Time-dependent density functional theory beyond Kohn–Sham Slater determinants

Abstract

When running time-dependent density functional theory (TDDFT) calculations for real-time simulations of non-equilibrium dynamics, the user has a choice of initial Kohn-Sham state, and typically a Slater determinant is used. We explore the impact of this choice on the exchange-correlation potential when the physical system begins in a 50 : 50 superposition of the ground and first-excited state of the system. We investigate the possibility of judiciously choosing a Kohn-Sham initial state that minimizes errors when adiabatic functionals are used. We find that if the Kohn-Sham state is chosen to have a configuration matching the one that dominates the interacting state, this can be achieved for a finite time duration for some but not all such choices. When the Kohn-Sham system does not begin in a Slater determinant, we further argue that the conventional splitting of the exchange-correlation potential into exchange and correlation parts has limited value, and instead propose a decomposition into a "single-particle" contribution that we denote v, and a remainder. The single-particle contribution can be readily computed as an explicit orbital-functional, reduces to exchange in the Slater determinant case, and offers an alternative to the adiabatic approximation as a starting point for TDDFT approximations.

Exact partition potential for model systems of interacting electrons in 1-D

“…We note that v p,kin (x) has a well from the peak in v (−) s [n GS ](x). The peak in v p,XC (x) has the same origin [28,29,30,31] and it nearly cancels the well in v p,kin (x). This cancelation is not exact and the fine features in We turn off the electron-electron interaction in the system by setting λ = 0.…”

Exact functionals for correlated electron–photon systems

“…For dn a step can be found that becomes steeper with increasing correlation in the system. This feature translates to different functionals of the density, and corresponds to the full real-space behavior of steps and peaks in the exact xc potential [23][24][25][26]. In QEDFT we have besides the electron-electron correlations also electron-photon correlations.…”

Charge transfer in time-dependent density functional theory

“…The electron that transfers now has its "own" KohnSham orbital, not tied to an electron that remains, so the orbitals in principle need not become delocalized over time. There is the question of adiabatic TDDFT making errors from the very start, as this uses a ground-state xc functional to describe an initially excited state, however the error from this effect can be relatively small when the initial Kohn-Sham configuration is chosen close to that of the exact wavefunction [137,146]. In fact, real simulations of photo-induced processes often begin with the Kohn-Sham system initially excited (e.g.…”

“…For cases involving more than two electrons, or with two electrons in an initial Kohn-Sham state chosen to involve more than one orbital, an iterative method must be used to find the exact xc potential; Refs. [134,[137][138][139][140][141] contain examples.…”