Spin-dependent Optimized Effective Potential formalism for open and closed systems

Abstract

Orbital-based exchange (x) correlation (c) energy functionals, leading to the Optimized Effective Potential (OEP) formalism of density-functional theory (DFT), are gaining increasing importance in ground-stateDFT, as applied to the calculation of the electronic structure of closed systems with a fixed number of particles, like atoms and molecules. These types of functionals prove also to be extremely valuable for dealing with solid-state systems with reduced dimensionality, such as is the case ofelectrons trapped at the interface between two different semiconductors, or narrow metallic slabs.In both cases, electrons build a quasi-two-dimensional electron gas, or Q2DEG.We provide here a general DFT-OEP formal scheme valid both for Q2DEG´s either isolated (closed) or in contact with a particle bath (open), and show that both possible representations are equivalent, being the choice of one or the other essentially a question of convenience. Based on this equivalence, a calculation scheme is proposed which avoids the non-invertibility problem of the density response function forclosed systems.We also consider the case of spontaneously spin-polarized Q2DEG´s, and findthat far from the region where the Q2DEG is localized, the exact $x$-only exchange potential approaches two different, spin-dependent asymptotic limits. As an example, besides these formal results, we also provide numerical results for a spin-polarized jellium slab, using the new OEP formalism for closed systems. The accuracy of the Krieger-Li-Iafrate (KLI) approximation has been also tested for the same system, and found to be as good as it is for atoms and molecules.