Replacing hybrid density functional theory: motivation and recent advances

Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density

ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional. Its exact form is unknown, or better "unknowable", and therefore the derivation of ever more accurate yet efficiently applicable approximate functionals is the "holy grail" in the field. In this context, the simultaneous minimization of so-called delocalization errors and static correlation errors is the greatest challenge that needs to be overcome as we move toward more accurate yet computationally efficient methods. In many cases, an improvement on one of these two aspects (also often termed fractional-charge and fractional-spin errors, respectively) generates a deterioration in the other one. Here we report on recent notable progress in escaping this so-called "zero-sum-game" by constructing new functionals based on the exact-exchange energy density. In particular, local hybrid and range-separated local hybrid functionals are discussed that incorporate additional terms that deal with static correlation as well as with delocalization errors. Taking hints from other coordinate-space models of nondynamical and strong electron correlations (the B13 and KP16/B13 models), position-dependent functions that cover these aspects in real space have been devised and incorporated into the local-mixing functions determining the position-dependence of exact-exchange admixture of local hybrids as well as into the treatment of range separation in range-separated local hybrids. While initial functionals followed closely the B13 and KP16/B13 frameworks, meanwhile simpler real-space functions based on ratios of semilocal and exact-exchange energy densities have been found, providing a basis for relatively simple and numerically convenient functionals. Notably, the correction terms can either increase or decrease exact-exchange admixture locally in real space (and in interelectronic-distance space), leading even to regions with negative admixture in cases of particularly strong static correlations. Efficient implementations into a fast computer code (Turbomole) using seminumerical integration techniques make such local hybrid and range-separated local hybrid functionals promising new tools for complicated composite systems in many research areas, where simultaneously small delocalization errors and static correlation errors are crucial. First real-world application examples of the new functionals are provided, including stretched bonds, symmetry-breaking and hyperfine coupling in open-shell transition-metal complexes, as well as a reduction of static correlation errors in the computation of nuclear shieldings and magnetizabilities. The newest versions of range-separated local hybrids (e.g., ωLH23tdE) retain the excellent frontier-orbital energies and correct asymptotic exchange-correlation potential of the underlying ωLH22t functional while improving substantially on strong-correlation cases. The form of these functionals can be further linked to the performance of the recent impactful deep-neural-network "black-box" functional DM21, which itself may be viewed as a range-separated local hybrid.

Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian

This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.

Subsurface A-site vacancy activates lattice oxygen in perovskite ferrites for methane anaerobic oxidation to syngas

Tuning the oxygen activity in perovskite oxides (ABO3) is promising to surmount the trade-off between activity and selectivity in redox reactions. However, this remains challenging due to the limited understanding in its activation mechanism. Herein, we propose the discovery that generating subsurface A-site cation (Lasub.) vacancy beneath surface Fe-O layer greatly improved the oxygen activity in LaFeO3, rendering enhanced methane conversion that is 2.9-fold higher than stoichiometric LaFeO3 while maintaining high syngas selectivity of 98% in anaerobic oxidation. Experimental and theoretical studies reveal that absence of Lasub.-O interaction lowered the electron density over oxygen and improved the oxygen mobility, which reduced the barrier for C-H bond cleavage and promoted the oxidation of C-atom, substantially boosting methane-to-syngas conversion. This discovery highlights the importance of A-site cations in modulating electronic state of oxygen, which is fundamentally different from the traditional scheme that mainly credits the redox activity to B-site cations and can pave a new avenue for designing prospective redox catalysts.

Exploring Cr and molten salt interfacial interactions for molten salt applications

Molten salts play an important role in various energy-related applications such as high-temperature heat transfer fluids and reaction media. However, the extreme molten salt environment causes the degradation of materials, raising safety and sustainability challenges. A fundamental understanding of material-molten salt interfacial evolution is needed. This work studies the transformation of metallic Cr in molten 50/50 mol% KCl-MgCl2via multi-modal in situ synchrotron X-ray nano-tomography, diffraction and spectroscopy combined with density functional theory (DFT) and ab initio molecular dynamics (AIMD) simulations. Notably, in addition to the dissolution of Cr in the molten salt to form porous structures, a δ-A15 Cr phase was found to gradually form as a result of the metal-salt interaction. This phase change of Cr is associated with a change in the coordination environment of Cr at the interface. DFT and AIMD simulations provide a basis for understanding the enhanced stability of δ-A15 Cr vs. bcc Cr, by revealing their competitive phase thermodynamics at elevated temperatures and probing the interfacial behavior of the molten salt at relevant facets. This study provides critical insights into the morphological and chemical evolution of metal-molten salt interfaces. The combination of multimodal synchrotron analysis and atomic simulation also offers an opportunity to explore a broader range of systems critical to energy applications.

