  Kohn-Sham density functional theory calculations using conventional
diagonalization based methods become increasingly expensive as temperature
increases due to the need to compute increasing numbers of partially occupied
states. We present a density matrix based method for Kohn-Sham calculations at
high temperature that eliminates the need for diagonalization entirely, thus
reducing the cost of such calculations significantly. Specifically, we develop
real-space expressions for the electron density, electronic free energy,
Hellmann-Feynman forces, and Hellmann-Feynman stress tensor in terms of an
orthonormal auxiliary orbital basis and its density kernel transform, the
density kernel being the matrix representation of the density operator in the
auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we
next develop an approach akin to Clenshaw-Curtis spectral quadrature to
calculate the individual columns of the density kernel based on the Fermi
operator expansion in Chebyshev polynomials; and employ a similar approach to
evaluate band structure and entropic energy components. We implement the
proposed formulation in the SPARC electronic structure code, using which we
show systematic convergence of the aforementioned quantities to exact
diagonalization results, and obtain significant speedups relative to
conventional diagonalization based methods. Finally, we employ the new method
to compute the self-diffusion coefficient and viscosity of aluminum at 116,045
K from Kohn-Sham quantum molecular dynamics, where we find agreement with
previous more approximate orbital-free density functional methods.
