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Plasmonic near-field transducers (NFTs) play a key role in administering nanoscale heating for a number of applications ranging from medical devices to next generation data processing technology. We present a novel multi-scale approach, combining quantum many-body perturbation theory with finite-element modelling, to predict the electric and thermal material parameters of various Au-based, noble metal (M) alloys. Specifically, we focus on modelling their performance within an NFT designed to focus high-intensity, sub-diffracted light for technologies such as nanoscale etching, manipulation, sensing, and heat-assisted magnetic recording (HAMR). Elemental Au is the long-standing general-purpose NFT medium due its excellent plasmonic performance at relevant wavelengths. However, elemental Au is a soft, ductile material that tends to extrude and deform in response to extreme temperature gradients. Therefore, alloying Au with other noble metals such as Ag, Cu, Pd or Pt, has attracted considerable interest for improved mechanical and thermal robustness while reaching threshold plasmonic generation at standard optoelectronics operating wavelengths (e.g., $\approx 830$~nm) and approximate high-power NFT temperatures ($\approx 400$~K). We predict that certain Au-Ag alloys may offer improved thermal stability as whole-NFT media compared to elemental Au, alongside plasmonic figures of merit comparable to that of Au. Simulations of certain solid solution Au-Pd/Pt alloys enable us to predict significantly enhanced thermal conductivity. We predict that alloying with Pd at low concentrations $\sim 10\%$ may preserve the NFT performance of Au, while offering the benefits of improved thermal and mechanical stability., Comment: 8 pages, 4 figures, 1 table. Includes Supplemental Material with 10 tables

Burgess et al. have recently introduced the BLOR corrective exchange-correlation functional that is, by construction, the unique simplified rotationally-invariant DFT+U functional that enforces the flat-plane condition separately on each effective orbital of a localized subspace. Detached from the Hubbard model, functionals of this type are both double-counting correction free and, when optimized in situ using appropriate error quantifiers, effectively parameter free. In this work, the extension of the BLOR functional to address many-body errors (mBLOR) is derived. The mBLOR functional is built to enforce the flat-plane condition on the entire subspace, rather than on each orbital individually. In this way inter-orbital errors are corrected on the same footing as the single-particle ones. Focusing on exact test cases with strong inter-orbital interactions, the BLOR and mBLOR functionals were benchmarked against contemporary DFT+U functionals using the total energy extensivity condition on stretched homo-nuclear p-block dimers that represent various self-interaction and static-correlation error regimes. The BLOR functional outperformed all other DFT+$U$ functionals tested, which often act to increase total-energy errors, yet it still yielded large errors in some systems. mBLOR instead yielded low energy errors across all four strongly-correlated dimers, while being constructed using only semi-local approximation ingredients. As mBLOR would not otherwise introduce a band-gap correction in the manner that is a desirable feature of DFT+U, we developed a cost-free technique to reintroduce it automatically by moving the functional's unusual explicit derivative discontinuity into the potential. With this in place, mBLOR is the only known DFT$+U$ functional that opens the bandgap of stretched neutral homo-nuclear dimers without the aid of unphysical spin-symmetry breaking., Comment: As accepted for publication in Phys. Rev. B. 22 pages, 9 figures, and 4 tables

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 L\"owdin subspace representations are implemented and compared. Full analytical DFT+$U$+$J$ forces are implemented and benchmarked for the tensorial and L\"owdin 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 L\"owdin orthonormalization on the occupancies, calculated parameters, and derived properties.

Members of the DFT+U family of functionals are increasingly prevalent methods of addressing errors intrinsic to (semi-) local exchange-correlation functionals at minimum computational cost, but require their parameters U and J to be calculated in situ for a given system of interest, simulation scheme, and runtime parameters. The SCF linear response approach offers ab initio acquisition of the U and has recently been extended to compute the J analogously, which measures localized errors related to exchange-like effects. We introduce a renovated post-processor, the lrUJ utility, together with this detailed best-practices guide, to enable users of the popular, open-source Abinit first-principles simulation suite to engage easily with in situ Hubbard parameters and streamline their incorporation into material simulations of interest. Features of this utility, which may also interest users and developers of other DFT codes, include $n$-degree polynomial regression, error analysis, Python plotting facilities, didactic documentation, and avenues for further developments. In this technical introduction and guide, we place particular emphasis on the intricacies and potential pitfalls introduced by the projector augmented wave (PAW) method, SCF mixing schemes, and non-linear response, several of which are translatable to DFT+U(+J) implementations in other packages., Comment: 46 pages, 6 figures (+3 figures in appendix), 2 tables (+1 table in appendix)