First Principles Investigation of C, Cl2 and CO Co-Adsorption on ZrSiO4 Surfaces for Carbochlorination Reaction

The study of the adsorption behavior of C, CO and Cl2 on the surface of ZrSiO4 is of great significance for the formulation of the technological parameters in the carbochlorination reaction process. Based on first principles, the adsorption structure, adsorption energy, Barder charge, differential charge density, partial density of states and energy barrier were calculated to research the adsorption and reaction mechanism of C and Cl2 on ZrSiO4 surfaces. The results indicated that when C, CO and Cl2 co-adsorbed on the surface of ZrSiO4, they interacted with surface atoms and the charge transfer occurred. The Cl2 molecules dissociated and formed Zr-Cl bonds, while C atoms formed C1=O1 bonds with O atoms. Compared with CO, the co-adsorption energy and reaction energy barrier of C and Cl2 are lower, and the higher the C content, the lower the adsorption energy and energy barrier, which is beneficial for promoting charge transfer and the dissociation of Cl2. The 110-2C-2Cl2 has the lowest adsorption energy and the highest reaction activity, with adsorption energy and energy barriers of -13.45 eV and 0.02 eV. The electrons released by C are 2.30 e, while the electrons accepted by Cl2 are 2.37 e.

How well do one-electron self-interaction-correction methods perform for systems with fractional electrons?

Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (zσ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew-Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of H2+ and He2+ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li+ to F- at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.

Correlation consistent basis sets designed for density functional theory: Third-row atoms (Ga-Br)

The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga-Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn-Sham limit is improved relative to other basis sets where convergence to the Kohn-Sham limit is typically not observed.

A First-Principles Study of Mechanical and Electronic Properties of Cr0.5-xAl0.5TMxN Hard Coatings (TM = Ti, V, Y, Zr, Hf, and Ta)

The structural, mechanical, and electronic properties of cubic Cr0.5-xAl0.5TMxN, doped with TM (transition metal) elements (TM = Ti, V, Y, Zr, Hf, and Ta) at low concentrations (x = 0.03 and 0.06), was investigated by first-principles calculations. The results of the structural properties calculations reveal that the addition of Ti, Y, Hf, Zr, and Ta expand the volume, while V has the opposite effect. All doped compounds are thermodynamically stable, and Cr0.5-xAl0.5TMxN with TM = Ti is energetically more favorable than other doped compounds. At the same doping concentration, Cr0.5-xAl0.5VxN possesses the highest stiffness, hardness, and resistance to external forces due to its greatest mechanical properties, and Cr0.5-xAl0.5TaxN possesses the highest elastic anisotropy and the lowest Young's modulus. Substituting Cr atoms with TM atoms in a stepwise manner results in a decrease in the bulk modulus, shear modulus, Young's modulus, and theoretical hardness of Cr0.5-xAl0.5TMxN, while increasing its toughness. Based on the calculation results of the total and partial density of states of Cr0.5Al0.5N and Cr0.47Al0.5TM0.03N, all compounds exhibit metallic behavior as indicated by the finite density of states at the Fermi level. The contribution of Ti-3d, V-3d, and Ta-3d orbitals at Fermi level is significantly higher than that of other TM atoms, resulting in a more pronounced metallic character for Cr0.47Al0.5Ti0.03N, Cr0.47Al0.5V0.03N, and Cr0.47Al0.5Ta0.03N.

Novel room-temperature full-Heusler thermoelectric material Li2TlSb

High lattice thermal conductivity stemming from the intrinsically ordered crystal and strong interatomic bonds tends to be seen as the bottleneck for achieving excellent thermoelectric properties in full-Heusler (FH) semiconductors. In this work, we propose a novel Li-based FH compound Li2TlSb by substituting one Li atom with a Tl atom in Li3Sb. Then we systematically investigated its transport and thermoelectric properties based on self-consistent phonon (SCP) theory, electron-phonon scattering, and the Boltzmann transport equation. The theoretical calculation confirms that it exhibits outstanding mechanical properties and extreme environment adaptability. Surprisingly, the combination of an unexpectedly high spatial degeneracy and light electron dispersion at valence bands results in a high power factor in p-type systems. Additionally, the rattling behavior governed by the Tl atom and resonant bonding is responsible for ultra-low lattice thermal conductivity with 0.79 W m-1 K-1 at room temperature. Finally, a maximum p-type ZT value of 1.77 at 300 K has been achieved, which surpasses those of most of the traditional thermoelectric (TE) materials. Our results demonstrate that Li2TlSb serves as a potential candidate for room-temperature thermoelectric materials and simultaneously provides new insights for rationally designing novel FH materials in the future.

