Studies of spuriously shifting resonances in time-dependent density functional theory

Abstract

Adiabatic approximations in time-dependent density functional theory (TDDFT) will in general yield unphysical time-dependent shifts in the resonance positions of a system driven far from its ground-state. This spurious time-dependence is explained in [J. I. Fuks, K. Luo, E. D. Sandoval and N. T. Maitra, Phys. Rev. Lett. 114, 183002 (2015)] in terms of the violation of an exact condition by the non-equilibrium exchange-correlation kernel of TDDFT. Here we give details on the derivation and discuss reformulations of the exact condition that apply in special cases. In its most general form, the condition states that when a system is left in an arbitrary state, the TDDFT resonance position for a given transition in the absence of time-dependent external fields and ionic motion, is independent of the state. Special cases include the invariance of TDDFT resonances computed with respect to any reference interacting stationary state of a fixed potential, and with respect to any choice of appropriate stationary Kohn-Sham reference state. We then present several case studies, including one that utilizes the adiabatically-exact approximation, that illustrate the conditions and the impact of their violation on the accuracy of the ensuing dynamics. In particular, charge-transfer across a long-range molecule is hampered, and we show how adjusting the frequency of a driving field to match the time-dependent shift in the charge-transfer resonance frequency, results in a larger charge transfer over time.

Density Functional Theory for Electronic Excited States

“…Unlike LR-TDDFT, which operates by definition in the limit of a vanishingly weak external field, the TDKS approach is non-perturbative and in principle can be used to simulate electron dynamics in strong laser fields, e.g., to simulate nonlinear optical properties of materials, 433 or to make contact with emerging attosecond spectroscopies 57 that create electronic wave packets that are out of equilibrium with the nuclei and thus outside of the Born-Oppenheimer approximation. [53][54][55][56] In practice, there are various issues related to the use of the adiabatic approximation (Section 2.1.2), 290,434,435 meaning the use of ground-state functionals with no memory, such that the time dependence is carried solely by the time-evolving density, E xc [ρ(r, t)]. On the other hand, within the adiabatic approximation the initial-state dependence vanishes since the XC kernel is fully specified in terms of the instantaneous time-evolving density.…”

Charge transfer in time-dependent density functional theory

“…The reason for this is that they violate an exact condition of TDDFT, which is a condition on the non-equilibrium densityresponse function, stating that the excitation frequency of a given transition is independent of the state around which the response is taken. Within the TDDFT nonequilibrium response formalism [129,[148][149][150], this re-quires a subtle cancellation between time-dependences of the Kohn-Sham response function and a generalized xc kernel, which is not respected by most approximations. For this particular case of two electrons occupying different spin-orbitals (but not in the general case), exact exchange can be shown to satisfy this "resonance condition", and therefore gives good dynamics.…”

Time-resolved exciton wave functions from time-dependent density-functional theory

“…Again, this is not unexpected: as the population of the bands changes significantly, the energy levels shift and the laser field detunes; this makes the excitation process less effective. In TDDFT, this detuning effect is a well-known weak-ness of adiabatic approximations to the time-dependent xc potential, leading, among other things, to inability to describe Rabi oscillations [57,58].…”