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. 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.
The PEXSI library and documentation can be found here
The PEXSI library has recently been integrated into the Siesta for demonstrating efficient and accurate ab initio materials simulation on massively parallel machines, and can regularly handle systems with 10,000 to 100,000 electrons. It has also just recently been added to CP2K.