Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory

TL;DR

This paper reveals that the exchange-correlation kernel's discontinuity in time-dependent density functional theory is crucial for accurately describing long-range charge-transfer excitations, addressing a key challenge in the field.

Contribution

It identifies the necessary discontinuity in the XC kernel and explains its role in correcting charge-transfer excitation energies in TDDFT.

Findings

Discontinuity of the XC potential induces a diverging space- and frequency-dependent XC kernel.

The discontinuity compensates for vanishing orbital overlap in donor-acceptor systems.

The mechanism is demonstrated at first order in Coulomb interaction.

Abstract

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a space -and frequency-dependent discontinuity of the XC kernel which diverges as $r\to\infty$. In a combined donor-acceptor system, the same discontinuity compensates for the vanishing overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction.