Dynamic kinetic energy potential for orbital-free density functional theory

Abstract

A dynamic kinetic energy potential (DKEP) is developed for time-dependent orbital-free (TDOF) density function theory applications. This potential is constructed to affect only the dynamical (ω ≠ 0) response of an orbital-free electronic system. It aims at making the orbital-free simulation respond in the same way as that of a noninteracting homogenous electron gas (HEG), as required by a correct kinetic energy, therefore enabling extension of the success of orbital-free density functional theory in the static case (e.g., for embedding and description of processes in bulk materials) to dynamic processes. The potential is constructed by expansions of terms, each of which necessitates only simple time evolution (concurrent with the TDOF evolution) and a spatial convolution at each time-step. With 14 such terms a good fit is obtained to the response of the HEG at a large range of frequencies, wavevectors, and densities. The method is demonstrated for simple jellium spheres, approximating Na(9)(+) and Na(65)(+) clusters. It is applicable both to small and large (even ultralarge) excitations and the results converge (i.e., do not blow up) as a function of time. An extension to iterative frequency-resolved extraction is briefly outlined, as well as possibly numerically simpler expansions. The approach could also be extended to fit, instead of the HEG susceptibility, either an experimental susceptibility or a theoretically derived one for a non-HEG system. The DKEP potential should be a powerful tool for embedding a dynamical system described by a more accurate method (such as time-dependent density functional theory, TDDFT) in a large background described by TDOF with a DKEP potential. The type of expansions used and envisioned should be useful for other approaches, such as memory functionals in TDDFT. Finally, an appendix details the formal connection between TDOF and TDDFT.

Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

“…In fact, this constitutes the only essential difference with TD-DFT. The study of more refined OF kinetic energy functionals adapted to specific systems is the focus of ongoing research 37,[52][53][54] and the interest of the DFT community in this topic has been growing in the recent years.…”

“…The main goal of our SC-HDM is therefore to provide an alternative computational tool for particles and structures of larger sizes and lower symmetry than TD-DFT currently can handle. We do this by means of an orbital-free (OF) approach [34][35][36][37] . Below we discuss the kinetic-and XC-energy functionals separately.…”

Size-Dependent Plasmonic Resonances from Large-Scale Quantum Simulations

“…The crucial ingredient of the formalism is the ν ker d term in eq 4, introduced to ensure the proper frequency-dependent linear response or the correct dynamic susceptibility of the electron gas. 26 It manifestly vanishes for the static response and is written as …”

“…On the basis of the TD-OFDFT formalism, one can derive the dynamic (wave-vector-and frequency-dependent) susceptibility, χ 0 (q,ω,ρ 0 ), for an initial charge density ρ 0 . 26 These parameters are then obtained by fitting the TD-OFDFT dynamic susceptibility χ 0 (q,ω,ρ 0 ) to the exact dynamic susceptibility of a homogeneous electron gas with the same density of ρ 0 (see the Supporting Information). Note that the The Journal of Physical Chemistry Letters theoretical formalism and numerical fitting procedure are general and can be applied to alkali and even noble metals.…”

“…The success of TD-OFDFT is due to the incorporation of two important elements that are missing in previous theoretical efforts. 25 The first is introduction of a dynamic kinetic energy potential (DKEP) 26 that ensures the correct frequencydependent and wave-vector-dependent linear response of electron gas; the second is the use of ab initio pseudopotentials 27 for describing the positive charge background beyond the jellium model.…”