From density response to energy functionals and back: An ab initio perspective on matter under extreme conditions

Energy functionals serve as the basis for different models and methods in quantum and classical many-particle physics. Arguably, one of the most successful and widely used approaches in material science at both ambient and extreme conditions is density functional theory (DFT). Various flavors of DFT methods are being actively used to study material properties at extreme conditions, such as in warm dense matter, dense plasmas, and nuclear physics applications. In this review, we focus on the warm dense matter regime, which occurs in the core of giant planets and stellar atmospheres, and as a transient state in inertial confinement fusion experiments. We discuss the connection between linear density response functions and free energy functionals as well as the utility of the linear response formalism for the construction of advanced functionals. As a new result, we derive the stiffness theorem linking the change in the intrinsic free energy to the density response properties of electrons. We review and summarize recent works that assess various exchange–correlation (XC) functionals for an inhomogeneous electron gas that is perturbed by a harmonic external field and for warm dense hydrogen using exact path integral quantum Monte Carlo data as an unassailable benchmark. This constitutes a valuable guide for selecting an appropriate XC functional for DFT calculations in the context of investigating the inhomogeneous electronic structure of warm dense matter. We stress that correctly simulating the strongly perturbed electron gas necessitates the correct UEG limit of the XC and non-interacting free-energy functionals.