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

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