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DFT+U provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a DFT+U(+J) calculation hinges on the accurate determination of its Hubbard U and Hund J parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the U and J values for transition metal d-electron states in a representative set of over 1000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use DFT+U to study transition metal oxides. In order to perform this high-throughput study, an atomate workflow is developed for calculating U and J values automatically on massively parallel supercomputing architectures. To demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine LiNiPO4 are calculated using the computed Hubbard U and Hund J values for Ni-d and O-p states, and are compared with experiment. Both the Ni-dU and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-pU value results in a significantly improved agreement between the computed lattice parameters and experiment.

Ab initio many-body perturbation theory within the GW approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn–Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange–correlation functional “starting point”, are used to construct G and W, and then perturbatively corrected by the resultant GW self-energy. In practice, there are several ways to construct the GW self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO2, the GW fundamental gaps reported in the literature can vary by more than 1 eV depending on the GW code used. In this work, we calculate and analyze GW quasiparticle (QP) energies of these and other systems with three different GW codes: BERKELEYGW, ABINIT and YAMBO. Through a systematic analysis of the GW implementation of these three codes, we identify the primary origin of major discrepancies between codes reported in prior literature to be the different implementations the Coulomb divergence in the Fock exchange term and the frequency integration scheme of the GW self-energy. We then eliminate these discrepancies by using common numerical methods and algorithms, demonstrating that the same quasiparticle energies for a given material can be obtained with different codes, within numerical differences ascribable to the technical details of the underling implementations. This work will be important for users and developers in assessing the precision of future GW applications and methods.

It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 − 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof, nonetheless, confirms a stringent constraint on the exact exchange–correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn–Sham bandgap and the exchange–correlation derivative discontinuity of DFT. [ABSTRACT FROM AUTHOR]

We propose a mechanism for binding of diatomic ligands to heme based on a dynamical orbital selection process. This scenario may be described as bonding determined by local valence fluctuations. We support this model using linear-scaling first-principles calculations, in combination with dynamical mean-field theory, applied to heme, the kernel of the hemoglobin metalloprotein central to human respiration. We find that variations in Hund's exchange coupling induce a reduction of the iron 3d density, with a concomitant increase of valence fluctuations. We discuss the comparison between our computed optical absorption spectra and experimental data, our picture accounting for the observation of optical transitions in the infrared regime, and how the Hund's coupling reduces, by a factor of 5, the strong imbalance in the binding energies of heme with CO and O2 ligands. [ABSTRACT FROM AUTHOR]

Vanadium dioxide undergoes a first order metal-insulator transition at 340 K. In this Letter, we develop and carry out state-of-the-art linear scaling density-functional theory calculations refined with nonlocal dynamical mean-field theory. We identify a complex mechanism, a Peierls-assisted orbital selection Mott instability, which is responsible for the insulating M1 phase, and which furthermore survives a moderate degree of disorder. [ABSTRACT FROM AUTHOR]

Localized Wannier functions provide an efficient and intuitive means by which to compute dielectric properties from first principles. They are most commonly constructed in a post-processing step, following total-energy minimization. Nonorthogonal generalized Wannier functions (NGWFs) [Skylaris et al, Phys. Rev. B 66, 035119 (2002); Skylaris et al, J. Chem. Phys. 122, 084119 (2005)] may also be optimized in situ, in the process of solving for the ground-state density. We explore the relationship between NGWFs and orthonormal, maximally localized Wannier functions (MLWFs) [Marzari and Vanderbilt, Phys. Rev. B 56, 12847 (1997); Souza, Marzari, and Vanderbilt, ibid. 65, 035109 (2001)], demonstrating that NGWFs may be used to compute electric dipole polarizabilities efficientiy, with no necessity for post-processing optimization, and with an accuracy comparable to MLWFs. [ABSTRACT FROM AUTHOR]

We present an approach to the DFT+ U method (density functional theory + Hubbard model) within which the computational effort for calculation of ground-state energies and forces scales linearly with system size. We employ a formulation of the Hubbard model using nonorthogonal projector functions to define the localized subSpaces, and we apply it to a local orbital DFT method including m situ orbital optimization. The resulting approach thus combines linear-scaling and systematic variational convergence. We demonstrate the scaling of the method by applying it to nickel-oxide nanoclusters with sizes exceeding 7000 atoms. [ABSTRACT FROM AUTHOR]

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed. [ABSTRACT FROM AUTHOR]

Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT. [ABSTRACT FROM AUTHOR]

