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

Sheng-Lun Liao, Tak-San Ho, Herschel Rabitz and Shih-I Chu ()
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Sheng-Lun Liao: Center for Quantum Science and Engineering and Department of Physics, National Taiwan University
Tak-San Ho: Princeton University
Herschel Rabitz: Princeton University
Shih-I Chu: Center for Quantum Science and Engineering and Department of Physics, National Taiwan University

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 7, 1-8

Abstract: 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.

Date: 2018
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DOI: 10.1140/epjb/e2018-90084-x

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