arXiv subjects

Edward Linscott

Publications and source records attributed to Edward Linscott.

13 recordsLinked to original sources

arXiv2026

DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors

Hubbard-corrected density-functional theory (DFT+$U$) is a popular tool for first-principles modeling of materials with localized $d$ or $f$ electrons, but its on-site corrections tend to over-localize charge and break covalent bonds. Inter-site $+V$ corrections were introduced to counter this and are now widely used, but a formal justification has been lacking. Here we show that -- to first order in $V/U$ -- inter-site corrections are exactly equivalent to on-site DFT+$U$ evaluated on a density-matrix-dependent redefinition of the Hubbard projectors, hybridized with those of neighboring sites, providing insight into the explicit mechanism by which $V$ affects covalency. If the projectors are held frozen, as is common practice, the equivalence partially breaks down. Beyond reinterpreting the formalism, these results sharpen the questions of how $V$ should be computed and what the Hubbard subspaces fundamentally are.

cond-mat.mtrl-sci↗

arXiv2024

Predicting the suitability of photocatalysts for water splitting using Koopmans spectral functionals: The case of TiO$_2$ polymorphs

Photocatalytic water splitting has attracted considerable attention for renewable energy production. Since the first reported photocatalytic water splitting by titanium dioxide, this material remains one of the most promising photocatalysts, due to its suitable band gap and band-edge positions. However, predicting both of these properties is a challenging task for existing computational methods. Here we show how Koopmans spectral functionals can accurately predict the band structure and level alignment of rutile, anatase, and brookite TiO$_2$ using a computationally efficient workflow that only requires (a) a DFT calculation of the photocatalyst/vacuum interface and (b) a Koopmans spectral functional calculation of the bulk photocatalyst. The success of this approach for TiO$_2$ suggests that this strategy could be deployed for assessing the suitability of novel photocatalyst candidates.

cond-mat.mtrl-sci↗

arXiv2024

Predicting electronic screening for fast Koopmans spectral functional calculations

Koopmans spectral functionals are a powerful extension of Kohn-Sham density-functional theory (DFT) that enable the prediction of spectral properties with state-of-the-art accuracy. The success of these functionals relies on capturing the effects of electronic screening through scalar, orbital-dependent parameters. These parameters have to be computed for every calculation, making Koopmans spectral functionals more expensive than their DFT counterparts. In this work, we present a machine-learning model that -- with minimal training -- can predict these screening parameters directly from orbital densities calculated at the DFT level. We show on two prototypical use cases that using the screening parameters predicted by this model, instead of those calculated from linear response, leads to orbital energies that differ by less than 20 meV on average. Since this approach dramatically reduces run-times with minimal loss of accuracy, it will enable the application of Koopmans spectral functionals to classes of problems that previously would have been prohibitively expensive, such as the prediction of temperature-dependent spectral properties. More broadly, this work demonstrates that measuring violations of piecewise linearity (i.e. curvature in total energies with respect to occupancies) can be done efficiently by combining frozen-orbital approximations and machine learning.

cond-mat.mtrl-sci↗

arXiv2024

On-site and inter-site Hubbard corrections in magnetic monolayers: The case of FePS$_3$ and CrI$_3$

Hubbard-corrected density-functional theory has proven to be successful in addressing self-interaction errors in 3D magnetic materials. However, the effectiveness of this approach for 2D magnetic materials has not been extensively explored. Here, we use PBEsol+$\textit{U}$ and its extensions PBEsol+$\textit{U}$+$\textit{V}$ to investigate the electronic, structural, and vibrational properties of 2D antiferromagnetic FePS$_3$ and ferromagnetic CrI$_3$, and compare the monolayers with their bulk counterparts. Hubbard parameters (on-site $\textit{U}$ and inter-site $\textit{V}$) are computed self-consistently using density-functional perturbation theory, thus avoiding any empirical assumptions. We show that for FePS$_3$ the Hubbard corrections are crucial in obtaining the experimentally observed insulating state with the correct crystal symmetry, providing also vibrational frequencies in good agreement with Raman experiments. For ferromagnetic CrI$_3$, we discuss how a straightforward application of Hubbard corrections worsens the results and introduces a spurious separation between spin-majority and minority conduction bands. Promoting the Hubbard $\textit{U}$ to be a spin-resolved parameter - that is, applying different (first-principles) values to the spin-up and spin-down manifolds - recovers a more physical picture of the electronic bands and delivers the best comparison with experiments.

cond-mat.mtrl-sci↗

arXiv2023

The Convexity Condition of Density-Functional Theory

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.

