The adiabatic strictly-correlated-electrons functional: kernel and exact properties

TL;DR

This paper explores the formal properties of the adiabatic strictly-correlated electrons (SCE) functional, focusing on its theoretical constraints and deriving an analytical kernel for 1D systems to improve linear response TDDFT.

Contribution

It provides a detailed analysis of the SCE functional's properties and derives an analytical expression for its kernel, addressing limitations of local and semi-local functionals.

Findings

The adiabatic SCE functional satisfies key many-body theory constraints.

An analytical expression for the 1D SCE Hartree exchange-correlation kernel is derived.

Numerical analysis reveals non-local features of the kernel relevant for challenging problems.

Abstract

We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.