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Spectral differences in real-space electronic structure calculations.

Real-space grids for electronic structure calculations are efficient because the potential is diagonal while the second derivative in the kinetic energy may be sparsely evaluated with finite differences or finite elements. In applications to vibrational problems in chemical physics a family of methods known as spectral differences has improved finite differences by several orders of magnitude. In this paper the use of spectral differences for electronic structure is studied. Spectral differences are implemented in two electronic structure programs PARSEC and HARES which currently employ finite differences. Applications to silicon clusters and lattices indicate that spectral differences achieve the same accuracy as finite differences with less computational work.