arXiv subjects

Eli Kraisler

Publications and source records attributed to Eli Kraisler.

At least 19 recordsLinked to original sources

arXiv2026

Many-electron systems with fractional electron number and spin: exact properties above and below the equilibrium total spin value

In this work, we analyze the fundamental question of what is the ensemble ground state of a general, finite, many-electron system at zero temperature, with a given, possibly fractional, electron number $N_{tot}$ and a given $z$-projection of the spin, $M_{tot}$, distinguishing between low- and high-spin cases. For the low-spin case, the general form of the ensemble ground state has been rigorously derived in J. Phys. Chem. Lett. 15, 2337 (2024), finding the presence of an ambiguity in the ground state. Here we further discuss this ambiguity, and show that it can be removed via maximization of the entropy. For the high-spin case, we find that the form of the ensemble ground state strongly depends on the system in question. Furthermore, we prove three general properties which characterize the ensemble, and narrow the list of pure states it may consist of. We relate the frontier Kohn-Sham orbital energies to total energy differences, providing a generalization of the ionization potential theorem to systems with arbitrary fractional $M_{tot}$. Furthermore, we derive expressions for new derivative discontinuities, which appear as jumps in the KS potentials when crossing a boundary in the $N_{\uparrow}$-$N_{\downarrow}$ plane. Our analytical results are supported by an extensive numerical analysis of the Atomic Spectra Database of the National Institute of Standards. The new exact conditions for many-electron systems derived in this work are instrumental for development of advanced approximations in density functional theory and other many-electron methods.

cond-mat.mtrl-sci↗

arXiv2024

Spin migration in density functional theory: energy, potential and density perspectives

Spin is a fundamental property of any many-electron system. The ability of density functional theory to accurately predict the physical properties of a system, while varying its spin, is crucial for describing magnetic materials and high-spin molecules, spin flip, magnetization and demagnetization processes. Within density functional theory, when using various exchange-correlation approximations, the exact dependence of the energy on the spin often deviates from the exact constant or piecewise-linear behavior, which is directly related to the problem of strong (static) correlation and challenges the description of molecular dissociation. In this paper, we study the behavior of the energy, the frontier Kohn-Sham (KS) orbitals, the KS potentials and the electron density, with respect to fractional spin, in different atomic systems. We analyze five standard exchange-correlation functionals and find three main scenarios of deviation from the expected exact results. We clearly recognize a jump in the frontier orbital energies upon spin variation in the exact exchange and in hybrid functionals, and the related plateau in the corresponding KS potential. Our results are instrumental for the assessment of the quality of existing approximations from a new perspective and for the development of advanced functionals with sensitivity to magnetic properties.

physics.chem-ph↗

arXiv2024

Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized

Description of many-electron systems with a fractional electron number $N_\textrm{tot}$ and fractional spin $M_\textrm{tot}$ is of great importance in physical chemistry, solid state physics and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system, and characterize the dependence of the energy and the spin-densities on both $N_\textrm{tot}$ and $M_\textrm{tot}$, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at constant $N_\textrm{tot}$, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

cond-mat.mtrl-sci↗

arXiv2023

Physics-enhanced neural networks for equation-of-state calculations

Rapid access to accurate equation-of-state (EOS) data is crucial in the warm-dense matter regime, as it is employed in various applications, such as providing input for hydrodynamic codes to model inertial confinement fusion processes. In this study, we develop neural network models for predicting the EOS based on first-principles data. The first model utilizes basic physical properties, while the second model incorporates more sophisticated physical information, using output from average-atom calculations as features. Average-atom models are often noted for providing a reasonable balance of accuracy and speed; however, our comparison of average-atom models and higher-fidelity calculations shows that more accurate models are required in the warm-dense matter regime. Both the neural network models we propose, particularly the physics-enhanced one, demonstrate significant potential as accurate and efficient methods for computing EOS data in warm-dense matter.

physics.comp-ph↗

arXiv2023

Ionization Potentials and Fundamental Gaps in Atomic Systems from the Ensemble-DFT Approach

