Discontinuity of the chemical potential in reduced-density-matrix-functional theory

TL;DR

This paper introduces a new method within reduced-density-matrix-functional theory to accurately compute the fundamental gap by analyzing the discontinuity of the chemical potential with respect to fractional particle numbers.

Contribution

It generalizes reduced-density-matrix-functional theory to fractional particle numbers, linking the derivative discontinuity to the fundamental gap, and demonstrates its effectiveness through numerical examples.

Findings

Accurately predicts the fundamental gap in various systems.

Shows excellent agreement with CI calculations and experimental data.

Reveals the non-stationary nature of the energy minimum in this framework.

Abstract

We present a novel method for calculating the fundamental gap. To this end, reduced-density-matrix-functional theory is generalized to fractional particle number. For each fixed particle number, $M$, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to a function, $E_{\mathrm{tot}}^M$, whose derivative with respect to the particle number has a discontinuity identical to the gap. In contrast to density functional theory, the energy minimum is generally not a stationary point of the total-energy functional. Numerical results, presented for alkali atoms, the LiH molecule, the periodic one-dimensional LiH chain, and solid Ne, are in excellent agreement with CI calculations and/or experimental data.