A discontinuous functional for linear response time-dependent density functional theory: the exact-exchange kernel and approximate forms

TL;DR

This paper analyzes the discontinuity in the exact-exchange kernel of time-dependent density functional theory, emphasizing its impact on molecular dissociation and charge transfer excitations, and compares different approximations.

Contribution

It provides a detailed comparison of the PGG and CEDA approximations to the EXX kernel, highlighting the importance of the discontinuity for accurate long-range excitation modeling.

Findings

CEDA includes the discontinuity explicitly, unlike PGG.

Discontinuity affects the description of molecular dissociation and charge transfer.

Frequency dependence is crucial for modeling long-range and inner-shell excitations.

Abstract

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. A, 022514 (2012)]. To further analyze the discontinuity of the kernel we here make use of two different approximations to the EXX kernel: the PGG approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field counter-acting effect in the density functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge transfer excitations as well as inner-shell excitations.