The Niobium surface is almost always covered by a native oxide layer which greatly influences the performance of superconducting devices. Here we investigate the highly stable Niobium oxide overlayer of Nb(110), which is characterised by its distinctive nanocrystal structure as observed by scanning tunnelling microscopy (STM). Our ab-initio density functional theory (DFT) calculations show that a subtle reconstruction in the surface Niobium atoms gives rise to rows of 4-fold coordinated oxygen separated by regions of 3-fold coordinated oxygen. The 4-fold oxygen rows are determined to be the source of the nanocrystal pattern observed in STM, and the two chemical states of oxygen observed in core-level X-ray photoelectron spectroscopy (XPS) are ascribed to the 3-fold and 4-fold oxygens. Furthermore, we find excellent agreement between the DFT calculated electronic structure with scanning tunnelling spectroscopy and valence XPS measurements., Comment: 8 pages, 4 figures, plus 3 pages of Supporting Information

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 2 E_v[N_0] <= E_v[N_0 - 1] + E_v[N_0 + 1]. Using the infinite-separation-limit technique, this article 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 band-gap and the exchange-correlation derivative discontinuity of DFT., Comment: This Communication has been published in the Journal of Chemical Physics 159, 211102 (2023) which can be found at the following link: https://doi.org/10.1063/5.0174159

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 (DFT). The magnetic analog of the DFT Koopmans' theorem 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 non-integer 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., Comment: 13 pages, 7 figures

High-performance batteries, heterogeneous catalysts and next-generation photovoltaics often centrally involve transition metal oxides (TMOs) that undergo charge or spin-state changes. Demand for accurate DFT modeling of TMOs has increased in recent years, driving improved quantification and correction schemes for approximate DFT's characteristic errors, notably those pertaining to self-interaction and static correlation. Of considerable interest, meanwhile, is the use of DFT-accessible quantities to compute parameters of coarse-grained models such as for magnetism. To understand the interference of error corrections and model mappings, we probe the prototypical Mott-Hubbard insulator NiO, calculating its electronic structure in its antiferromagnetic I/II and ferromagnetic states. We examine the pronounced sensitivity of the first principles calculated Hubbard U and Hund's J parameters to choices concerning Projector Augmented Wave (PAW) based population analysis, we reevaluate spin quantification conventions for the Heisenberg model, and we seek to develop best practices for calculating Hubbard parameters specific to energetically meta-stable magnetic orderings of TMOs. Within this framework, we assess several corrective functionals using in situ calculated U and J parameters, e.g., DFT+U and DFT+U+J. We find that while using a straightforward workflow with minimal empiricism, the NiO Heisenberg parameter RMS error with respect to experiment was reduced to 13%, an advance upon the state-of-the-art. Methodologically, we used a linear-response implementation for calculating the Hubbard U available in the open-source plane-wave DFT code Abinit. We have extended its utility to calculate the Hund's exchange coupling J, however our findings are anticipated to be applicable to any DFT+U implementation., Comment: 19 pages, 5 figures (+2 in SI), 7 tables (+1 in SI). Accepted Nov. 14, 2023 to Physical Review B

We study the modification of the magnetocrystalline anisotropy (MCA) of Co slabs induced by several different conjugated molecular overlayers, i.e., benzene, cyclooctatetraene, naphthalene, pyrene and coronene. We perform first-principles calculations based on Density Functional Theory and the magnetic force theorem. Our results indicate that molecular adsorption tends to favour a perpendicular MCA at surfaces. A detailed analysis of various atom-resolved quantities, accompanied by an elementary model, demonstrates that the underlying physical mechanism is related to the metal-molecule interfacial hybridization and, in particular, to the chemical bonding between the molecular C $p_z$ and the out-of-plane Co $d_{z^2}$ orbitals. This effect can be estimated from the orbital magnetic moment of the surface Co atoms, a microscopic observable accessible to both theory and experiments. As such, we suggest a way to directly assess the MCA modifications at molecule-decorated surfaces, overcoming the limitations of experimental studies that rely on fits of magnetization hysteresis loops. Finally, we also study the interface between Co and both C$_{60}$ and Alq$_3$, two molecules that find widespread use in organic spintronics. We show that the modification of the surface Co MCA is similar upon adsorption of these two molecules, thereby confirming the results of recent experiments., Comment: 10 figures in main text and 3 in the SM, 20 pages