Calculations in Kohn-Sham density functional theory crucially rely on high-quality approximations for the exchange-correlation (xc) functional. Standard local and semi-local approximations fail to predict the ionization potential (IP) and the fundamental gap, departing from the Kohn-Sham orbital energies, due to the deviation of the total energy from piecewise-linearity and the absence of the derivative discontinuity. The ensemble generalization procedure introduced in Phys. Rev. Lett. 110, 126403 (2013) restores, to a large extent, these features in any approximate xc functional and improves its ability to predict the IP and the fundamental gap with negligible additional computational effort. In this work we perform an extensive study of atoms and first ions across the Periodic Table, generalizing the local spin-density and the Perdew-Burke-Ernzerhof approximations. By applying the ensemble generalization to a variety of systems, with s-, p- and d-character, we assess the accuracy of the method and identify important trends. In particular, we find that the accuracy of our approach heavily depends on the character of the frontier orbitals: when d-orbitals are involved, the performance is far less accurate. Possible sources of error are discussed and ways for further improvement are outlined.

cond-mat.mtrl-sci↗

arXiv2023

Improved calculations of mean ionization states with an average-atom model

The mean ionization state (MIS) is a critical property in dense plasma and warm dense matter research, for example as an input to hydrodynamics simulations and Monte-Carlo simulations. Unfortunately, however, the best way to compute the MIS remains an open question. Average-atom (AA) models are widely-used in this context due to their computational efficiency, but as we show here, the canonical approach for calculating the MIS in AA models is typically insufficient. We therefore explore three alternative approaches to compute the MIS. Firstly, we modify the canonical approach to change the way electrons are partitioned into bound and free states; secondly, we develop a novel approach using the electron localization function; finally, we extend a method which uses the Kubo-Greenwood conductivity to our average-atom model. Through comparisons with higher-fidelity simulations and experimental data, we find that any of the three new methods usually out-performs the canonical approach, with the electron localization function and Kubo-Greenwood methods showing particular promise.

physics.plasm-ph↗

arXiv2022

atoMEC: An open-source average-atom Python code

Average-atom models are an important tool in studying matter under extreme conditions, such as those conditions experienced in planetary cores, brown and white dwarfs, and during inertial confinement fusion. In the right context, average-atom models can yield results with similar accuracy to simulations which require orders of magnitude more computing time, and thus can greatly reduce financial and environmental costs. Unfortunately, due to the wide range of possible models and approximations, and the lack of open-source codes, average-atom models can at times appear inaccessible. In this paper, we present our open-source average-atom code, atoMEC. We explain the aims and structure of atoMEC to illuminate the different stages and options in an average-atom calculation, and to facilitate community contributions. We also discuss the use of various open-source Python packages in atoMEC, which have expedited its development.

physics.plasm-ph↗

arXiv2022

The Geometric Potential of the Exact Electron Factorization: Meaning, significance and application

The theoretical and computational description of materials properties is a task of utmost scientific and technological importance. A first-principles description of electron-electron interactions poses an immense challenge that is usually approached by converting the many-electron problem to an effective one-electron problem. There are different ways to obtain an exact one-electron theory for a many-electron system. An emergent method is the exact electron factorization (EEF) -- one of the branches of the Exact Factorization approach to many-body systems. In the EEF, the Schrödinger equation for one electron, in the environment of all other electrons, is formulated. The influence of the environment is reflected in the potential $v^{\rm H}$, which represents the energy of the environment, and in a potential $v^{\rm G}$, which has a geometrical meaning. In this paper, we focus on $v^{\rm G}$ and study its properties in detail. We investigate the geometric origin of $v^{\rm G}$ as a metric measuring the change of the environment, exemplify how translation and scaling of the state of the environment are reflected in $v^{\rm G}$, and explain its shape for homo- and heteronuclear diatomic model systems. Based on the close connection between the EEF and density functional theory, we also use $v^{\rm G}$ to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.

physics.chem-ph↗

arXiv2022

First-principles derivation and properties of density-functional average-atom models

Finite-temperature Kohn--Sham density-functional theory (KS-DFT) is a widely-used method in warm dense matter (WDM) simulations and diagnostics. Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with temperature and there remains uncertainty regarding the performance of existing approximate exchange-correlation (XC) functionals under WDM conditions. Of particular concern is the expected explicit dependence of the XC functional on temperature, which is absent from most approximations. Average-atom (AA) models, which significantly reduce the computational cost of KS-DFT calculations, have therefore become an integral part of WDM modelling. In this paper, we present a derivation of a first-principles AA model from the fully-interacting many-body Hamiltonian, carefully analysing the assumptions made and terms neglected in this reduction. We explore the impact of different choices within this model -- such as boundary conditions and XC functionals -- on common properties in WDM, for example equation-of-state data, ionization degree and the behaviour of the frontier energy levels. Furthermore, drawing upon insights from ground-state KS-DFT, we discuss the likely sources of error in KS-AA models and possible strategies for mitigating such errors.

