Anti-adiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas

Abstract

We express the high-frequency (anti-adiabatic) limit of the exchange-correlation kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the kinetic stress tensor, the pair-correlation function, and the ground-state exchange-correlation potential. Of these quantities, the first three are amenable to exact evaluation by Quantum Monte Carlo methods, while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The anti-adiabatic xc kernels should be useful in calculations of excitation energies by time-dependent DFT in atoms, molecules, and solids, and provides a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.

9 pages, 3 figures, to be submitted to PRB

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• Non-local and non-adiabatic effects in the charge-density response of solids: a time-dependent density functional approach
• Exact exchange-correlation kernels for optical spectra of model systems
• Time-dependent localized Hartree-Fock potential
• Design of effective kernels for spectroscopy and molecular transport: time-dependent current-density-functional theory
• Quantum continuum mechanics in a strong magnetic field
• High frequency limit of spectroscopy