Efficient Decomposition of Perfluoroalkyl Substances by Low Concentration Indole: New Insights into the Molecular Mechanisms

Perfluoroalkyl substances (PFAS) are a class of persistent organic pollutants known as "forever chemicals". Currently, the hydrated electron-based advanced reduction process (ARP) holds promise for the elimination of PFAS. However, the efficiency of ARP is often challenged by an oxygen-rich environment, resulting in the consumption of hydrated electron source materials in exchange for the high PFAS decomposition efficiency. Herein, we developed a ternary system constructed by indole and isopropyl alcohol (IPA), and the addition of IPA significantly enhanced the PFOA degradation and defluorination efficiency in the presence of low-concentration indole (<0.4 mM). Meanwhile, opposite results were obtained with a higher amount of indole (>0.4 mM). Further exploring the molecular mechanism of the reaction system, the addition of IPA played two roles. On one hand, IPA built an anaerobic reaction atmosphere and improved the yield and utilization efficiency of hydrated electrons with a low concentration of indole. On the other hand, IPA suppressed the attraction between indole and PFOA, thus reducing the hydrated electron transfer efficiency, especially with more indole. In general, the indole/PFAS/IPA system significantly improved the PFAS destruction efficiency with a small amount of hydrated electron donors, which provided new insights for development of simple and efficient techniques for the treatment of PFAS-contaminated wastewater.

First-Principles Calculations of Magnetite (Fe3O4) above the Verwey Temperature by Using Self-Consistent DFT + U + V

In this report, we have used the DFT + U + V approach, an extension of the DFT + U approach that takes into account both on-site and intersite interactions, to simulate structural, magnetic, and electronic properties together with the Fe and O K-edge XAS spectra of Fe3O4 above the Verwey temperature (Tv). Moreover, we compared the simulated XAS spectra with experimental XAS data. We examined both orthogonalized and nonorthogonalized atomic orbital projectors and compared DFT + U + V to DFT, DFT + U, and HSE as a hybrid functional. It is noteworthy that, despite the widespread use of the same Hubbard U value for Feoct and Fetet at the DFT + U level in the literature, the HP code identified two distinct values for them using the Hubbard approaches (DFT + U and DFT + U + V). The resulting Hubbard U and V parameters are strongly dependent on the chosen orbital projectors. This study demonstrates how DFT + U + V can improve the structural, magnetic, and electronic properties of Fe3O4 compared to approximate DFT and DFT + U. In this context, DFT + U + V supports the half-metallic character of the bulk crystal Fe3O4 above Tv, since the Fermi level is found in the t2g band with a Feoct down-spin. Thus, the observations in the current study emphasize the significance of intersite interactions in the theoretical analysis of Fe3O4 above the Tv.

Comparing Density Functional Theory Metal-Ligand Bond Dissociation Enthalpies with Experimental Solution-Phase Enthalpies of Activation for Bond Dissociation

The predictive ability of density functional theory is fundamental to its usefulness in chemical applications. Recent work has compared solution-phase enthalpies of activation for metal-ligand bond dissociation to enthalpies of reaction for bond dissociation, and the present work continues those comparisons for 43 density functional methods. The results for ligand dissociation enthalpies of 30 metal-ligand complexes tested in this work reveal significant inadequacies of some functionals as well as challenges from the dispersion corrections to some functionals. The analysis presented here demonstrates the excellent performance of a recent density functional, M11plus, which contains nonlocal rung-3.5 correlation. We also find a good agreement between theory and experiment for some functionals without empirical dispersion corrections such as M06, r2SCAN, M06-L, and revM11, as well as good performance for some functionals with added dispersion corrections such as ωB97X-D (which always has a correction) and BLYP, B3LYP, CAM-B3LYP, and PBE0 when the optional dispersion corrections are added.

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.

Molecular simulation of Cu, Ag, and Au-decorated Si-doped graphene quantum dots (Si@QD) nanostructured as sensors for SO2 trapping

