 or LDA. To understand the implications of these highly reactive regions, we then add a strong nucleophile in the form of an excess electron and find that although PBE0 and LDA predict stable hydrated electrons, the excess electron reacts nearly instantaneously with SCAN0 water via proton abstraction to form a hydrogen atom and hydroxide ion. We show that the DD provides the ability to not only predict whether or not liquid water will react with a hydrated electron but also which particular waters will be involved solely from analyzing pure water configurations generated with each functional. We rationalize this result in terms of the known trap-seeking behavior of injected hydrated electrons, which are able to find the most electronegative region in bulk water. These results highlight the utility of the dual descriptor as a fast and interpretable method for investigating condensed-phase reactivity with excess electrons.

First-Principles Linear Combination of Atomic Orbitals Calculations of K2SiF6 Crystal: Structural, Electronic, Elastic, Vibrational and Dielectric Properties.

The results of first-principles calculations of the structural, electronic, elastic, vibrational, dielectric and optical properties, as well as the Raman and infrared (IR) spectra, of potassium hexafluorosilicate (K2SiF6; KSF) crystal are discussed. KSF doped with manganese atoms (KSF:Mn4+) is known for its ability to function as a phosphor in white LED applications due to the efficient red emission from Mn⁴⁺ activator ions. The simulations were performed using the CRYSTAL23 computer code within the linear combination of atomic orbitals (LCAO) approximation of the density functional theory (DFT). For the study of KSF, we have applied and compared several DFT functionals (with emphasis on hybrid functionals) in combination with Gaussian-type basis sets. In order to determine the optimal combination for computation, two types of basis sets and four different functionals (three advanced hybrid-B3LYP, B1WC, and PBE0-and one LDA functional) were used, and the obtained results were compared with available experimental data. For the selected basis set and functional, the above-mentioned properties of KSF were calculated. In particular, the B1WC functional provides us with a band gap of 9.73 eV. The dependencies of structural, electronic and elastic parameters, as well as the Debye temperature, on external pressure (0-20 GPa) were also evaluated and compared with previous calculations. A comprehensive analysis of vibrational properties was performed for the first time, and the influence of isotopic substitution on the vibrational frequencies was analyzed. IR and Raman spectra were simulated, and the calculated Raman spectrum is in excellent agreement with the experimental one.

Physics-Inspired Evolutionary Machine Learning Method: From the Schrödinger Equation to an Orbital-Free-DFT Kinetic Energy Functional.

We introduce a machine learning (ML)-supervised model function (which is in fact a functional rather than a regular function) that is inspired by the variational principle of physics. This ML hypothesis evolutionary method, termed ML-Ω, allows us to go from data to differential equation(s) underlying the physical (chemical, engineering, etc.) phenomena from which the data are derived from. The fundamental equations of physics can be derived from this ML-Ω evolutionary method when the proper training data is used. By training the ML-Ω model function with only three hydrogen-like atom energies, the method can find Schrödinger's exact functional and, from it, Schrödinger's fundamental equation. Then, in the field of density functional theory (DFT), when the model function is trained with the energies from the known Thomas-Fermi (TF) formula , it correctly finds the exact TF functional. Finally, the method is applied to find a local orbital-free (OF) functional expression of the independent electron kinetic energy functional Ts based on the γTFλvW model. By considering the theoretical energies of only five atoms (He, Be, Ne, Mg, and Ar) as the training set, the evolutionary ML-Ω method finds an ML-Ω-OF-DFT local Ts functional (γTFλvW(0.964,1/4)) that outperforms all the OF-DFT functionals of a representative group. Moreover, our ML-Ω-OF functional overcomes the difficulty of LDA's and some local generalized gradient approximation (GGA)-DFT's functionals to describe the stretched bond region at the correct spin configuration of diatomic molecules. Nonsmooth and nonclosed form functionals can be considered in the ML-Ω model function and still be effectively trained. Although our evolutionary ML-Ω model function can work without an explicit prior-form functional, by using the techniques of symbolic regression, in this work, we exploit prior-form functional expressions to make the training process simpler and faster. The ML-Ω method can be considered at the intersection of ML and the natural sciences.