Multi-principal element materials (MPEMs) have been attracting a rapidly growing interest due to their exceptional performance under extreme conditions, from cryogenic conditions to extreme-high temperatures and pressures. Despite the simple conceptual premise behind their formation, computational high-throughput first-principles design of such materials is extremely challenging due to the large number of realizations required for sufficient statistical sampling of their design space. Furthermore, MPEMs are also known to develop short-ranged orderings (SROs) which can play a significant role in their stability and properties. Here, we present an expedient and efficient first-principles computational framework for assessing the compositional and mechanical properties of MPEMs, including SRO effects. This heuristic methodology systematically corrects phase-averaged free-energies of MPEMs to include SRO phases, while imposing constraints for materials design. To illustrate the methodology, we study the stability and mechanical properties of equi-molar refractory-metal high-entropy alloy carbonitrides (RHEA-CNs) such as ZrNbMoHfTaWC3N3. We show that SRO, arising due to preferential neighboring among refractory metals, is necessary for thermodynamic and mechanical stability and to satisfy the imposed design criteria, leading to complex compositions for which their molar fraction and mechanical properties are predicted., Comment: 7 pages, 4 figures, and 1 table. Supplemental Material of 20 pages, 10 figures, and 4 tables. 17MB

A new DFT+U type corrective functional is derived from first principles to enforce the flat plane condition on localized subspaces, thus dispensing with the need for an ad hoc derivation from the Hubbard model. The newly derived functional as given by equation 5 yields relative errors below 0.6% in the total energy of the dissociated s-block dimers as well as the dissociated H5+ ring system. In comparison bare PBE and PBE+U (using Dudarev's 1998 Hubbard functional) yields relative energetic errors as high as 8.0% and 20.5% respectively., Comment: 8 pages, 5 figures, plus 13 pages of Supplementary Information

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's 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 2000 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-d U and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-p U value results in a significantly improved agreement between the computed lattice parameters and experiment., Comment: 18 pages, 6 figures

First-principles Hubbard-corrected approximate density-functional theory (DFT+U) is a low-cost, potentially high throughput method of simulating materials, but it has been hampered by empiricism and inconsistent band-gap correction in transition-metal oxides. DFT+U property prediction of non-magnetic systems such as d0 and d10 transition-metal oxides is typically faced with excessively large calculated Hubbard U values, and with difficulty in obtaining acceptable band-gaps and lattice volumes. Meanwhile, Hund's exchange coupling J is an important but often neglected component of DFT+U, and the J parameter has proven challenging to directly calculate by means of linear response. In this work, we provide a revised formula for computing Hund's J using established self-consistent field DFT+U codes. For non-magnetic systems, we introduce a non-approximate technique for calculating U and J simultaneously in such codes, at no additional cost. Using unmodified Quantum ESPRESSO, we assess the resulting values using two different DFT+U functionals incorporating J, namely the widely used DFT+(U-J) and the readily available DFT+U+J. We assess a test set comprising TiO2, ZrO2, HfO2, Cu2O and ZnO, and apply the corrections both to metal and oxygen centered pseudoatomic subspaces. Starting from the PBE functional, we find that DFT+(U-J) is significantly out-performed in band-gap accuracy by DFT+U+J, the RMS band-gap error of which matches that of the hybrid functional HSE06. ZnO, a long-standing challenge case for DFT+U, is addressed by means of Zn 4s instead of Zn 3d correction, in which case the first-principles DFT+U+J band-gap error is half of that reported for HSE06., Comment: 32 pages 7 figures, 10 tables

Single atoms and few-atom nanoclusters are of high interest in catalysis and plasmonics, but pathways for their fabrication and stable 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 exact atomic arrangements of the In atoms depend strongly on the original coordination of the Si anchors in the graphene lattice: Single In atoms and In clusters with 3-fold symmetry readily form on 3-fold coordinated Si atoms, whereas 4-fold symmetric clusters are found attached to 4-fold coordinated Si atoms. All structures are produced by our fabrication route without the requirement for 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 dynamics of the Si-anchored In structures: Hexagon-centered 4-fold symmetric In clusters can (reversibly) transform into In chains or In dimers, whereas C-centered 3-fold symmetric In clusters can move along the zig-zag direction of the graphene lattice due to the migration of Si atoms during electron-beam irradiation, or transform to Si-anchored single In atoms. Our results provide a novel framework for the controlled self-assembly and heteroatomic anchoring of single atoms and few-atom clusters on graphene.

