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

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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.

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Authors and Affiliations

  1. Center for Quantum Science and Engineering and Department of Physics, National Taiwan University, Taipei, 10617, Taiwan

    Sheng-Lun Liao & Shih-I Chu

  2. Department of Chemistry, Princeton University, Princeton, New Jersey, 08544, USA

    Tak-San Ho & Herschel Rabitz

  3. Department of Chemistry, University of Kansas, Lawrence, Kansas, 66045, USA

    Shih-I Chu

Authors
  1. Sheng-Lun Liao
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  2. Tak-San Ho
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  3. Herschel Rabitz
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  4. Shih-I Chu
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Correspondence to Shih-I Chu.

Additional information

Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, M.A.L. Marques.

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Liao, SL., Ho, TS., Rabitz, H. et al. Exact-exchange optimized effective potential and memory effect in time-dependent density functional theory. Eur. Phys. J. B 91, 147 (2018). https://doi.org/10.1140/epjb/e2018-90084-x

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  • DOI: https://doi.org/10.1140/epjb/e2018-90084-x

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