In approximate density-functional theory (DFT), the self-interaction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to correction using efficient, constraint-resembling methods such as DFT + Hubbard U (DFT+U). Constrained DFT (cDFT) enforces conditions on DFT exactly, by means of self-consistently optimized Lagrange multipliers, and while its use to automate error corrections is a compelling possibility, we show that it is limited by a fundamental incompatibility with constraints beyond linear order. We circumvent this problem by utilizing separate linear and quadratic correction terms, which may be interpreted either as distinct constraints, each with its own Hubbard U type Lagrange multiplier, or as the components of a generalized DFT+U functional. The latter approach prevails in our tests on a model one-electron system, H2+, in that it readily recovers the exact total energy while symmetry-preserving pure constraints fail to do so. The generalized DFT+U functional moreover enables the simultaneous correction of the total energy and ionization potential, or the correction of either together with the enforcement of Koopmans' condition. For the latter case, we outline a practical, approximate scheme by which the required pair of Hubbard parameters, denoted as U1 and U2, may be calculated from first principles. [ABSTRACT FROM AUTHOR]

Singlet fission (SF) is a multiexciton generation process that could be harnessed to improve the efficiency of photovoltaic devices. Experimentally, systems derived from the pentacene molecule have been shown to exhibit ultrafast SF with high yields. Charge-transfer (CT) configurations are likely to play an important role as intermediates in the SF process in these systems. In molecular crystals, electrostatic screening effects and band formation can be significant in lowering the energy of CT states, enhancing their potential to effectively participate in SF. In order to simulate these, it desirable to adopt a computational approach which is acceptably accurate, relatively inexpensive, and which scales well to larger systems, thus enabling the study of screening effects. We propose an electrostatically corrected constrained density functional theory (cDFT) approach as a low-cost solution to the calculation of CT energies in molecular crystals such as pentacene. Here we consider an implementation in the context of the onetep linear-scaling DFT code, but our electrostatic correction method is in principle applicable in combination with any constrained DFT implementation, also outside the linear-scaling framework. Our newly developed method allows us to estimate CT energies in the infinite crystal limit, and with these to validate the accuracy of the cluster approximation. [ABSTRACT FROM AUTHOR]

We present the implementation of the Hubbard ( U ) and Hund ( J ) corrected Density Functional Theory (DFT + U + J ) functionality in the Quickstep program, which is part of the CP2K suite. The tensorial and Löwdin subspace representations are implemented and compared. Full analytical DFT + U + J forces are implemented and benchmarked for the tensorial and Löwdin representations. We also present the implementation of the recently proposed minimum-tracking linear-response method that enables the U and J parameters to be calculated on first-principles basis without reference to the Kohn-Sham eigensystem. These implementations are benchmarked against recent results for different materials properties including DFT + U band gap opening in NiO, the relative stability of various polaron distributions in TiO 2 , the dependence of the calculated TiO 2 band gap on + J corrections, and, finally, the role of the + U and + J corrections for the computed properties of a series of the hexahydrated transition metals. Our implementation provides results consistent with those already reported in the literature from comparable methods. We conclude the contribution with tests on the influence of the Löwdin orthonormalization on the occupancies, calculated parameters, and derived properties.

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived. Moving to fractional electron count, the tilted-plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat-plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat-plane structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at noninteger values. A diverse set of tilted-plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.

We carried out first-principles density-functional theory calculations to study the work of separation for five different metal-metal interfaces, each of them comprising thin layers of selected metals (Cr, W, Ta, Al or Ti) lying on top of Au surfaces. We found that the highest work of separation is obtained for one-atom-thick layers. Increasing the number of atomic layers leads the work of separation to oscillate with the thickness, and ultimately tend to a limiting value for a large number of layers. Interestingly, for most cases the lowest work of separation is obtained for two-atom layers. We find that this behaviour is mirrored by the quantity of charge transferred between the two metals on the one hand, and their spatial distance on the other., (Creative Commons Attribution license.)

Enhancement of fluorescence through the application of plasmonic metal nanostructures has gained substantial research attention due to the widespread use of fluorescence-based measurements and devices. Using a microfabricated plasmonic silver nanoparticle-organic semiconductor platform, we show experimentally the enhancement of fluorescence intensity achieved through electro-optical synergy. Fluorophores located sufficiently near silver nanoparticles are combined with diphenylalanine nanotubes (FFNTs) and subjected to a DC electric field. It is proposed that the enhancement of the fluorescence signal arises from the application of the electric field along the length of the FFNTs, which stimulates the pairing of low-energy electrons in the FFNTs with the silver nanoparticles, enabling charge transport across the metal-semiconductor template that enhances the electromagnetic field of the plasmonic nanoparticles. Many-body perturbation theory calculations indicate that, furthermore, the charging of silver may enhance its plasmonic performance intrinsically at particular wavelengths, through band-structure effects. These studies demonstrate for the first time that field-activated plasmonic hybrid platforms can improve fluorescence-based detection beyond using plasmonic nanoparticles alone. In order to widen the use of this hybrid platform, we have applied it to enhance fluorescence from bovine serum albumin and Pseudomonas fluorescens . Significant enhancement in fluorescence intensity was observed from both. The results obtained can provide a reference to be used in the development of biochemical sensors based on surface-enhanced fluorescence., Competing Interests: The authors declare no competing financial interest., (© 2021 The Authors. Published by American Chemical Society.)