In view of the numerous environmental hazards and health challenges linked to sulfur (iv) oxide (SO2), an indirect greenhouse gas, and the resultant need to develop efficient gas nanosensor devices, this research had as its principal focus on the theoretical evaluation of the gas sensing potential of metals: Ag, Au and Cu functionalized silicon-doped quantum dots (Si@QD) for the detection and adsorption of SO2 gas investigated using the first-principles density functional theory (DFT) computation at the B3LYP-D3(BJ)/def2-SVP level of theory. Eight (8) possible adsorption modes: SO2_O_Si@QD, SO2_O_Ag_Si@QD, SO2_O_Au_Si@QD, SO2_O_Cu_Si@QD, SO2_S_Si@QD, SO2_S_Ag_Si@QD, SO2_S_Au_Si@QD, and SO2_S_Cu_Si@QD were considered based on SO2 interactions with the studied materials at the -S and -O sites of the SO2 molecule. The counterpoise correction (BSSE) showed that five of the eight interactions had favorable Ead + BSSE values ranging from -0.31 to -1.98 eV. All the eight interactions were observed to be thermodynamically favorable with ΔG and ΔH ranging from -129.01 to -200.24 kcal/mol and -158.26 to -229.73 kcal/mol respectively. Results from the topology analysis reveal that van der Waals forces occurred the greatest at the gas-sensor interphase while SO2_S_ Cu_Si@QD is predicted to have the highest sensing potency based on the conductivity and recovery time estimations. These results confirm the potential efficient feasibility of real-world device application of the metals (Ag, Au, Cu) functionalized Si-doped QDs.

Diversity of Behavior after Collisions of Sn and Si Nanoparticles Found Using a New Density Functional Tight-Binding Method

We present a new approach to studying nanoparticle collisions using density functional based tight binding (DFTB). A novel DFTB parametrization has been developed to study the collision process of Sn and Si clusters (NPs) using molecular dynamics (MD). While bulk structures were used as training sets, we show that our model is able to accurately reproduce the cohesive energy of the nanoparticles using density functional theory (DFT) as a reference. A surprising variety of phenomena are revealed for the Si/Sn nanoparticle collisions, depending on the size and velocity of the collision: from core-shell structure formation to bounce-off phenomena.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Enhancing the photocatalytic efficiency of two-dimensional aluminum nitride materials through strategic rare earth doping

Two-dimensional (2D) materials demonstrate promising potential as high-efficiency photocatalysts. However, the intrinsic limitations of aluminum nitride (AlN), such as inadequate oxidation capacity, a high carrier recombination rate, and limited absorption of visible light, pose considerable challenges. In this paper, we introduce a novel co-doping technique with dysprosium (Dy) and carbon (C) on a 2D AlN monolayer, aiming to enhance its photocatalytic properties. Our first-principles calculations reveal a reduction in the bandgap and a significant enhancement in the visible light absorption rate of the co-doped Al24N22DyC2 structure. Notably, the distribution of the highest occupied molecular orbital and the lowest unoccupied molecular in proximity to Dy atoms demonstrates favorable conditions for carrier separation. Theoretical assessments of the hydrogen evolution reaction and oxygen evolution reaction activities further corroborate the potential of Al24N22DyC2 as a competent catalyst for photocatalytic reactions. These findings provide valuable theoretical insights for the experimental design and fabrication of novel, high-efficiency AlN semiconductor photocatalysts.

Anisotropic magnetoresistance and electronic features of the candidate topological compound praseodymium monobismuthide

PrBi, a sister member of the rare-earth monopnictide family, is an excellent candidate for studying extreme magnetoresistance and nontrivial topological electronic states. In this study, we perform angular magnetoresistance measurements as well as bulk and surface band structure calculations on this compound. PrBi's magnetoresistance is revealed to be significantly angle-dependent and shows a fourfold symmetry as always observed in the nonmagnetic isostructural counterparts, including LaSb, LaBi, and LuBi. Its angular magnetoresistance can be reproduced well using the semiclassical two-band model. The deduced parameters suggest that PrBi hosts an elongated electron pocket with a mobility anisotropy of ∼3.13 and is slightly uncompensated in its carrier concentration. Our bulk and surface band structure calculations confirm the anisotropic electronic features. Moreover, we reveal that a nodal-line-shaped surface state appears at the X̄ point, and is associated with the quadratic dispersion along the -X̄ direction, and the linear type-I Dirac dispersion along the X̄-M̄ direction. Owing to the type-I Dirac dispersion feature, PrBi could serve as a promising material platform for studying many unexpected physical properties, such as the highly anisotropic transport and valley polarization of electrons.

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r2SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew-Burke-Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r2SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

A computational study of 2D group-III ternary chalcogenide monolayer compounds MNTe2(M, N = In, Ga, Al)

First principle calculations of novel two-dimensional (2D) group-III ternary chalcogenide monolayer (G3TCM) compounds have been carried out using density functional theory. The 2D hexagonal structure has a honeycomb-like appearance from both the top and bottom views. Both pristine and G3TCM compounds are energetically favourable and have been found to be dynamically stable via phonon calculations. Theab-initiomolecular dynamics calculations show the thermodynamical stability of the G3TCM compounds. The G3TCM compounds exhibit semiconductor behaviour with a decreased indirect bandgap compared to the pristine monolayers. Chalcogen atoms contribute mainly to the valence bands, while group-III atoms have a major contribution to the conduction band. A red shift has been observed in the absorption of light, mainly in the visible and ultraviolet regions, and the refractive index is increased compared to the pristine material. Both pristine and G3TCM compounds have been found to be more active in the ultraviolet region, and low reflection has been observed. In the 6-8 eV range of the ultraviolet region, zero reflection and the highest absorption are observed. The monolayer has shown potential applications in optoelectronics devices as an ultraviolet and visible light detector, absorber, coating material, and more. The band alignment of the 2D G3TCM monolayer is calculated to observe its photo-catalyst behaviour.

