Excitation Energies from Time-Dependent Density-Functional Theory

Abstract

The role of the exchange-correlation potential and the exchange-correlation kernel in the calculation of excitation energies from time-dependent density functional theory is studied. Excitation energies of the helium and beryllium atoms are calculated, both from the exact Kohn-Sham ground-state potential, and from two orbital-dependent approximations. These are exact exchange and self-interaction corrected local density approximation (SIC-LDA), both calculated using Krieger-Li-Iafrate approximation. For the exchangecorrelation kernels, three adiabatic approximations were tested: the local density approximation, exact exchange, and SIC-LDA. The choice of the ground-state exchange correlation potential has the largest impact on the absolute position of most excitation energies. In particular, orbital-dependent approximate potentials result in a uniform shift of the transition energies to the Rydberg states.

Electronic excitations: density-functional versus many-body Green’s-function approaches

“…Results for finite systems beyond the single-pole approximation which have been particularly discussed are those of TDLDA Yabana and Bertsch, 1996Vasiliev et al, 1999Vasiliev et al, , 2002Marques et al, 2001) and the results obtained within the OEP scheme 41 (Gö rling, 1999;Gross et al, 1996;Petersilka et al, 1996Petersilka et al, , 2000Grabo et al, 2000aGrabo et al, , 2000b. The latter approach gives an exchange-correlation potential with the correct Ϫ1/r behavior at long distances .…”

“…Equation (5.15) can be simplified by an expansion around one particular Kohn-Sham transition 1→2, i.e., by calculating the transition energy ϭ⍀ in first-order perturbation theory (single-pole approximation). Following Petersilka et al (1996) and considering explicitly the spin degrees of freedom, 39 one obtains from Eq. (5.15)…”

“…A back-transformation to the physical time directly provides the desired causal response functions (see for mathematical details of this technique). 43 See, for example, (Stott and Zaremba, 1980;Zangwill and Soven, 1980;Dobson et al, 1988;Tsuei et al, 1990;Casida, 1995;Petersilka et al, 1996;Rubio et al, 1996Rubio et al, , 1997Liebsch, 1997;Vasiliev et al, 1999Vasiliev et al, , 2002. 44 Note that the lower the density the larger the frequency dependence of the kernel.…”

“…III.A). Petersilka et al (1996) (5.12) Equation (5.11) corresponds to Eq. (2.17) of the Introduction.…”

“…This was derived by Petersilka et al (1996) in the context of exact exchange time-dependent optimized effective potentials and kernels Gö rling, 1998) (x-TDOEP), and it is equivalent to the so-called Slater approximation in Hartree-Fock calculations (Langhoff et al, 1972). It is a frequency-independent kernel that in real space reads…”