Multireference calculations on bond dissociation and biradical polycyclic aromatic hydrocarbons as guidance for fractional occupation number weighted density analysis in DFT calculations

This study explores open-shell biradical and polyradical molecular compounds based on extended multireference (MR) methods (MR-configuration interaction with singles and doubles (CISD) and MR-averaged quadratic coupled cluster (AQCC) approach) using the numbers of unpaired densities NU. These results were used to guide the analysis of the fractional occupation number weighted density (FOD) calculated within the finite temperature (FT) density functional theory (DFT) approach. As critical test examples, the dissociation of carbon–carbon (CC) single, double and triple bonds and a benchmark set of polycyclic aromatic hydrocarbons (PAHs) have been chosen. By examining single, double, and triple bond dissociations, we demonstrate the utility and accuracy but also limitations of the FOD analysis for describing these dissociation processes. In significant extension of previous work (Phys Chem Chem Phys 25: 27380–27393), the assessment of FOD applications for different classes of DFT functionals was performed examining the range-separated functionals ωB97XD, ωB97M-V, CAM-B3LYP, LC-ωPBE, and MN12-SX, the hybrid (M06-2X) functional and the double hybrid (B2P-LYP) functional. In all cases, strong correlations between NFOD and NU values are found. The major task was to develop a new linear regression formula for range-separated functionals allowing a convenient determination of the optimal electronic temperature Tel for the FT-DFT calculation. We also established an optimal temperature for the semiempirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semiempirical methods.

Toward Reliable Conformational Energies of Amino Acids and Dipeptides─The DipCONFS Benchmark and DipCONL Datasets.

Simulating peptides and proteins is becoming increasingly important, leading to a growing need for efficient computational methods. These are typically semiempirical quantum mechanical (SQM) methods, force fields (FFs), or machine-learned interatomic potentials (MLIPs), all of which require a large amount of accurate data for robust training and evaluation. To assess potential reference methods and complement the available data, we introduce two sets, DipCONFL and DipCONFS, which cover large parts of the conformational space of 17 amino acids and their 289 possible dipeptides in aqueous solution. The conformers were selected from the exhaustive PeptideCS dataset by Andris et al. [ J. Phys. Chem. B 2022, 126, 5949-5958]. The structures, originally generated with GFN2-xTB, were reoptimized using the accurate r2SCAN-3c density functional theory (DFT) composite method including the implicit CPCM water solvation model. The DipCONFS benchmark set contains 918 conformers and is one of the largest sets with highly accurate coupled cluster conformational energies so far. It is employed to evaluate various DFT and wave function theory (WFT) methods, especially regarding whether they are accurate enough to be used as reliable reference methods for larger datasets intended for training and testing more approximated SQM, FF, and MLIP methods. The results reveal that the originally provided BP86-D3(BJ)/DGauss-DZVP conformational energies are not sufficiently accurate. Among the DFT methods tested as an alternative reference level, the revDSD-PBEP86-D4 double hybrid performs best with a mean absolute error (MAD) of 0.2 kcal mol-1 compared with the PNO-LCCSD(T)-F12b reference. The very efficient r2SCAN-3c composite method also shows excellent results, with an MAD of 0.3 kcal mol-1, similar to the best-tested hybrid ωB97M-D4. With these findings, we compiled the large DipCONFL set, which includes over 29,000 realistic conformers in solution with reasonably accurate r2SCAN-3c reference conformational energies, gradients, and further properties potentially relevant for training MLIP methods. This set, also in comparison to DipCONFS, is used to assess the performance of various SQM, FF, and MLIP methods robustly and can complement training sets for those.

Quantum mechanical investigation of the choline chloride/carboxylic acid deep eutectic solvents

Deep eutectic solvents (DES) have received substantial applications and development in the field of green chemistry during the last decade. Using computational density functional theory (DFT), DESs composed of Choline Chloride (ChCl), as the hydrogen bond acceptor (HBA), and six carboxylic acids (CA) including Glycolic acid (Gly), Glutaric acid (Glu), Oxalic acid (Oxa), Lactic acid (La), Itaconic acid (Ita), and Levulinic acid (Lev), as the hydrogen bond donner (HBD), were investigated. Geometry optimization and vibrational frequency assignment were performed by applying three DFT functionals, i.e., B3LYP-D3(BJ), M06-2X, and ωB97XD in combination with Pople’s 6-311+g(d,p) basis set. Then, using of the QTAIM, NBO, and the NCI analyses, different sorts of interactions have been evaluated to indicate the most stable structure between ChCl and various CAs, and the hydrogen bonding in the studied DESs. The results confirm that the Cl ion in choline chloride created a strong hydrogen-bond with HBDs, and the mixed ionic-covalent interaction is the main interaction in construction of the DESs of ChCl with the studied carboxylic acids.

Design and Optimization of Molecularly Imprinted Polymer Targeting Epinephrine Molecule: A Theoretical Approach.

