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The Pole EXpansion and Selected Inversion (PEXSI) method is a fast method for electronic structure calculation based on Kohn-Sham density functional theory. It efficiently evaluates certain selected elements of matrix functions, e.g., the Fermi-Dirac function of the KS Hamiltonian, which yields a density matrix. It can be used as an alternative to diagonalization methods for obtaining the density, energy and forces in electronic structure calculations. The PEXSI library is written in C++, and uses message passing interface (MPI) to parallelize the computation on distributed memory computing systems and achieve scalability on more than 10,000 processors.