Liquid phase exfoliation is a commonly used method to produce 2D nanosheets from a range of layered crystals. However, such nanosheets display broad size and thickness distributions and correlations between area and thickness, issues that limit nanosheet application potential. To understand the factors controlling the exfoliation process, we have liquid-exfoliated 11 different layered materials, size-selecting each into fractions before using AFM to measure the nanosheet length, width, and thickness distributions for each fraction. The resultant data show a clear power-law scaling of nanosheet area with thickness for each material. We have developed a simple nonequilibrium thermodynamics-based model predicting that the power-law prefactor is proportional to both the ratios of in-plane-tearing/out-of-plane-peeling energies and in-plane/out-of-plane moduli. By comparing the experimental data with the modulus ratio calculated from first-principles, we find close agreement between experiment and theory. This supports our hypothesis that energy equipartition holds between nanosheet tearing and peeling during sonication-assisted exfoliation., Comment: Accepted Manuscript (30 pages) and Supporting Information (68 pages)

Titanium dioxide (TiO$_2$) presents a long-standing challenge for approximate Kohn-Sham density-functional theory (KS-DFT), as well as to its Hubbard-corrected extension, DFT+$U$. We find that a previously proposed extension of first-principles DFT+$U$ to incorporate a Hund's $J$ correction, termed DFT+$U$+$J$, in combination with parameters calculated using a recently proposed linear-response theory, predicts fundamental band-gaps accurate to well within the experimental uncertainty in rutile and anatase TiO$_2$. Our approach builds upon established findings that Hubbard correction to both titanium $3d$ and oxygen $2p$ subspaces in TiO$_2$, symbolically giving DFT+$U^{d,p}$, is necessary to achieve acceptable band-gaps using DFT+$U$. This requirement remains when the first-principles Hund's $J$ is included. We also find that the calculated gap depends on the correlated subspace definition even when using subspace-specific first-principles $U$ and $J$ parameters. Using the simplest reasonable correlated subspace definition and underlying functional, the local density approximation, we show that high accuracy results from using a relatively uncomplicated form of the DFT+$U$+$J$ functional. For closed-shell systems such as TiO$_2$, we describe how various DFT+$U$+$J$ functionals reduce to DFT+$U$ with suitably modified parameters, so that reliable band gaps can be calculated for rutile and anatase with no modifications to a conventional DFT+$U$ code., Comment: 13 pages, 3 figures, 5 tables + Supporting Information

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 TiO$_2$, reported $GW$ fundamental gaps can vary by more than 1 eV. In this work, we address the convergence and key approximations in contemporary $G_0W_0$ calculations, including frequency-integration schemes and the treatment of the Coulomb divergence in the exact-exchange term. We study several systems,and compare three different $GW$ codes: BerkeleyGW, Abinit and Yambo. We demonstrate, for the first time, that the same quasiparticle energies for systems in the condensed phase can be obtained with different codes, and we provide a comprehensive assessment of implementations of the $GW$ approximation.

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 (KS-DFT) band-structures. We show that non-local electronic exchange-correlation interactions sufficient to correct this, particularly for the fully-filled, relatively narrow $d$-bands that which contribute strongly throughout the low-energy spectral range ($0-6$ eV), may be modelled very expediently using band-stretching operators that imitate the effect of a perturbative G$_0$W$_0$ self-energy correction incorporating quasiparticle mass renormalization. We thereby establish a convenient work-flow for carrying out approximated G$_0$W$_0$+RPA spectroscopic calculations on alloys. 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 range of optical and plasmonic figures of merit are discussed at three representative solid-state laser wavelengths., Comment: 16 pages + 4 pages Supporting Information, 48 figures