physics.chem-ph↗

arXiv2023

koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity condition to the entire electronic manifold, ensuring that orbital energies match the corresponding electron removal/addition energy differences (in contrast to semi-local DFT, where a mismatch between the two lies at the heart of the band gap problem and, more generally, the unreliability of Kohn-Sham orbital energies). This strategy has proven to be very powerful, yielding molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost while preserving a functional formulation. This paper reviews the theory of Koopmans functionals, discusses the algorithms necessary for their implementation, and introduces koopmans, an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations and obtain reliable spectral properties of molecules and materials.

cond-mat.mtrl-sci↗

arXiv2023

The tilted-plane structure of the energy of finite quantum systems

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.

cond-mat.str-el↗

arXiv2023

Testing Koopmans spectral functionals on the analytically-solvable Hooke's atom

Koopmans spectral functionals are a class of orbital-density-dependent functionals designed to accurately predict spectroscopic properties. They do so markedly better than their Kohn-Sham density-functional theory counterparts, as demonstrated in earlier works on benchmarks of molecules and bulk systems. This work is a complementary study where -- instead of comparing against real, many-electron systems -- we test Koopmans spectral functionals on Hooke's atom, a toy two-electron system that has analytical solutions for particular strengths of its harmonic confining potential. As these calculations clearly illustrate, Koopmans spectral functionals do an excellent job of describing Hooke's atom across a range of confining potential strengths. This work also provides broader insight into the features and capabilities of Koopmans spectral functionals more generally.

physics.chem-ph↗

arXiv2022

A DFT+U type functional derived to explicitly address the flat plane condition

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.

cond-mat.str-el↗

arXiv2022

Koopmans spectral functionals in periodic-boundary conditions

Koopmans spectral functionals aim to describe simultaneously ground state properties and charged excitations of atoms, molecules, nanostructures and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically motivated orbital-density-dependent corrections. These corrections act on a set of localized orbitals that, in periodic systems, resemble maximally localized Wannier functions. At variance with the original, direct supercell implementation [Phys. Rev. X 8, 021051 (2018)], we discuss here i) the complex but efficient formalism required for a periodic-boundary code using explicit Brillouin zone sampling, and ii) the calculation of the screened Koopmans corrections with density-functional perturbation theory. In addition to delivering improved scaling with system size, the present development makes the calculation of band structures with Koopmans functionals straightforward. The implementation in the open-source Quantum ESPRESSO distribution and the application to prototypical insulating and semiconducting systems are presented and discussed.

cond-mat.mtrl-sci↗

arXiv2022

Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals

Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the occupation of any orbital. In crystalline materials, due to the orbital-density-dependent nature of the functionals, minimization of the total energy to a ground state provides a set of minimizing variational orbitals that are localized and thus break the periodicity of the underlying lattice. Despite this, we show that Bloch symmetry can be preserved and it is possible to describe the electronic states with a band-structure picture, thanks to the Wannier-like character of the variational orbitals. We also present a method to unfold and interpolate the electronic bands from supercell ($Γ$-point) calculations, which enables us to calculate full band structures with Koopmans-compliant functionals. The results obtained for a set of benchmark semiconductors and insulators show very good agreement with state-of-the-art many-body perturbation theory and experiments, underscoring the reliability of these spectral functionals in predicting band structures.

cond-mat.mtrl-sci↗

arXiv2022

High-throughput determination of Hubbard U and Hund J values for transition metal oxides via linear response formalism

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.

cond-mat.mtrl-sci↗

arXiv2019

Super-exchange mechanism and quantum many body excitations in the archetypal hemocyanin/tyrosinase di-Cu oxo-bridge

We perform first-principles quantum mechanical studies of dioxygen ligand binding to the hemocyanin protein. Electronic correlation effects in the functional site of hemocyanin are investigated using a state-of-the-art approach, treating the localised copper 3\emph{d} electrons with cluster dynamical mean field theory (DMFT) for the first time. This approach has enabled us to account for dynamical and multi-reference quantum mechanics, capturing valence and spin fluctuations of the 3\emph{d} electrons. Our approach explains the stabilisation of the experimentally observed di-Cu singlet for the butterflied Cu$_2$O$_2$ core, with localised charge and incoherent scattering processes across the oxo-bridge that prevent long-lived charge excitations, suggesting that the magnetic structure of hemocyanin is largely influenced by the many-body corrections. Our computational model is supported by agreement with experimental optical absorption data, and provides a revised understanding of the bonding of the peroxide to the di-Cu system \emph{in vivo}.

cond-mat.str-el↗