Double excitations within time-dependent density functional theory linear response

Abstract

Within the adiabatic approximation, time-dependent density functional theory yields only single excitations. Near states of double excitation character, the exact exchange-correlation kernel has a strong dependence on frequency. We derive the exact frequency-dependent kernel when a double excitation mixes with a single excitation, well separated from the other excitations, in the limit that the electron-electron interaction is weak. Building on this, we construct a nonempirical approximation for the general case, and illustrate our results on a simple model.

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“…Despite its successes, LR-TDDFT has some well-known shortcomings that are due to practical approximations required to make the method tractable. Such problems include the inability to properly treat excited states with charge transfer, 43 double excitation, [44][45] and Rydberg character. 46 More importantly, it fails to accurately describe CIs between the ground and excited states, which makes it unreliable for the study of reactions involving population transfer from an excited state to the ground state.…”

Long-range excitations in time-dependent density functional theory

“…2 is no longer zero, as these orbitals have significant overlap in both the atomic regions. However any adiabatic ap-proximation to the kernel will lead to drastically incorrect CT energies: The underlying reason is because the adiabatic approximation entirely neglects double-excitations [11,12], which are also absent in the non-interacting response function χ S . Yet the double excitation to the antibonding orbital is critical in this case to capture the correct nature of the true excitations in this subspace [24] (as well as the Heitler-London ground-state).…”

“…Refs. [11,12] showed how the mixing of a double excitation with a single can be incorporated in TDDFT via a dressed SPA, ω = ω q + 2[q|f HXC (ω)|q]: here the kernel has strong frequency-dependence. In Ref.…”

“…This feature is a signature of static correlation in the KS ground state. Since double excitations are missing in the KS linear response [11], it is the job of the xc kernel to fold them in (see shortly).…”

“…Understanding where it fails is important in constructing more accurate functional approximations. The lack of frequency-dependence is why adiabatic TDDFT (ATDDFT) fails for states of double excitation character [11,12,13,14,15].…”