State-of-the-art methods for calculating neutral excitation energies are typically demanding and limited to single electron-hole pairs and their composite plasmons. Here we introduce excitonic density-functional theory (XDFT) a computationally light, generally applicable, first-principles technique for calculating neutral excitations based on generalized constrained DFT. In order to simulate an M-particle excited state of an N-electron system, XDFT automatically optimizes a constraining potential to confine N-M electrons within the ground-state Kohn-Sham valence subspace. We demonstrate the efficacy of XDFT by calculating the lowest single-particle singlet and triplet excitation energies of the well-known Thiel molecular test set, with results which are in excellent agreement with time-dependent DFT. Furthermore, going beyond the capability of adiabatic time-dependent DFT, we show that XDFT can successfully capture double excitations. Overall our method makes optical gaps, excition bindings and oscillator strengths readily accessible at a computational cost comparable to that of standard DFT. As such, XDFT appears as an ideal candidate to work within high-throughput discovery frameworks and within linear-scaling methods for large systems., Comment: 6 pages, 4 figures

The density functional theory (DFT)+$U$ method is a pragmatic and effective approach for calculating the ground-state properties of strongly-correlated systems, and linear response calculations are widely used to determine the requisite Hubbard parameters from first principles. We provide a detailed treatment of spin within this linear response approach, demonstrating that the conventional Hubbard $U$ formula, unlike the conventional DFT+$U$ corrective functional, incorporates interactions that are off-diagonal in the spin indices and places greater weight on one spin channel over the other. We construct alternative definitions for Hubbard and Hund's parameters that are consistent with the contemporary DFT+$U$ functional, expanding upon the minimum-tracking linear response method. This approach allows Hund's $J$ and spin-dependent $U$ parameters to be calculated with the same ease as for the standard Hubbard $U$. Our methods accurately reproduce the experimental band gap, local magnetic moments, and the valence band edge character of manganese oxide, a canonical strongly-correlated system. We also apply our approach to a complete series of transition-metal complexes [M(H$_2$O)$_6$]$^{n+}$ (for M = Ti to Zn), showing that Hubbard corrections on oxygen atoms are necessary for preserving bond lengths, and demonstrating that our methods are numerically well-behaved even for near-filled subspaces such as in zinc. However, spectroscopic properties appear beyond the reach of the standard DFT+$U$ approach. Collectively, these results shed new light on the role of spin in the calculation of the corrective parameters $U$ and $J$, and point the way towards avenues for further development of DFT+$U$-type methods., Comment: 19 pages, 10 figures, 8 tables

We have developed a new and user-friendly interface energy calculation method that avoids problems deriving from numerical differences between bulk and slab calculations, such as the number of k points along the direction perpendicular to the interface. We have applied this to 36 bcc-fcc metal interfaces in the (100) orientation and found a clear dependence of the interface energy on the difference between the work functions of the two metals, on the one hand, and the total number of d electrons on the other. Greater mechanical deformations were observed in fcc crystals than in their bcc counterparts. For each bcc metal, the interface energy was found to follow the position of its d band, whereas the same was not observed for fcc., Comment: 10 pages, 7 figures, and 3 tables, with supporting information provided as an ancillary file. As accepted on 10th January 2018 for publication in Materials and Design, for which see https://doi.org/10.1016/j.matdes.2018.01.019

Pulay terms arise in the Hellman-Feynman forces in electronic structure calculations when one employs a basis set made of localized orbitals that move with their host atoms. If the total energy of the system depends on a subspace population defined in terms of the localized orbitals across multiple atoms, then unconventional Pulay terms will emerge due to the variation of the orbital nonorthogonality with ionic translation. Here, we derive the required exact expressions for such terms, which cannot be eliminated by orbital orthonormalization. We have implemented these corrected ionic forces within the linear-scaling density functional theory (DFT) package ONETEP, and have used constrained DFT to calculate the reorganization energy of a pentacene molecule adsorbed on a graphene flake. The calculations are performed by including ensemble DFT, corrections for periodic boundary conditions, and empirical Van der Waals interactions. For this system we find that tensorially invariant population analysis yields an adsorbate subspace population that is very close to integer-valued when based upon nonorthogonal Wannier functions, and also but less precisely when using pseudoatomic functions. Thus, orbitals can provide a very effective population analysis for constrained DFT. Our calculations show that the reorganization energy of the adsorbed pentacene is typically lower than that of pentacene in the gas phase. We attribute this effect to steric hindrance., Comment: 12 pages, 6 figures, and 2 tables. As accepted for publication in Physical Review B on 25th April 2018

