Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude and location. We use systems of a few electrons, where the exact electron density is known, to demonstrate general properties of steps. We find that steps occur at points in the electron density where there is a change in the 'local effective ionization energy' of the electrons. We provide practical arguments, based on the electron density, for determining the position, shape and height of steps for ground-state systems, and extend the concepts to time-dependent systems. These arguments are intended to inform the development of approximate functionals, such as the mixed localization potential (MLP), which already demonstrate their capability to produce steps in the Kohn-Sham potential.PACS numbers: 31.15. 71.15.Mb, 31.15.A,
Accurate density functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features in this regard are the spatially uniform shift in the potential, as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form, for example, between the atoms of stretched molecules. Although both aforementioned concepts are well known, the exact relationship between them remained unclear. Here we establish this relationship via an analytical derivation. We support our result by numerically solving the many-electron Schrödinger equation to extract the exact Kohn-Sham potential and directly observe its features. Spatial steps in the exact xc potential of a full configuration-interaction (FCI) calculation of a molecule are presented in three dimensions.
By propagating the many-body Schrödinger equation, we determine the exact time-dependent Kohn-Sham potential for a system of strongly correlated electrons which undergo field-induced tunneling. Numerous features are entirely absent from the approximations commonly used in time-dependent density-functional theory. The self-interaction correction is strong and time dependent, owing to electron localization, and prominent dynamic spatial potential steps arise from minima in the charge density, as modified by the Coulomb interaction experienced by the partially tunneled electron.
We introduce a new functional for simulating ground-state and time-dependent electronic systems within density-functional theory. The functional combines an expression for the exact Kohn-Sham (KS) potential in the limit of complete electron localization with a measure of the actual localization. We find accurate self-consistent charge densities, even for systems where the exact exchangecorrelation potential exhibits non-local dependence on the density, such as potential steps. We compare our results to the exact KS potential for each system. The self-interaction correction is accurately described, avoiding the need for orbital-dependent potentials.PACS numbers: 71.15. Mb, 73.63.Nm, Density-functional theory (DFT) [1] is the most widely used tool for the simulation of many-electron systems in numerous fields of physics, chemistry and materials science. Its success hinges on approximations [2,3] to the exchange-correlation (xc) part of the Kohn-Sham (KS) functional, which perform well across a range of groundstate systems. However, these approximations become much less secure in the presence of strong correlation [4,5] and/or current flow [6][7][8][9][10]. Particular attention has been given to improving the time-dependent xc potential, used within time-dependent DFT (TDDFT) [11], where the use of adiabatic functionals of the electron density ignores the role of currents and memory effects.In this Letter we demonstrate that electron localization, driven by the Coulomb interaction and the Pauli principle, can form a powerful ingredient in approximations for the KS potential. The electron localization function (ELF), L(x), as in Ref. 12, provides a useful indicator of localization: L = 1 is complete localization, i.e. the chance of finding one electron in the vicinity of another is zero. L(x) ranges from 0 to 1, and a homogeneous electron gas (HEG) has L = 0.5.Our starting point is the KS potential of Refs. 13 and 14, originally derived for a system of two spinful electrons in their spin-zero ground state. We observe that the logic applies exactly to any one-electron system, and, indeed, in a general system, to all regions of space where the electron density is dominated by any one Kohn-Sham orbital [15]. For such a region the KS equations may be approximated as [16] − 1 2 2 + V KS √ n = ε k √ n for the dominant orbital φ k , where n ≈ |φ k | 2 in the region, yielding the ground-state KS potential, which we term the single orbital approximation (SOA),(Here the zero of energy in the KS system is at ε k .) We begin by considering Eq. 1 as an approximation to the universal KS functional. We find that the SOA not only works well for the strongly localized orbital regions, but also accounts for non-local features and corrects selfinteraction in the KS potential in regions of low localization. We compare the SOA to the exact KS potential for a variety of ground-state and time-dependent systems that exhibit non-local behavior in the xc potential. We then extend our approach by combining the SOA with a potential suited to d...
We have evaluated the contribution to the temperature dependence of the indirect band gap of silicon arising from electron-phonon interactions using a first-principle pseudopotential technique. This represents the first parameter-free calculation of the temperature dependence of the band gap of a real material. Numerical results are in reasonable agreement with experiment. At high temperatures we find that each phonon branch gives approximately the same contribution to the temperature dependence of the gap.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.