Linear Response of Current-Dependent Density Functional Approximations in Magnetic Fields

This Letter outlines the steps and derivations that are necessary to apply density functional approximations that depend on the current and kinetic energy density rigorously within the framework of linear-response methods, including adiabatic time-dependent current density functional theory. This includes systems with a non-zero current density in the ground state. The necessary exchange-correlation kernel for these density functional approximations is derived, and the matrix elements are given explicitly. Due to the gauge variance of the kinetic energy density in an external magnetic field, having access to the proper current-dependent exchange-correlation kernel is necessary to recover gauge invariance for excited states. As a proof of principle application, the excited states of two small molecules in strong external magnetic fields are calculated using linear-response time-dependent current density functional theory. Finally, the implications of the derived current density-dependent exchange-correlation kernel for systems with strong spin-orbit coupling are discussed.

Automated summary

The letter outlines the steps and derivations necessary to apply density functional approximations that depend on the current and kinetic energy density within linear-response methods. It also discusses the necessary exchange-correlation kernel and its implications for systems in strong external magnetic fields and with strong spin-orbit coupling. An application to calculating excited states of small molecules in strong external magnetic fields using linear-response time-dependent current density functional theory is presented as well.