cond-mat.mtrl-sci↗

arXiv2021

On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory

There are different ways to obtain an exact one-electron theory for a many-electron system, and the exact electron factorization (EEF) is one of them. In the EEF, the Schrödinger equation for one electron in the environment of other electrons is constructed. The environment provides the potentials that appear in this equation: A scalar potential $v^{\rm H}$ representing the energy of the environment and another scalar potential $v^{\rm G}$ as well as a vector potential that have geometric meaning. By replacing the interacting many-electron system with the non-interacting Kohn-Sham (KS) system, we show how the EEF is related to density functional theory (DFT) and we interpret the Hartree-exchange-correlation potential as well as the Pauli potential in terms of the EEF. In particular, we show that from the EEF viewpoint, the Pauli potential does not represent the difference between a fermionic and a bosonic non-interacting system, but that it corresponds to $v^{\rm G}$ and partly to $v^{\rm H}$ for the (fermionic) KS system. We then study the meaning of $v^{\rm G}$ in detail: Its geometric origin as a metric measuring the change of the environment is presented. Additionally, its behavior for a simple model of a homo- and heteronucler diatomic is investigated and interpreted with the help of a two-state model. In this way, we provide a physical interpretation for the one-electron potentials that appear in the EEF and in DFT.

physics.chem-ph↗

arXiv2021

Charge-transfer steps in Density Functional Theory from the perspective of the Exact Electron Factorization

When a molecule dissociates, the exact Kohn-Sham (KS) and Pauli potentials may form step structures. Reproducing these steps correctly is central for the description of dissociation and charge-transfer processes in density functional theory (DFT): The steps align the KS eigenvalues of the dissociating subsystems relative to each other and determine where electrons localize. While the step height can be calculated from the asymptotic behavior of the KS orbitals, this provides limited insight into what causes the steps. We give an explanation of the steps with an exact mapping of the many-electron problem to a one-electron problem, the exact electron factorizaton (EEF). The potentials appearing in the EEF have a clear physical meaning that translates to the DFT potentials by replacing the interacting many-electron system with the KS system. With a simple model of a diatomic, we illustrate that the steps are a consequence of spatial electron entanglement and are the result of a charge transfer. From this mechanism, the step height can immediately be deduced. Moreover, two methods to approximately reproduce the potentials during dissociation suggest themselves. One is based on the states of the dissociated system, while the other one is based on an analogy to the Born-Oppenheimer treatment of a molecule. The latter method also shows that the steps connect adiabatic potential energy surfaces. The view of DFT from the EEF thus provides a better understanding of how many-electron effects are encoded in a one-electron theory and how they can be modeled.

physics.chem-ph↗

arXiv2021

From Kohn-Sham to many-electron energies via step structures in the exchange-correlation potential

Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy ($Δ$), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential, in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

cond-mat.mtrl-sci↗

arXiv2015

One-electron self-interaction and the asymptotics of the Kohn-Sham potential: an impaired relation

One-electron self-interaction and an incorrect asymptotic behavior of the Kohn-Sham exchange-correlation potential are among the most prominent limitations of many present-day density functionals. However, a one-electron self-interaction-free energy does not necessarily lead to the correct long-range potential. This is here shown explicitly for local hybrid functionals. Furthermore, carefully studying the ratio of the von Weizsäcker kinetic energy density to the (positive) Kohn-Sham kinetic energy density, $τ_\mathrm{W}/τ$, reveals that this ratio, which frequently serves as an iso-orbital indicator and is used to eliminate one-electron self-interaction effects in meta-generalized-gradient approximations and local hybrid functionals, can fail to approach its expected value in the vicinity of orbital nodal planes. This perspective article suggests that the nature and consequences of one-electron self-interaction and some of the strategies for its correction need to be reconsidered.

