Article,
Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation
The Journal of Chemical Physics, 121 (1): 28-35 (2004)
DOI: 10.1063/1.1756865
Abstract
Time-dependent density-functional theory in the adiabatic approximation
has been very successful for calculating excitation energies in molecular
systems. This paper studies nonadiabatic effects for excitation energies,
using the current–density functional of Vignale and Kohn Phys. Rev.
Lett. 77, 2037 (1996). We derive a general analytic expression for
nonadiabatic corrections to excitation energies of finite systems
and calculate singlet s-->s and s-->p excitations of closed-shell
atoms. The approach works well for s-->s excitations, giving a small
improvement over the adiabatic local-density approximation, but tends
to overcorrect s-->p excitations. We find that the observed problems
with the nonadiabatic correction have two main sources: (1) the currents
associated with the s-->p excitations are highly nonuniform and,
in particular, change direction between atomic shells, (2) the so-called
exchange-correlation kernels of the homogeneous electron gas, f<sub>xc</sub><sup>L</sup>
and f<sub>xc</sub><sup>T</sup>, are incompletely known, in particular
in the high-density atomic core regions.