High Concentration Intrinsic Defects in MnSb2Te4

MnSb2Te4 has a similar structure to an emerging material, MnBi2Te4. According to earlier theoretical studies, the formation energy of Mn antisite defects in MnSb2Te4 is negative, suggesting its inherent instability. This is clearly in contrast to the successful synthesis of experimental samples of MnSb2Te4. Here, the growth environment of MnSb2Te4 and the intrinsic defects are correspondingly investigated. We find that the Mn antisite defect is the most stable defect in the system, and a Mn-rich growth environment favors its formation. The thermodynamic equilibrium concentrations of the Mn antisite defects could be as high as 15% under Mn-poor conditions and 31% under Mn-rich conditions. It is also found that Mn antisite defects prefer a uniform distribution. In addition, the Mn antisite defects can modulate the interlayer magnetic coupling in MnSb2Te4, leading to a transition from the ideal antiferromagnetic ground state to a ferromagnetic state. The ferromagnetic coupling effect can be further enhanced by controlling the defect concentration.

Theoretical study of local S coordination environment on Fe single atoms for peroxymonosulfate-based advanced oxidation processes

Tuning the electronic structure of single atom catalysts (SACs) is an effective strategy to promote the catalytic activity in peroxymonosulfate (PMS)-based advanced oxidation processes (AOPs). Herein, a series of Fe-based SACs with S_1/2/3/4-coordination numbers on graphene were designed to regulate the electronic structural of SACs at molecular level, and their effects on PMS activation were investigated via density function theory (DFT). The calculation results demonstrate that the electron structure of the active center can be adjusted by coordination environment, which further affects the activation of PMS. Among the studied Fe-S_X-C_4-X catalysts, with the increase of the S coordination number, the electron density of the Fe-S_X-C_4-X active center was optimized. The active center of the Fe-S₄-C₀ catalyst has a largest positive charge density, exhibiting the highest number of electron transfer. It also has a lower kinetic energy barrier (0.28 eV) for PMS dissociation. Organic pollutant such as bisphenol A (BPA) can achieve stable adsorption on Fe-S_X-C_4-X catalysts, which is conducive to subsequent oxidation by radicals. The dual index ∆f(r) indicates that the para-carbon atom of the hydroxyl group on the benzene ring of BPA is vulnerable to radical attack. This study highlights a theoretical support and a certain guide for designing efficient SACs to activate PMS.

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.

Reimagining the Wave Function in Density Functional Theory: Exploring Strongly Correlated States in Pancake-Bonded Radical Dimers

Pancake bonding between π-conjugated radicals challenges conventional electronic structure approximations, due to the presence of both dispersion (van der Waals) interactions and "strong" electron correlation. Here we use a reimagined wave function-in-density functional theory (DFT) approach to model pancake bonds. Our generalized self-interaction correction extends DFT's reference system of noninteracting electrons, by introducing electron-electron interactions within an active space. We show that a small variation on our previous derivation recovers a DFT-corrected complete active space method proposed by Pijeau and Hohenstein. Comparison of the two approaches shows that the latter provides reasonable dissociation curves for single bonds and pancake bonds, including excited states inaccessible to conventional linear response time-dependent DFT. The results motivate broader adoption of wavefunction-in-DFT approaches for modeling pancake bonds.

Metal Oxide-Supported Metal Catalysts for Electrocatalytic Oxygen Reduction Reaction: Characterization Methods, Modulation Strategies, and Recent Progress

The sluggish kinetics of the oxygen reduction reaction (ORR) with complex multielectron transfer steps significantly limits the large-scale application of electrochemical energy devices, including metal-air batteries and fuel cells. Recent years witnessed the development of metal oxide-supported metal catalysts (MOSMCs), covering single atoms, clusters, and nanoparticles. As alternatives to conventional carbon-dispersed metal catalysts, MOSMCs are gaining increasing interest due to their unique electronic configuration and potentially high corrosion resistance. By engineering the metal oxide substrate, supported metal, and their interactions, MOSMCs can be facilely modulated. Significant progress has been made in advancing MOSMCs for ORR, and their further development warrants advanced characterization methods to better understand MOSMCs and precise modulation strategies to boost their functionalities. In this regard, a comprehensive review of MOSMCs for ORR is still lacking despite this fast-developing field. To eliminate this gap, advanced characterization methods are introduced for clarifying MOSMCs experimentally and theoretically, discuss critical methods of boosting their intrinsic activities and number of active sites, and systematically overview the status of MOSMCs based on different metal oxide substrates for ORR. By conveying methods, research status, critical challenges, and perspectives, this review will rationally promote the design of MOSMCs for electrochemical energy devices.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Rapid Interlayer Charge Separation and Extended Carrier Lifetimes due to Spontaneous Symmetry Breaking in Organic and Mixed Organic-Inorganic Dion-Jacobson Perovskites

