Plane-wave-based stochastic-deterministic density functional theory for extended systems

Traditional finite-temperature Kohn-Sham density functional theory (KSDFT) has an unfavorable scaling with respect to the electron number or at high temperatures. The evaluation of ground-state in KSDFT can be replaced by Chebyshev trace (CT) method. In addition, use stochastic orbitals within CT method leads [Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed stochastic-deterministic 125, 055002 (2020)] (MDFT). We have implemented above four methods first-principles package ABACUS. All are based on plane-wave basis set norm-conserving pseudopotentials periodic boundary conditions $k$-point sampling Brillouin zone. By using calculation results as benchmarks, we systematically evaluate accuracy efficiency CT, SDFT, MDFT via examining a series physical properties, which include density, free energy, atomic forces, stress, states for few condensed phase systems. suggest that our implementations not only reproduce accuracy, but also exhibit several advantages over tradition expect these great help studying high-temperature large-size extended systems such warm dense matter plasma.