Mixed resolution of the identity compressed exchange for predicting the electronic structure of warm dense matter and hot dense plasmas from first principles

Mixed deterministic-stochastic density functional theory (mDFT) allows for the prediction of electronic structure and transport properties in warm dense matter (WDM) and hot dense plasma (HDP) with high efficiency. Predicting excited electronic state energies in WDM/HDP requires wavefunction-based methods with one of the simplest yet most effective being hybrid exact exchange functionals. Compressed hybrid functionals have come to prominence in computational materials science but must be reformulated for application to mDFT for WDM/HDP. We formulate a mixed resolution of the identity compressed exchange (mRICE) to compress the exact exchange operator and implement this approach in the SHRED planewave DFT code. We demonstrate the strengths of mRICE by calculating the electronic density of states of warm dense neon and carbon between temperatures 10 and 50 eV. We can achieve significant compression of the exchange operator to nearly 50%, rendering a significant speedup in calculations of electronic structure with hybrid exchange in WDM/HDP while maintaining accuracy. We compare the accuracy of our approach to the fully deterministic adaptively compressed exchange formulated by Lin. We find that mRICE is a powerful compression scheme to perform hybrid exact exchange calculations in WDM and HDP.