Promising alternatives to three-dimensional perovskites, two-dimensional (2D) layered metal halide perovskites have proven their potential in optoelectronic applications due to improved photo- and chemical stability. Nevertheless, photovoltaic devices based on 2D perovskites suffer from poor efficiency owing to unfavorable charge carrier dynamics and energy losses. Focusing on the 2D Dion-Jacobson perovskite phase that is rapidly rising in popularity, we demonstrate that doping of complementary cations into the 3-(aminomethyl)piperidinium perovskite accelerates spontaneous charge separation and slows down charge recombination, both factors improving the photovoltaic performance. Employing ab initio nonadiabatic (NA) molecular dynamics combined with time-dependent density functional theory, we demonstrate that cesium doping broadens the bandgap by 0.4 eV and breaks structural symmetry. Assisted by thermal fluctuations, the symmetry breaking helps to localize electrons and holes in different layers and activates additional vibrational modes. As a result, the charge separation is accelerated. Simultaneously, the charge carrier lifetime grows due to shortened coherence time between the ground and excited states. The established relationships between perovskite composition and charge carrier dynamics provide guidelines toward future material discovery and design of perovskite solar cells.

Generating Exchange-Correlation Functionals with a Simplified, Self-Consistent Correlation Factor Model

We focus on the spherically averaged exchange-correlation hole ρ_XC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρ_X^model(r, u) is multiplied by a CF (f_C(r, u)) to yield an approximation to the exchange-correlation hole ρ_XC(r, u) = f_C(r, u) ρ_X^model(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.

Active Learning Exploration of Transition-Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores

Transition-metal chromophores with earth-abundant transition metals are an important design target for their applications in lighting and nontoxic bioimaging, but their design is challenged by the scarcity of complexes that simultaneously have well-defined ground states and optimal target absorption energies in the visible region. Machine learning (ML) accelerated discovery could overcome such challenges by enabling the screening of a larger space but is limited by the fidelity of the data used in ML model training, which is typically from a single approximate density functional. To address this limitation, we search for consensus in predictions among 23 density functional approximations across multiple rungs of "Jacob's ladder". To accelerate the discovery of complexes with absorption energies in the visible region while minimizing the effect of low-lying excited states, we use two-dimensional (2D)efficient global optimization to sample candidate low-spin chromophores from multimillion complex spaces. Despite the scarcity (i.e., ∼0.01%) of potential chromophores in this large chemical space, we identify candidates with high likelihood (i.e., >10%) of computational validation as the ML models improve during active learning, representing a 1000-fold acceleration in discovery. Absorption spectra of promising chromophores from time-dependent density functional theory verify that 2/3 of candidates have the desired excited-state properties. The observation that constituent ligands from our leads have demonstrated interesting optical properties in the literature exemplifies the effectiveness of our construction of a realistic design space and active learning approach.

Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization

This work introduces a new class of hybrid density functional theory (DFT) approximations, which incorporate different fractions of nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are related to range-separated hybrid functionals, which incorporate different fractions of nonlocal exchange at different electron-electron separations. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, introduces the projected operator into the noninteracting Kohn-Sham reference system, and employs a formally exact density functional to model the remaining electron-electron interactions. Projected hybrids, like range-separated hybrids, approximate the partially interacting reference system's ground-state wave function as a single Slater determinant. Projected hybrids are readily implemented into existing density functional codes, requiring only a projection of the one-particle density matrices and exchange operators entering existing routines. This work also presents an application to core electron ionization. Projecting onto core atomic orbitals allows us to introduce additional nonlocal exchange into atomic core regions. This reduces the impact of self-interaction error on computed core electron properties. Benchmark studies are reported for PBE0c70, a core-projected variant of the Perdew-Burke-Ernzerhof global hybrid PBE0, in which the fraction of nonlocal exchange is increased from 25% to 70% in atomic core regions. PBE0c70-predicted core orbital energies accurately recover nonrelativistic core-electron binding energies of second-period elements Li-Ne and third-period elements Na-Ar, without degrading the good performance of PBE0 for atomization energies and valence ionization potentials.

