Calculations of Hubbard U from first-principles

TL;DR

This paper presents a first-principles method to calculate the Hubbard U parameter for transition metals and oxides, highlighting its frequency dependence and comparing it with constrained LDA results.

Contribution

The authors introduce a scheme based on the random-phase approximation to estimate Hubbard U, providing insights into its frequency dependence and discrepancies with constrained LDA.

Findings

Calculated Hubbard U values generally agree with literature but are sometimes smaller.

Frequency dependence of U suggests static U may not always be appropriate.

Discrepancies with constrained LDA are likely due to technical calculation issues.

Abstract

The Hubbard \emph{U} of the \emph{3d} transition metal series as well as SrVO$_{3}$, YTiO$_{3}$, Ce and Gd has been estimated using a recently proposed scheme based on the random-phase approximation. The values obtained are generally in good accord with the values often used in model calculations but for some cases the estimated values are somewhat smaller than those used in the literature. We have also calculated the frequency-dependent \emph{U} for some of the materials. The strong frequency dependence of \emph{U} in some of the cases considered in this paper suggests that the static value of \emph{U} may not be the most appropriate one to use in model calculations. We have also made comparison with the constrained LDA method and found some discrepancies in a number of cases. We emphasize that our scheme and the constrained LDA method theoretically ought to give similar results and the discrepancies may be attributed to technical difficulties in performing calculations based on currently implemented constrained LDA schemes.