Fast and Universal Kohn Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Abstract

Understanding many processes, e.g. fusion experiments, planetary interiors and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter (WDM) and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly-free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham Density Functional Theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the WDM regime. A recently-developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (¡50 eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

A Kinetic Model for Electron-Ion Transport in Warm Dense Matter

“…Interestingly, in the degenerate regime there is a quantitative difference in the predicted relaxation rates for momentum versus energy. Ultimately, current and near-future experimental measurements [1,49,50] and ab-initio simulations [39][40][41][42][43][44] will be able to shed light on the applicability of the different models of transport for WDM. This work can be improved through inclusion of electron-electron collisions and higher-order terms of a Chapman-Enskog expansion.…”

“…Since electrons are often treated using the Born-Oppenhiemer approximation in simulations, they are also limited to treat only the electron-ion contribution to transport processes. Although electron-electron interactions are expected to contribute to the total conductivity, it is only recently becoming possible to simulate dynamic electrons in WDM following advancements in wave-packet MD [39], mixed quantum-classical MD [40,41], Bohmian quantum methods [42], Kohn-Sham DFT [43] and quantum Monte Carlo [44]. Addressing contributions from both electron and ion dynamics will be the next step in both the theory and simulation development.…”

“…For comparison we select the Lee-Moore model, the model of Shaffer and Starrett [35] and the QMD simulations of Witte et al [28]. The electrical conductivity coefficient predicted by the LM model [17] is (43) which we relate to the friction force density R and thus the scattering rate: ν…”