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

First-principles calculations of hematite (α-Fe2O3) by self-consistent DFT+U+V

Owing to the confined Fe-3d orbitals and self-interaction error of exchange-correlation functionals, approximate DFT fails to describe iron oxides electronic structure and magnetic properties accurately. Hybrid DFT or DFT + U can solve these problems, but the former is expensive, and the latter only considers on-site interactions. Here, we used DFT + U + V, a DFT + U extension including inter-site interactions, to simulate the structural, magnetic, and electronic properties, along with Fe and O K-edge XAS spectra of α-Fe₂O₃. Two types of atomic orbital projectors were studied, orthogonalized and non-orthogonalized. DFT + U + V improves the description of the structural, magnetic, and electronic properties of α-Fe₂O₃ compared to approximate DFT. The accuracy of the correction depends on the orbital projector used. DFT + U + V with orthogonalized projectors achieves the best experimental agreement at a fraction of hybrid DFT cost. This work emphasizes the importance of inter-site interactions and the type of atomic orbital projectors used in the theoretical research of α-Fe₂O₃.

The fourth-order expansion of the exchange hole and neural networks to construct exchange–correlation functionals

The curvature Q σ of spherically averaged exchange (X) holes ρX, σ(r, u) is one of the crucial variables for the construction of approximations to the exchange–correlation energy of Kohn–Sham theory, the most prominent example being the Becke–Roussel model [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)]. Here, we consider the next higher nonzero derivative of the spherically averaged X hole, the fourth-order term T σ. This variable contains information about the nonlocality of the X hole and we employ it to approximate hybrid functionals, eliminating the sometimes demanding calculation of the exact X energy. The new functional is constructed using machine learning; having identified a physical correlation between T σ and the nonlocality of the X hole, we employ a neural network to express this relation. While we only modify the X functional of the Perdew–Burke–Ernzerhof functional [Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], a significant improvement over this method is achieved.

Unification of Perdew-Zunger self-interaction correction, DFT+U, and Rung 3.5 density functionals

This Communication presents a unified derivation of three different approximations used in density functional theory (DFT): the Perdew-Zunger self-interaction correction (PZSIC), the Hubbard correction DFT+U, and the Rung 3.5 density functionals. All three approximations can be derived by introducing electron self-interaction into the Kohn-Sham (KS) reference system of noninteracting electrons. The derivation uses the Adiabatic Projection formalism: one projects the electron-electron interaction operator onto certain states, introduces the projected operator into the reference system, and defines a density functional for the remainder. Projecting onto individual localized KS orbitals recovers our previous derivation of the PZSIC [B. G. Janesko, J. Phys. Chem. Lett. 13, 5698-5702 (2022)]. Projecting onto localized atom-centered orbitals recovers a variant of DFT+U. Projecting onto localized states at each point in space recovers Rung 3.5 approaches. New results include an "atomic state PZSIC" that does not require localizing the KS orbitals, a demonstration that typical Hubbard U parameters reproduce a scaled-down PZSIC, and a Rung 3.5 variant of DFT+U that does not require choosing atom-dependent states.

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange-correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π_⊥ ^* excitations are heavily gauge-dependent with average changes of -0.17 and -0.28 eV, respectively, while π→π_‖ ^* excitations are marginally affected (-0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

A Review of Performance Prediction Based on Machine Learning in Materials Science

With increasing demand in many areas, materials are constantly evolving. However, they still have numerous practical constraints. The rational design and discovery of new materials can create a huge technological and social impact. However, such rational design and discovery require a holistic, multi-stage design process, including the design of the material composition, material structure, material properties as well as process design and engineering. Such a complex exploration using traditional scientific methods is not only blind but also a huge waste of time and resources. Machine learning (ML), which is used across data to find correlations in material properties and understand the chemical properties of materials, is being considered a new way to explore the materials field. This paper reviews some of the major recent advances and applications of ML in the field of properties prediction of materials and discusses the key challenges and opportunities in this cross-cutting area.

Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn–Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment (μ), static dipole polarizability (α), and first hyperpolarizability (β), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of “adiabatic connection theorem” and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory

Perdew-Zunger self-interaction correction (PZSIC) reintroduces an exact constraint to approximate density functional theory (DFT). However, PZSIC can paradoxically degrade performance, and standard DFT approximations (with or without PZSIC) are not systematically improvable. We use the adiabatic projection formalism (Janesko, B. G. J. Chem. Phys. 2022, 156, 014111, https://doi.org/10.1063/5.0076144) to derive PZSIC in terms of a reference system experiencing only electron self-interaction. Generalization to a "self-and-some-others" interaction introduces correlation into the reference system, systematically bridging from PZSIC to exact wave function theory without the double counting of correlation. Minimal active spaces accurately treat nearly one electron, near-equilibrium, and strongly correlated model systems at modest computational expense.

