Eur. Phys. J. B (2018) 91: 147
https://doi.org/10.1140/epjb/e2018-90084-x

Regular Article

Exact-exchange optimized effective potential and memory effect in time-dependent density functional theory^★

¹ Center for Quantum Science and Engineering and Department of Physics, National Taiwan University, Taipei 10617, Taiwan
² Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³ Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA

^a e-mail: sichu@ku.edu

Received: 21 February 2018
Received in final form: 5 May 2018
Published online: 4 July 2018

Abstract

The memory effect in time-dependent density functional theory (TDDFT) is important in simulating many time-dependent physical processes, and its implementation in real time has been a longstanding challenge, thus limiting most of TDDFT applications to either adiabatic or linear-response regime. In this paper, we conduct the non-adiabatic calculations for a one-dimensional two-electron Helium model in a triplet state using the recently formulated Sturm-Liouville-type time-local equation for the time-dependent optimized effective potential (TDOEP) with the exact exchange functional, and the results agree with the exact time-dependent Schrödinger equation solutions. It is also found that the time-dependent dipole moment and probability density calculated from the TDOEP approach are more accurate than those from the adiabatic time-dependent Krieger-Li-Iafrate (TDKLI) approximation and the adiabatic local spin density approximation. Specifically, the non-adiabatic and memory-dependent terms in the time-local TDOEP equation correctly describe the time-dependent structure of exchange-correlation potential and yield the probability density evolution. These findings should provide important insights toward future studies on memory effects in TDDFT.