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
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.
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2018