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

TL;DR

This paper derives the high-frequency limit of exchange-correlation kernels for an inhomogeneous electron gas using equilibrium properties, revealing a long-range behavior that can improve excitation energy calculations in time-dependent DFT.

Contribution

It provides an exact expression for the anti-adiabatic exchange-correlation kernel in terms of ground-state properties, enabling better modeling of excitation energies.

Findings

The anti-adiabatic xc kernel is long-range in space.

The kernel can be computed from ground-state density, stress tensor, pair-correlation, and xc potential.

This approach offers a basis for interpolating xc kernels across frequency regimes.

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.