We perform comprehensive density-functional theory calculations on strained two-dimensional phosphorus (P), arsenic (As) and antimony (Sb) in the monolayer, bilayer, and bulk $\alpha$-phase, from which we compute the key mechanical and electronic properties of these materials. Specifically, we compute their electronic band structures, band gaps, and charge-carrier effective masses, and identify the qualitative electronic and structural transitions that may occur. Moreover, we compute the elastic properties such as the Young's modulus $Y$; shear modulus $G$; bulk modulus $\mathcal{B}$; and Poisson ratio $\nu$ and present their isotropic averages of as well as their dependence on the in-plane orientation, for which the relevant expressions are derived. We predict strain-induced Dirac states in the monolayers of As and Sb and the bilayers of P, As, and Sb, as well as the possible existence of Weyl states in the bulk phases of P and As. These phases are predicted to support charge velocities up to $10^6$~$\textrm{ms}^{-1}$ and, in some highly anisotropic cases, permit one-dimensional ballistic conductivity in the puckered direction. We also predict numerous band gap transitions for moderate in-plane stresses. Our results contribute to the mounting evidence for the utility of these materials, made possible by their broad range in tuneable properties, and facilitate the directed exploration of their potential application in next-generation electronics., Comment: Final version accepted for publication in 2D Materials on 1/9/17. Keywords: phosphorene, arsenene, and antimonene. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence [http://creativecommons.org/licenses/by/3.0]. Any further distribution of this work must maintain attribution to the authors and the title of the work, journal citation and DOI

In electronic structure methods based on the correction of approximate density-functional theory (DFT) for systematic inaccuracies, Hubbard $U$ parameters may be used to quantify and amend the self-interaction errors ascribed to selected subspaces. Here, in order to enable the accurate, computationally convenient calculation of $U$ by means of DFT algorithms that locate the ground-state by direct total-energy minimization, we introduce a reformulation of the successful linear-response method for $U$ in terms of the fully-relaxed constrained ground-state density. Defining $U$ as an implicit functional of the ground-state density implies the comparability of DFT + Hubbard $U$ (DFT+$U$) total-energies, and related properties, as external parameters such as ionic positions are varied together with their corresponding first-principles $U$ values. Our approach provides a framework in which to address the partially unresolved question of self-consistency over $U$, for which plausible schemes have been proposed, and to precisely define the energy associated with subspace many-body self-interaction error. We demonstrate that DFT+$U$ precisely corrects the total energy for self-interaction error under ideal conditions, but only if a simple self-consistency condition is applied. Such parameters also promote to first-principles a recently proposed DFT+$U$ based method for enforcing Koopmans' theorem., Comment: 14 pages, 4 figures

We develop a generalization of the Kohn-Sham density functional theory (KS-DFT) + Hubbard $U$ (DFT+$U$) method to the excited-state regime. This has the form of Hubbard $U$ corrected linear-response time-dependent DFT, or `TDDFT+$U$'. Combined with calculated linear-response Hubbard $U$ parameters, it may provide a computationally light, first-principles method for the simulation of tightly-bound excitons on transition-metal ions. Our presented implementation combines linear-scaling DFT+$U$ and linear-scaling TDDFT, but the approach is broadly applicable. In detailed benchmark tests on two Ni-centred diamagnetic coordination complexes with variable $U$ values, it is shown that the Hubbard $U$ correction to an approximate adiabatic semi-local exchange-correlation interaction kernel lowers the excitation energies of transitions exclusively within the targeted localized subspace, by increasing the exciton binding of the corresponding electron-hole pairs. This partially counteracts the Hubbard $U$ correction to the exchange-correlation potential in KS-DFT, which increases excitation energies into, out of, and within the targeted localised subspace by modifying the underlying KS-DFT eigenspectrum. This compensating effect is most pronounced for optically dark transitions between localized orbitals of the same angular momentum, for which experimental observation may be challenging and theoretical approaches are at their most necessary. Overall, our results point to shortcomings in the contemporary DFT+$U$ corrective potential, either in its functional form, or when applied to transition-metal orbitals but not to ligand ones, or both., Comment: 21 pages, 36 figures, and 6 tables

