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We present an accurate and efficient real-space formulation of theHellmann-Feynman stress tensor for $\mathcal{O}(N)$ Kohn-Sham densityfunctional theory (DFT). While applicable at any temperature, the formulationis most efficient at high temperature where the Fermi-Dirac distributionbecomes smoother and density matrix becomes correspondingly more localized. Wefirst rewrite the orbital-dependent stress tensor for real-space DFT in termsof the density matrix, thereby making it amenable to $\mathcal{O}(N)$ methods.We then describe its evaluation within the $\mathcal{O}(N)$ infinite-cellClenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicableto metallic as well as insulating systems, is highly parallelizable, becomesincreasingly efficient with increasing temperature, and provides resultscorresponding to the infinite crystal without the need of Brillouin zoneintegration. We demonstrate systematic convergence of the resulting formulationwith respect to SQ parameters to exact diagonalization results, and showconvergence with respect to mesh size to established planewave results. Weemploy the new formulation to compute the viscosity of hydrogen at a millionkelvin from Kohn-Sham quantum molecular dynamics, where we find agreement withprevious more approximate orbital-free density functional methods.

Real-space formulation of the stress tensor for $\mathcal{O}(N)$ density functional theory: application to high temperature calculations