Autoionizing resonances in time-dependent density functional theory

Abstract

Autoionizing resonances that arise from the interaction of a bound single-excitation with the continuum can be accurately captured with the presently used approximations in time-dependent density functional theory (TDDFT), but those arising from a bound double excitation cannot. In the former case, we explain how an adiabatic kernel, which has no frequency-dependence, can yet generate the strongly frequency-dependent resonant structures in the interacting response function, not present in the Kohn-Sham response function. In the case of the bound double-excitation, we explain that a strongly frequency-dependent kernel is needed, and derive one as an a posteriori correction to the usual adiabatic approximations in TDDFT. Our approximation becomes exact for an isolated resonance in the limit of weak interaction, where one discrete state interacts with one continuum. We derive a "Fano TDDFT kernel" that reproduces the Fano lineshape within the TDDFT formalism, and also a dressed kernel, that operates on top of an adiabatic approximation. We illustrate our results on a simple model system.

All-electron time-dependent density functional theory with finite elements: Time-propagation approach

“…The current XC functionals for TDDFT are known not to perform well in all cases, but they perform adequately in many cases and are under active development. 7,8 The time-propagation approach has also advantages from the numerical point of view, which makes it suitable for large systems. The computational cost scales well with respect to increasing system size, 9 and it allows efficient parallelization over TDKS states.…”

Probing the role of excited states in ionization of acetylene

“…The description of autoionizing resonances arising from double excitations is problematic in TDDFT. However, in the present work resonance phenomena primarily arise from single excitations which are described well using TDDFT [49]. In particular, previous TDDFT studies of photoionization of acetylene have shown a good level of accuracy [15].…”

Autoionization in time-dependent density-functional theory

“…Due to the electron-electron interaction these discrete states couple to the continuum leading to emission of an electron. Previous studies of this process within TDDFT have been concentrated on the linear response regime [12]. It is well known that doubly excited states can only be described in a TDDFT treatment if the exchange-correlation kernel is frequency dependent [3].…”