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Kohn-Sham density functional theory calculations using conventionaldiagonalization based methods become increasingly expensive as temperatureincreases due to the need to compute increasing numbers of partially occupiedstates. We present a density matrix based method for Kohn-Sham calculations athigh temperature that eliminates the need for diagonalization entirely, thusreducing the cost of such calculations significantly. Specifically, we developreal-space expressions for the electron density, electronic free energy,Hellmann-Feynman forces, and Hellmann-Feynman stress tensor in terms of anorthonormal auxiliary orbital basis and its density kernel transform, thedensity kernel being the matrix representation of the density operator in theauxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, wenext develop an approach akin to Clenshaw-Curtis spectral quadrature tocalculate the individual columns of the density kernel based on the Fermioperator expansion in Chebyshev polynomials; and employ a similar approach toevaluate band structure and entropic energy components. We implement theproposed formulation in the SPARC electronic structure code, using which weshow systematic convergence of the aforementioned quantities to exactdiagonalization results, and obtain significant speedups relative toconventional diagonalization based methods. Finally, we employ the new methodto compute the self-diffusion coefficient and viscosity of aluminum at 116,045K from Kohn-Sham quantum molecular dynamics, where we find agreement withprevious more approximate orbital-free density functional methods.

Real-space density kernel method for Kohn-Sham density functional theory calculations at high temperature