Abstract
A natural way to describe mathematically a valence wave function in a periodic crystal is in terms of a Fourier series. However, convergence of such a plane-wave series is very poor because thousands of plane-wave terms are required to simulate the rapid oscillations of the wave function close to the atomic nuclei. To improve convergence, Herring1 proposed the Orthogonalized-Plane-Wave (OPW) method in which the plane-wave terms making up the Fourier series are orthogonalized to all the tightly-bound, core-wave functions. This orthogonalization vastly improves the convergence because the core functions present in the valence wave function expansion correctly simulate the behavior of the valence wave function in the core regions; while the plane-wave terms adequately describe the overall crystalline behavior of the function.
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