physics.chem-ph↗

arXiv2015

Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

There are several approximations to the exchange-correlation functional in density-functional theory that accurately predict total energy-related properties of many-electron systems, such as binding energies, bond lengths, and crystal structures. Other approximations are designed to describe potential-related processes, such as charge transfer and photoemission. However, the development of a functional which can serve the two purposes simultaneously is a long-standing challenge. Trying to address it, we employ in the current work the ensemble generalization procedure proposed in Phys. Rev. Lett. 110, 126403 (2013). Focusing on the prediction of the ionization potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety of exchange-correlation approximations: the local spin-density approximation, semi-local generalized gradient approximations, and global and local hybrid functionals. Results for a test set of 26 diatomic molecules and single atoms are presented. We find that the aforementioned ensemble generalization systematically improves the prediction of the ionization potential, for various systems and exchange-correlation functionals, without compromising the accuracy of total energy-related properties. We specifically examine hybrid functionals. These depend on a parameter controlling the ratio of semi-local to non-local functional components. The ionization potential obtained with ensemble-generalized functionals is found to depend only weakly on the parameter value, contrary to common experience with non-generalized hybrids, thus eliminating one aspect of the so-called `parameter dilemma' of hybrid functionals.

physics.chem-ph↗

arXiv2015

Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations

The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation (xc) energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional - the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.

cond-mat.mtrl-sci↗

arXiv2015

Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density functional theory using the ensemble-generalization approach

Many approximations within density-functional theory spuriously predict that a many-electron system can dissociate into fractionally charged fragments. Here, we revisit the case of dissociated diatomic molecules, known to exhibit this problem when studied within standard approaches, including the local spin-density approximation (LSDA). By employing our recently proposed [E. Kraisler and L. Kronik, Phys. Rev. Lett. 110, 126403 (2013)] ensemble-generalization we find that asymptotic fractional dissociation is eliminated in all systems examined, even if the underlying exchange-correlation (xc) is still the LSDA. Furthermore, as a result of the ensemble generalization procedure, the Kohn-Sham potential develops a spatial step between the dissociated atoms, reflecting the emergence of the derivative discontinuity in the xc energy functional. This step, predicted in the past for the exact Kohn-Sham potential and observed in some of its more advanced approximate forms, is a desired feature that prevents any fractional charge transfer between the system's fragments. It is usually believed that simple xc approximations such as the LSDA cannot develop this step. Our findings show, however, that ensemble generalization to fractional electron densities automatically introduces the desired step even to the most simple approximate xc functionals and correctly predicts asymptotic integer dissociation.

physics.chem-ph↗

arXiv2014

A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues

We present and test a new approximation for the exchange-correlation (xc) energy of Kohn-Sham density functional theory. It combines exact exchange with a compatible non-local correlation functional. The functional is by construction free of one-electron self-interaction, respects constraints derived from uniform coordinate scaling, and has the correct asymptotic behavior of the xc energy density. It contains one parameter that is not determined ab initio. We investigate whether it is possible to construct a functional that yields accurate binding energies and affords other advantages, specifically Kohn-Sham eigenvalues that reliably reflect ionization potentials. Tests for a set of atoms and small molecules show that within our local-hybrid form accurate binding energies can be achieved by proper optimization of the free parameter in our functional, along with an improvement in dissociation energy curves and in Kohn-Sham eigenvalues. However, the correspondence of the latter to experimental ionization potentials is not yet satisfactory, and if we choose to optimize their prediction, a rather different value of the functional's parameter is obtained. We put this finding in a larger context by discussing similar observations for other functionals and possible directions for further functional development that our findings suggest.

physics.chem-ph↗

arXiv2014

Higher Ionization Energies of Atoms in Density Functional Theory

Density functional theory (DFT) is an exact alternative formulation of quantum mechanics, in which it is possible to calculate the total energy, the spin and the charge density of many-electron systems in the ground state. In practice, it is necessary to use uncontrolled approximations that can mainly be verified against experimental data. Atoms and ions are simple systems, where the approximations of DFT can be easily tested. We have calculated within DFT the total energies, spin and higher ionization energies of all the ions of elements with 1 $\leq$ Z $\leq$ 29. We find the calculations in close agreement with experiment, with an error of typically less than ca. 1% for 1 $\leq$ Z $\leq$ 29. Surprisingly, the error depends on the electronic configuration of the ion in both local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof general gradient approximation (PBE-GGA) and independent of both self-interaction correction (SIC) and relativistic corrections. Larger errors are found for systems in which the spin-spin correlation is significant, which indicates the possible benefit from an orbital-dependent formulation of the correlation energy functional.

physics.atom-ph↗