Almost Exact Exchange At Almost No Cost

TL;DR

This paper demonstrates a semiclassical exchange approximation in one dimension that is nearly exact and computationally inexpensive, outperforming traditional local density functional methods.

Contribution

It introduces a nearly exact semiclassical exchange approximation with minimal computational cost and validates its stability and accuracy against exact exchange calculations.

Findings

The approximation is almost exact in one dimension.

It is more accurate than local density functional calculations.

Orbital-free potential-functional calculations show minimal error.

Abstract

A recently developed semiclassical approximation to exchange in one dimension is shown to be almost exact, with essentially no computational cost. The variational stability of this approximation is tested, and its far greater accuracy relative to local density functional calculations demonstrated. Even a fully orbital-free potential-functional calculation (no orbitals of any kind) yields little error relative to exact exchange, for more than one orbital.