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Register a new userOn the relationship between the Kohn-Sham potential, the Pauli potential, and the Exact Electron Factorization
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The one-electron density of a many-electron system is the ground-state density of a one-electron Schrodinger equation. The potential $v$ appearing in this Schrodinger equation can be constructed in two ways: In density functional theory (DFT), $v$ is the sum of the Kohn-Sham (KS) potential and the Pauli potential, where the latter can be explicitly expressed in terms of the KS system of non-interacting electrons. As the KS system is fictitious, this construction is only indirectly related to the interacting many-electron system. In contrast, in the exact electron factorization (EEF), $v$ is a functional of the conditional wavefunction $phi$ that describes the spatial entanglement of the electrons in the interacting system. We compare the two constructions of the potential, provide a physical interpretation of the contributions to $v$ in the EEF, and relate it to DFT. With numerical studies of one-dimensional two- and three-electron systems, we illustrate how features of $phi$ translate to the one-electron potential $v$. We show that a change in $phi$ corresponds to a repulsive contribution to $v$, and we explain step structures of $v$ with a charge transfer encoded in $phi$. Furthermore, we provide analytic formulas for the components of $v$ by using a two-state model. Our work thus presents the mapping of a many-electron system to a one-electron system from another angle and provides insights into what determines the shape of the exact one-electron potential. We expect our findings to be helpful for the search of suitable approximations in DFT and in related theories.
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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 Weizsacker kinetic energy density to the (positive) Kohn-Sham kinetic energy density, $tau_mathrm{W}/tau$, 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.
We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) which shares that density. Our method employs the concept of screening density, which is naturally constrained by the inversion procedure and thus ensures the density being inverted leads to a smooth KS potential with correct asymptotic behaviour. We demonstrate the applicability of our method by inverting both local (LDA) and non-local (Hartree-Fock and Coupled Cluster) densities; we also show how the method can be used to mitigate the effects of self-interactions in common DFT potentials with appropriate constraints on the screening density.
The reliability of density-functional calculations hinges on accurately approximating the unknown exchange-correlation (xc) potential. Common (semi-)local xc approximations lack the jump experienced by the exact xc potential as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form in the potential as a result of the change in the decay rate of the density. These features are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Although well-known concepts, the exact relationship between them remained unclear. In this Letter, we establish the common fundamental origin of these two features of the exact xc potential via an analytical derivation. We support our result with an exact numerical solution of the many-electron Schroedinger equation for a single atom and a diatomic molecule in one dimension. Furthermore, we propose a way to extract the fundamental gap from the step structures in the potential.
Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential(DCEP) method of Kohut, Ryabinkin, and Staroverov to obtain SI corrected local effective potentials from the SI corrected Fermi-Lowdin orbitals and density in the FLOSIC scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.
It has recently been observed [Phys. Rev. Lett. 113, 113002 (2014)] that the ground-state energy may be obtained directly as a simple sum of augmented Kohn-Sham orbital energies, where it was ascertained that the corresponding one-body shifted Kohn-Sham effective potential has appealing features. With this in mind, eigenvalue and virial constraints are deduced for approximating this potential.
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