A universal density functional theory for ab-initio electronic structure and dynamics across the warm dense matter regime*

.Traditional Kohn-Sham density functional theory (KS-DFT) calculations quickly become intractable in much of the warm dense matter (WDM) regime due to a cubic scaling of the computational complexity with both temperature and system size. Orbital-Free (OF-) DFT methods have been traditionally been a more approximate theoretical alternative to KS-DFT. Recently developed stochastic KS-DFT (sDFT) methods provides an algorithmic alternative to KS-DFT. The sDFT method scales linearly with system size and inversely with temperature. This is promising for WDM, but the pre-factors make the method only practical for hot-dense plasmas, or extremely large systems.  We have developed universal mixed-deterministic-stochastic DFT (mDFT) which can capture the best of both approaches.[1] This method generalizes to time-dependent-DFT for electron response as well as quantum molecular dynamics. [2]

                We will discuss the general formulation of KS-DFT, sDFT and mDFT within the same context. All are forms of low-rank approximations for the electronic density matrix. This simple formulation provides a path to many potential advancements, including generalization to projector-augmented wave pseudopotential basis sets.[3] Additionally, we will discuss the preliminary applications of this method to calculation of electron and ion transport properties. We will highlight calculated stopping powers in warm dense carbon and hot dense CH. [5]