Molecularly imprinted polymers (MIPs) are a growing highlight in polymer chemistry. They are chemically and thermally stable, may be used in a variety of environments, and fulfill a wide range of applications. Computer-aided studies of MIPs often involve the use of computational techniques to design, analyze, and optimize the production of MIPs. Limited information is available on the computational study of interactions between the epinephrine (EPI) MIP and its target molecule. A rational design for EPI-MIP preparation was performed in this study. First, density functional theory (DFT) and molecular dynamic (MD) simulation were used for the screening of functional monomers suitable for the design of MIPs of EPI in the presence of a crosslinker and a solvent environment. Among the tested functional monomers, acrylic acid (AA) was the most appropriate monomer for EPI-MIP formulation. The trends observed for five out of six DFT functionals assessed confirmed AA as the suitable monomer. The theoretical optimal molar ratio was 1:4 EPI:AA in the presence of ethylene glycol dimethacrylate (EGDMA) and acetonitrile. The effect of temperature was analyzed at this ratio of EPI:AA on mean square displacement, X-ray diffraction, density distribution, specific volume, radius of gyration, and equilibrium energies. The stability observed for all these parameters is much better, ranging from 338 to 353 K. This temperature may determine the processing and operating temperature range of EPI-MIP development using AA as a functional monomer. For cost-effectiveness and to reduce time used to prepare MIPs in the laboratory, these results could serve as a useful template for designing and developing EPI-MIPs.

Toward Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory.

Accurate description of the static correlation poses a persistent challenge in electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development involves a hybrid machine learning strategy that integrates symbolic regression with nonlinear parameter optimization, aiming to achieve a balance between generalization capability, numerical accuracy, and interpretability. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of main-group chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict the whole energy profiles, activation barriers, and reaction pathways within a user-friendly "black-box" framework represents an important advance in the field of electronic structure theory.

Secondary structure determines electron transport in peptides

Proteins play a key role in biological electron transport, but the structure-function relationships governing the electronic properties of peptides are not fully understood. Despite recent progress, understanding the link between peptide conformational flexibility, hierarchical structures, and electron transport pathways has been challenging. Here, we use single-molecule experiments, molecular dynamics (MD) simulations, nonequilibrium Green's function-density functional theory (NEGF-DFT), and unsupervised machine learning to understand the role of secondary structure on electron transport in peptides. Our results reveal a two-state molecular conductance behavior for peptides across several different amino acid sequences. MD simulations and Gaussian mixture modeling are used to show that this two-state molecular conductance behavior arises due to the conformational flexibility of peptide backbones, with a high-conductance state arising due to a more defined secondary structure (beta turn or 310 helices) and a low-conductance state occurring for extended peptide structures. These results highlight the importance of helical conformations on electron transport in peptides. Conformer selection for the peptide structures is rationalized using principal component analysis of intramolecular hydrogen bonding distances along peptide backbones. Molecular conformations from MD simulations are used to model charge transport in NEGF-DFT calculations, and the results are in reasonable qualitative agreement with experiments. Projected density of states calculations and molecular orbital visualizations are further used to understand the role of amino acid side chains on transport. Overall, our results show that secondary structure plays a key role in electron transport in peptides, which provides broad avenues for understanding the electronic properties of proteins.

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

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

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

Molecular Hydrogen Acts as a Hydrogen Bond Proton Acceptor: From Protonated Betaine Tagging to the Weakest Hydrogen Bond.

In an attempt to gain further insights into the intermolecular interactions implied by Rizzo's group's cautionary tale related to molecular tagging in infrared multiple photon dissociation (IRMPD) spectroscopy with molecular messengers [Masson, A. . J. Chem. Phys. 2015, 143, 104313], in the present study, we provide an in-depth analysis of the noncovalent interaction between the molecular hydrogen and protonated betaine molecule in the gas phase. We aim to shed some new light on the fundamental issues concerning the wide diapason of hydrogen-bonding-type intermolecular interactions, with a wide variety of proton acceptors. We demonstrate that in the course of tagging the protonated betaine with molecular hydrogen from the OH group side, it is the σ bond of molecular hydrogen that plays the role of hydrogen-bonding proton acceptor. The tagging thus induces a small yet significant red shift of the protonated betaine O-H stretching mode. We investigate the performance of a wide range of density functional theory (DFT) functionals for the calculation of anharmonic vibrational frequency shifts of the studied system, which are essential for the correct interpretation of the experimental IRMPD data. For an accurate prediction of the OH stretching frequency shifts, specifically designed functionals such as Handy's group HCTH/407 should be applied. The empirical dispersion correction enhances the systematic overestimation of the anharmonic frequency shift, characteristic of the most widely used DFT functionals. Combining the full-wave function approach with the charge field perturbation and natural bond orbital (NBO) deletion analyses, we demonstrate that the frequency shift in the OH-tagged structure is governed by the σHH → σ*OH intermolecular charge transfer. This interaction stabilizes the OH-tagged dimer as well, in contrast to the dipole-quadrupole electrostatic interaction energy term. Topological analysis of the electron density reveals the presence of an intermolecular bond critical point with a positive value of the density Laplacian very close to the lower limit for hydrogen bonds. NCI analyses demonstrate that the OH···H2 interaction is weaker than the intramolecular CH···O one within the protonated betaine molecule, with the through of reduced density gradient appearing at less negative sign(λ2)·ρ values. Analyzing the O-H stretching vibrational potential with the second-generation absolutely localized molecular orbitals energy decomposition analysis (ALMO-EDA 2) revealed that in the case of betaineH(+) tagged from the OH group side, the permanent electrostatics (ΔEelec), polarization (ΔEpol), and charge-transfer (ΔEct) contributions to the total intermolecular interaction energy contribute favorably to the weak hydrogen bond formation and to the red shift of the fundamental O-H stretching frequency, the ΔEct contribution being the most significant in the last context. The Pauli repulsion term, on the other hand, favors an O-H stretching frequency blue shift as a consequence of the vibrational confinement effects.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions.