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, $H_2^+$, 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., Comment: 7 pages, 5 figures. Accepted for Physical Review B Rapid Communications on 30th November 2016

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 formalisation, 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 fibre 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. Generalised expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by non-orthogonal 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 non-orthogonal 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-differences time integrators, and also better understand those already proposed., Comment: 20 pages. Accepted for Physical Review B on 10th March 2017

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 optimisation 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 new, non-perturbative 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 multi-constraint cDFT., Comment: 15 pages, 6 figures

Singlet fission (SF) is a multi-exciton 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, which and scales well to larger systems, thus enabling the study of screening effects. We propose a novel, 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., Comment: 9 pages, 4 figures

We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory (DMFT). This combination of methods explicitly accounts for dynamical and multi-reference quantum physics, such as valence and spin fluctuations, of the 3d electrons, whilst treating a significant proportion of the protein (more than 1000 atoms) with density functional theory. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of many body-effects induced by the Hund's coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin., Comment: 7 pages, 5 figures. Accepted for publication in the Proceedings of the National Academy of Sciences of the United States of America (2014). For the published article see http://www.pnas.org/content/early/2014/04/09/1322966111.abstract

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., Comment: 15 pages, 3 figures. Supplementary material 8 pages, 3 figures. This version matches that accepted for J. Phys. Chem. Lett. on 10th May 2012

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 five, the strong imbalance in the binding energies of heme with CO and O_2 ligands., Comment: 5 pages, 4 figures. Supplementary material 12 pages, 5 figures. This version (v2) matches that accepted for Physical Review Letters on 31 January 2013

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 11 (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 efficiently, with no necessity for post-processing optimization, and with an accuracy comparable to MLWFs., Comment: 5 pages, 1 figure. This version matches that accepted for Physical Review B on 4th May 2012

Vanadium dioxide undergoes a first order metal-insulator transition at 340 K. In this work, we develop and carry out state of the art linear scaling DFT calculations refined with non-local dynamical mean-field theory. We identify a complex mechanism, a Peierls-assisted orbital selection Mott instability, which is responsible for the insulating M$_1$ phase, and furthermore survives a moderate degree of disorder., Comment: 5 pages, 4 figures. Supplementary material 8 pages, 4 figures. This version (v2) matches that accepted for Physical Review Letters on 16th May 2012

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 apply it to a local-orbital DFT method including in 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 nano-clusters with sizes exceeding 7,000 atoms., Comment: 10 pages, 4 figures. This version (v3) matches that accepted for Physical Review B on 30th January 2012

We present a generalized definition of subspace occupancy matrices in ab initio methods for strongly correlated materials, such as DFT+U and DFT+DMFT, which is appropriate to the case of nonorthogonal projector functions. By enforcing the tensorial consistency of all matrix operations, we are led to a subspace projection operator for which the occupancy matrix is tensorial and accumulates only contributions which are local to the correlated subspace at hand. For DFT+U in particular, the resulting contributions to the potential and ionic forces are automatically Hermitian, without resort to symmetrization, and localized to their corresponding correlated subspace. The tensorial invariance of the occupancies, energies and ionic forces is preserved. We illustrate the effect of this formalism in a DFT+U study using self-consistently determined projectors., Comment: 15 pages, 8 figures. This version (v2) matches that accepted for Physical Review B on 15th April 2011

We present a formulation of the density-functional theory + Hubbard model (DFT+U) method that is self-consistent over the choice of Hubbard projectors used to define the correlated subspaces. In order to overcome the arbitrariness in this choice, we propose the use of non-orthogonal generalized Wannier functions (NGWFs) as projectors for the DFT+U correction. We iteratively refine these NGWF projectors and, hence, the DFT+U functional, such that the correlated subspaces are fully self-consistent with the DFT+U ground-state. We discuss the convergence characteristics of this algorithm and compare ground-state properties thus computed with those calculated using hydrogenic projectors. Our approach is implemented within, but not restricted to, a linear-scaling DFT framework, opening the path to DFT+U calculations on systems of unprecedented size., Comment: 4 pages, 3 figures. This version (v2) matches that accepted for Physical Review B Rapid Communications on 26th July 2010