Moment potentials for spectral density functional theory: Exploiting the momentum distribution of the uniform electron gas

TL;DR

This paper develops a moment-based spectral density functional theory that accurately models spectral features of materials by using moments derived from the uniform electron gas, improving upon standard DFT methods.

Contribution

It introduces a method to determine third spectral moments from the UEG's momentum distribution, enabling more accurate spectral function modeling in MFbSDFT.

Findings

Reproduces experimental spectra of Ni, Pd, Na, SrVO3

Provides an efficient algorithm for spectral function computation

Models second and third moments consistent with UEG at low density

Abstract

In standard Kohn-Sham (KS) density-functional theory (DFT) the valence band satellites in Ni and Pd are missing, the band widths in Ni and Na are too large, and the formation of lower and upper Hubbard bands in SrVO$_3$ is not described. These spectral features may be corrected by constructing the spectral function from the first four spectral moments, which may be obtained numerically efficiently within a \textit{moment-functional based spectral density functional theory} (MFbSDFT). In order to obtain a suitable potential for the second moment, one may use existing models of the uniform electron gas (UEG). However, models for the third moment of the UEG are not yet available. Therefore, we show that reproducing the momentum distribution of the UEG within the two-pole approximation of the spectral function determines the third moment, when the second moment is given. This allows us to find a model for the second and third moment potentials, which reproduces the experimental spectra of Ni, Pd, Na, and SrVO$_3$, and which is consistent with the second moment of the UEG at low density. Additionally, we describe an efficient algorithm to compute the spectral function from the first $2P$ spectral moment matrices, which paves the way to increasing the accuracy of MFbSDFT by using more than 4 spectral moments.