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Developing New and Understanding Old Approximations in TDDFT

Abstract

When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, sometimes even quantitatively so. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange-correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn-Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange-correlation potential from a coupling-constant path integration.

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Article information


Submitted
29 Apr 2020
Accepted
02 Jun 2020
First published
02 Jun 2020

Faraday Discuss., 2020, Accepted Manuscript
Article type
Paper

Developing New and Understanding Old Approximations in TDDFT

L. Lacombe and N. T. Maitra, Faraday Discuss., 2020, Accepted Manuscript , DOI: 10.1039/D0FD00049C

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