Collapse of the Electron Gas to Two Dimensions in Density Functional Theory

TL;DR

This paper demonstrates that a nonlocal fifth-rung functional based on the inhomogeneous STLS approach accurately captures the collapse of the electron gas to two dimensions in density functional theory, overcoming limitations of local approximations.

Contribution

The study introduces a fully nonlocal fifth-rung functional that effectively models the dimensional crossover in electron gases, outperforming local and semilocal density-functional approximations.

Findings

Fifth-rung STLS functional recovers the true 2D limit.

Local and semilocal functionals fail in the zero-thickness limit.

Full exact exchange partially explains the functional's accuracy.

Abstract

Local and semilocal density-functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sj\"olander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.