Single atoms and few-atom nanoclusters are of high interest in catalysis and plasmonics, but pathways for their fabrication and placement remain scarce. We report here the self-assembly of room-temperature-stable single indium (In) atoms and few-atom In clusters (2-6 atoms) that are anchored to substitutional silicon (Si) impurity atoms in suspended monolayer graphene membranes. Using atomically resolved scanning transmission electron microscopy (STEM), we find that the symmetry of the In structures is critically determined by the three- or fourfold coordination of the Si "anchors". All structures are produced without electron-beam induced materials modification. In turn, when activated by electron beam irradiation in the STEM, we observe in situ the formation, restructuring, and translation of the Si-anchored In structures. Our results on In-Si-graphene provide a materials system for controlled self-assembly and heteroatomic anchoring of single atoms and few-atom nanoclusters on graphene.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

We present a detailed appraisal of the optical and plasmonic properties of ordered alloys of the form Au x Ag y Cu 1-x-y , as predicted by means of first-principles many-body perturbation theory augmented by a semi-empirical Drude-Lorentz model. In benchmark simulations on elemental Au, Ag, and Cu, we find that the random-phase approximation (RPA) fails to accurately describe inter-band transitions when it is built upon semi-local approximate Kohn-Sham density-functional theory band-structures. We show that non-local electronic exchange-correlation interactions sufficient to correct this, particularly for the fully-filled, relatively narrow d-bands which contribute strongly throughout the low-energy spectral range (0-6 eV), may be modeled very expediently using band-stretching operators that imitate the effect of a perturbative [Formula: see text] self-energy correction incorporating quasiparticle (QP) mass renormalization. We thereby establish a convenient work-flow for carrying out approximated [Formula: see text] spectroscopic calculations on alloys and, in particular here, we have considered alloy concentrations down to 12.5% in [Formula: see text], including all possible crystallographic orderings of face-centred cubic type. We develop a pragmatic procedure for calculating the Drude plasmon frequency from first principles, including self-energy effects, as well as a semi-empirical scheme for interpolating the plasmon inverse lifetimes between stoichiometries. A distinctive M-shaped profile is observed in both quantities for binary alloys, in qualitative agreement with previous experimental findings. A range of optical and plasmonic figures of merit are discussed, and plotted for ordered [Formula: see text] at three representative solid-state laser wavelengths. On this basis, we predict that certain compositions may offer improved performance over elemental Au for particular application types. We predict that while the loss functions for both bulk and surface plasmons are typically diminished in strength through binary alloying, certain stoichiometric ratios may exhibit higher-quality (longer-lived) localized surface-plasmons and surface-plasmon polaritons, at technologically-relevant wavelengths, than those in elemental Au.

Few-layer black phosphorus (BP) is a new two-dimensional material which is of great interest for applications, mainly in electronics. However, its lack of environmental stability severely limits its synthesis and processing. Here we demonstrate that high-quality, few-layer BP nanosheets, with controllable size and observable photoluminescence, can be produced in large quantities by liquid phase exfoliation under ambient conditions in solvents such as N-cyclohexyl-2-pyrrolidone (CHP). Nanosheets are surprisingly stable in CHP, probably due to the solvation shell protecting the nanosheets from reacting with water or oxygen. Experiments, supported by simulations, show reactions to occur only at the nanosheet edge, with the rate and extent of the reaction dependent on the water/oxygen content. We demonstrate that liquid-exfoliated BP nanosheets are potentially useful in a range of applications from ultrafast saturable absorbers to gas sensors to fillers for composite reinforcement.

Myoglobin modulates the binding of diatomic molecules to its heme group via hydrogen-bonding and steric interactions with neighboring residues, and is an important benchmark for computational studies of biomolecules. We have performed calculations on the heme binding site and a significant proportion of the protein environment (more than 1000 atoms) using linear-scaling density functional theory and the DFT+U method to correct for self-interaction errors associated with localized 3d states. We confirm both the hydrogen-bonding nature of the discrimination effect (3.6 kcal/mol) and assumptions that the relative strain energy stored in the protein is low (less than 1 kcal/mol). Our calculations significantly widen the scope for tackling problems in drug design and enzymology, especially in cases where electron localization, allostery, or long-ranged polarization influence ligand binding and reaction.