Constraint-based wave vector and frequency-dependent exchange-correlation kernel of the uniform electron gas

The accuracy of time-dependent density functional theory (TDDFT) is restricted by the limitations of the exchange-correlation kernels that are commonly in use. In addition to frequency-dependence a sophisticated spatial nonlocality of the kernel is also required. In this work a dynamic model exchange-correlation kernel, the MCP07 based on exact constraints is introduced [1]. For the static limit, we modified the model of CP07 at small wavevector q to recover the known second-order gradient expansion, plus other changes. For the zero-wavevector limit, we use the frequency-dependent Gross-Kohn kernel. The dynamic MCP07 exchange-correlation kernel predicts a static charge-density wave at low densities and delivers excellent quality correlation energies for the ground state, while it predicts a plausible finite plasmon lifetime at all wavevectors for the first time within TDDFT. We aim to make TDDFT more applicable to challenging physical situations by exploiting these attractive features of the dynamic MCP07 kernel.
[1] A. Ruzsinszky, N.K. Nepal, J.M. Pitarke, J.P. Perdew, Phys. Rev. B 101, 245135 (2020)