Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation
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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, fxcL and fxcT, are incompletely known, in particular in the high-density atomic core regions.