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

Accurate machine learning force fields via experimental and simulation data fusion

Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties were affected only mildly and mostly positively. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials.

Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO2.

VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.

Adsorption and evolution of hydrogen molecules on hexagonal boron nitride monolayer: a combined DFT and kinetic monte-carlo simulations study

Density functional theory (DFT) and kinetic Monte-Carlo (kMC) simulation code has been combinedly used to study the adsorption and evolution dynamics of hydrogen molecules over a hexagonal boron nitride (h-BN) monolayer. Maximum adsorption energy from van der Waals curve is predicted to be around 60 to 70 meV using two different DFT functionals. Repulsive lateral interaction between two hydrogen molecules plays a key role in determining the maximum number of adsorptions inside one unit cell of h-BN. Bader charge analysis, electron localization function (ELF), total and partial density of states (DOS) plots have been included to understand the weak interaction going on between the adsorbent and substrate. The input energy parameters from the DFT calculation has been used to perform the kMC simulation for describing the adsorption, desorption and the diffusion pattern of hydrogen molecules with a given time of exposure to an empty h-BN substrate along with the overall surface coverage.

Employing neural density functionals to generate potential energy surfaces.

With the union of machine learning (ML) and quantum chemistry, amid the debate between machine-learned functionals and human-designed functionals in density functional theory (DFT), this paper aims to demonstrate the generation of potential energy surfaces using computations with machine-learned density functional approximation (ML-DFA). A recent research trend is the application of ML in quantum sciences in the design of density functionals such as DeepMind's Deep Learning model (DeepMind21, DM21). Though science reported the state-of-the-art performance of DM21, the opportunity to utilize DeepMind's pretrained DM21 neural networks in computations in quantum chemistry has not yet been tapped. So far in the literature, the Deep Learning density functionals (DM21) have not been applied to generate potential energy surfaces. While the superior accuracy of DM21 has been reported, there is still a scarcity of publications that apply DM21 in calculations in the field. In this context, for the first time in literature, neural density functionals inferring 2D potential energy surfaces (ML-DFA-PES) based on machine-learned DFA-based computational method is contributed in this paper. This paper reports the ML-DFA-generated PES for C4H8, H2O, H2, and H2+ by employing a pretrained DM21m TensorFlow model with cc-pVDZ basis set. In addition, we also analyze the long-range behavior of DM21 based PES to investigate the ability to describe a system at long ranges. Furthermore, we compare PES diagrams from DM21 with popular DFT functionals (b3lyp/ PW6B95) and CCSD(T). In this method, 2D potential energy surfaces are obtained using a method that relies upon the neural network's ability to accurately learn the mapping between 3D electron density and exchange-correlation potential. By inserting Deep Learning inference in DFT with a pretrained neural network, self-consistent field (SCF) energy at different geometries along the coordinates of interest is computed, and then, potential energy surfaces are plotted. In this method, first, the electron density is computed mathematically, and this computed 3D electron density is used as a ML feature vector to predict the exchange correlation potential as a ML inference computed by a forward pass of pre-trained DM21 TensorFlow computational graph, followed by the computation of self-consistent field energy at multiple geometries, and then, SCF energies at different bond lengths/angles are plotted as 2D PES. We implement this in a python source code using frameworks such as PySCF and DM21. This paper contributes this implementation in open source. The source code and DM21-DFA-based PES are contributed at https://sites.google.com/view/MLfunctionals-DeepMind-PES .