Kohn-Sham equation for time-dependent ensembles

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation approximations.

X-ray Thomson Scattering in Warm Dense Matter without the Chihara Decomposition

X-ray Thomson scattering is an important experimental technique used to measure the temperature, ionization state, structure, and density of warm dense matter (WDM). The fundamental property probed in these experiments is the electronic dynamic structure factor. In most models, this is decomposed into three terms [J. Chihara, J. Phys. F 17, 295 (1987)] representing the response of tightly bound, loosely bound, and free electrons. Accompanying this decomposition is the classification of electrons as either bound or free, which is useful for gapped and cold systems but becomes increasingly questionable as temperatures and pressures increase into the WDM regime. In this work we provide unambiguous first principles calculations of the dynamic structure factor of warm dense beryllium, independent of the Chihara form, by treating bound and free states under a single formalism. The computational approach is real-time finite-temperature time-dependent density functional theory (TDDFT) being applied here for the first time to WDM. We compare results from TDDFT to Chihara-based calculations for experimentally relevant conditions in shock-compressed beryllium.