Detection and Correction of Delocalization Errors for Electron and Hole Polarons Using Density-Corrected DFT

Modeling polaron defects is an important aspect of computational materials science, but the description of unpaired spins in density functional theory (DFT) often suffers from delocalization error. To diagnose and correct the overdelocalization of spin defects, we report an implementation of density-corrected (DC-)DFT and its analytic energy gradient. In DC-DFT, an exchange-correlation functional is evaluated using a Hartree-Fock density, thus incorporating electron correlation while avoiding self-interaction error. Results for an electron polaron in models of titania and a hole polaron in Al-doped silica demonstrate that geometry optimization with semilocal functionals drives significant structural distortion, including the elongation of several bonds, such that subsequent single-point calculations with hybrid functionals fail to afford a localized defect even in cases where geometry optimization with the hybrid functional does localize the polaron. This has significant implications for traditional workflows in computational materials science, where semilocal functionals are often used for structure relaxation. DC-DFT calculations provide a mechanism to detect situations where delocalization error is likely to affect the results.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

Assessment of Various Density Functional Theory Methods for Finding Accurate Structures of Actinide Complexes

Density functional theory (DFT) is a widely used computational method for predicting the physical and chemical properties of metals and organometals. As the number of electrons and orbitals in an atom increases, DFT calculations for actinide complexes become more demanding due to increased complexity. Moreover, reasonable levels of theory for calculating the structures of actinide complexes are not extensively studied. In this study, 38 calculations, based on various combinations, were performed on molecules containing two representative actinides to determine the optimal combination for predicting the geometries of actinide complexes. Among the 38 calculations, four optimal combinations were identified and compared with experimental data. The optimal combinations were applied to a more complicated and practical actinide compound, the uranyl complex (UO₂(2,2′-(1E,1′E)-(2,2-dimethylpropane-1,3-dyl)bis(azanylylidene)(CH₃OH)), for further confirmation. The corresponding optimal calculation combination provides a reasonable level of theory for accurately optimizing the structure of actinide complexes using DFT.

Detection of multi-reference character imbalances enables a transfer learning approach for virtual high throughput screening with coupled cluster accuracy at DFT cost

Appropriately identifying and treating molecules and materials with significant multi-reference (MR) character is crucial for achieving high data fidelity in virtual high-throughput screening (VHTS). Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates the MR effect on a chemical property prediction is not well established. We evaluate MR diagnostics for over 10 000 transition-metal complexes (TMCs) and compare to those for organic molecules. We observe that only some MR diagnostics are transferable from one chemical space to another. By studying the influence of MR character on chemical properties (i.e., MR effect) that involve multiple potential energy surfaces (i.e., adiabatic spin splitting, ΔE_H–L, and ionization potential, IP), we show that differences in MR character are more important than the cumulative degree of MR character in predicting the magnitude of an MR effect. Motivated by this observation, we build transfer learning models to predict CCSD(T)-level adiabatic ΔE_H–L and IP from lower levels of theory. By combining these models with uncertainty quantification and multi-level modeling, we introduce a multi-pronged strategy that accelerates data acquisition by at least a factor of three while achieving coupled cluster accuracy (i.e., to within 1 kcal mol⁻¹ MAE) for robust VHTS.

We demonstrate that cancellation in multi-reference effect outweighs accumulation in evaluating chemical properties. We combine transfer learning and uncertainty quantification for accelerated data acquisition with chemical accuracy.

Data-Centric Architecture for Self-Driving Laboratories with Autonomous Discovery of New Nanomaterials

Artificial intelligence (AI) approaches continue to spread in almost every research and technology branch. However, a simple adaptation of AI methods and algorithms successfully exploited in one area to another field may face unexpected problems. Accelerating the discovery of new functional materials in chemical self-driving laboratories has an essential dependence on previous experimenters' experience. Self-driving laboratories help automate and intellectualize processes involved in discovering nanomaterials with required parameters that are difficult to transfer to AI-driven systems straightforwardly. It is not easy to find a suitable design method for self-driving laboratory implementation. In this case, the most appropriate way to implement is by creating and customizing a specific adaptive digital-centric automated laboratory with a data fusion approach that can reproduce a real experimenter's behavior. This paper analyzes the workflow of autonomous experimentation in the self-driving laboratory and distinguishes the core structure of such a laboratory, including sensing technologies. We propose a novel data-centric research strategy and multilevel data flow architecture for self-driving laboratories with the autonomous discovery of new functional nanomaterials.