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Time-Local Equation for the Exact Optimized Effective Potential in Time-Dependent Density Functional Theory
Sheng-Lun Liao1,2, Tak-San Ho2, Herschel Rabitz2
1Center for Quantum Science and Engineering and Department of Physics, National Taiwan University, Taipei 10617, Taiwan.
Abstract:
A long-standing challenge in the time-dependent density functional theory is to efficiently solve the exact time-dependent optimized effective potential (TDOEP) integral equation derived from orbital-dependent functionals, especially for the study of nonadiabatic dynamics in time-dependent external fields. In this Letter, we formulate a completely equivalent time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham and effective memory orbitals. The time-local formulation is numerically implemented, with the incorporation of exponential memory loss to address the unaccounted for correlation component in the exact-exchange-only functional, to enable the study of the many-electron dynamics of a one-dimensional hydrogen chain. It is shown that the long time behavior of the electric dipole converges correctly and the zero-force theorem is fulfilled in the current implementation.
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