Ab initio Static Exchange-Correlation Kernel across Jacob's Ladder without functional derivatives

TL;DR

This paper introduces a novel, exact method within DFT to compute the static exchange-correlation kernel for materials without using functional derivatives, enabling better insights into material properties at extreme conditions.

Contribution

A new, formally exact DFT-based methodology for calculating the static XC kernel without functional derivatives, applicable to real materials and extreme environments.

Findings

Excellent agreement with QMC data for uniform electron gas

Insights into XC functional performance at warm dense conditions

Demonstrates capability to capture nontrivial effects like isotropy breaking

Abstract

The electronic exchange-correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of material properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In practice, no reliable method has been known that allows to compute the kernel of real materials with arbitrary XC functionals. In this work, we overcome this long-standing limitation by introducing a new, formally exact methodology for the computation of the material specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives -- no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model at both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC-functionals, and has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that our framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.