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

Dec 2022

In standard Kohn-Sham (KS) density-functional theory (DFT) the valence bandsatellites in Ni and Pd are missing, the band widths in Ni and Na are toolarge, and the formation of lower and upper Hubbard bands in SrVO$_3$ is notdescribed. These spectral features may be corrected by constructing thespectral function from the first four spectral moments, which may be obtainednumerically efficiently within a \textit{moment-functional based spectraldensity functional theory} (MFbSDFT). In order to obtain a suitable potentialfor 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 withinthe two-pole approximation of the spectral function determines the thirdmoment, when the second moment is given. This allows us to find a model for thesecond and third moment potentials, which reproduces the experimental spectraof Ni, Pd, Na, and SrVO$_3$, and which is consistent with the second moment ofthe UEG at low density. Additionally, we describe an efficient algorithm tocompute the spectral function from the first $2P$ spectral moment matrices,which paves the way to increasing the accuracy of MFbSDFT by using more than 4spectral moments.

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