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Register a new userKohn-Sham potential for a strongly correlated finite system with fractional occupancy
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Using a simplified one-dimensional model of a diatomic molecule, the associated interacting density and corresponding Kohn-Sham potential have been obtained analytically for all fractional molecule occupancies $N$ between 0 and 2. For the homonuclear case, and in the dissociation limit, the exact Kohn-Sham potential builds a barrier at the midpoint between the two atoms, whose strength increases linearly with $N$, with $1 < N leq 2$. In the heteronuclear case, the disociating KS potential besides the barrier also exhibits a plateau around the atom with the higher ionization potential, whose size (but not its strength) depends on $N$. An anomalous zero-order scaling of the Kohn-Sham potential with regards to the strength of the electron-electron repulsion is clearly displayed by our model; without this property both the unusual barrier and plateau features will be absent.
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A Kohn-Sham (KS) inversion determines a KS potential and orbitals corresponding to a given electron density, a procedure that has applications in developing and evaluating functionals used in density functional theory. Despite the utility of KS
The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the Density Functional Theory framework, this surface barrier has two non-trivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential $V_{x}(z)$ has been generated by using the Optimized Effective Potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that $V_{x}(zto infty)to - e^{2}/z$; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulder-like structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.
We model a Kohn-Sham potential with a discontinuity at integer particle numbers derived from the GLLB approximation of Gritsenko et al. We evaluate the Kohn-Sham gap and the discontinuity to obtain the quasiparticle gap. This allows us to compare the Kohn-Sham gaps to those obtained by accurate many-body perturbation theory based optimized potential methods. In addition, the resulting quasiparticle band gap is compared to experimental gaps. In the GLLB model potential, the exchange-correlation hole is modeled using a GGA energy density and the response of the hole to density variations is evaluated by using the common-denominator approximation and homogeneous electron gas based assumptions. In our modification, we have chosen the PBEsol potential as the GGA to model the exchange hole, and add a consistent correlation potential. The method is implemented in the GPAW code, which allows efficient parallelization to study large systems. A fair agreement for Kohn-Sham and the quasiparticle band gaps with semiconductors and other band gap materials is obtained with a potential which is as fast as GGA to calculate.
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.
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 ($Delta$), 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.
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