Mixed Resolution-of-the-Identity Compressed Exchange for Hybrid Mixed Deterministic-Stochastic Density Functional Theory from Low to Extreme Temperatures.

Exact exchange contributions included in density functional theory calculations have rendered excellent electronic structure results on both cold and extremely hot matter. In this work, we develop a mixed deterministic-stochastic resolution-of-the-identity compressed exchange (mRICE) method for efficient calculation of exact and hybrid electron exchange, suitable for applications alongside mixed stochastic-deterministic density functional theory. mRICE offers accurate calculations of the electronic structure at a largely reduced computation time compared to other compression algorithms, such as Lin's adaptive compressed exchange, for the warm dense matter. mRICE grants flexibility in the number of exchange compression vectors used to resolve the approximated exchange operator kernel, reducing the computation time of the application of the exchange operator to the vectors by up to 40% while maintaining accuracy in electronic structure predictions. We demonstrate mRICE by computing the density of states of warm dense carbon and neon between temperatures of 10 and 50 eV (116,045 and 580,226 K) and comparing timing and accuracy at varying levels of compression. Finally, we carry out mRICE on the difference between the Fock exchange operator and the semilocal exchange potential kernels and show an enhanced convergence of electronic structure calculations at reduced stochastic sampling.