The single-particle orbitals of the Slater determinant have traditionally been represented by plane-wave sums for periodic systems. Plane waves form a complete basis and extend throughout all space, making them appropriate for representing these orbitals describing single particles.
However, using plane waves poses a problem in that the cutoff (the plane wave with the largest wave vector) depends on the number of particles being simulated (more particles mean more "wiggles" in the wave function and thus require higher frequency plane waves). To remove this scaling with system size, one can approximate the plane-wave sum with polynomials by either interpolating points on the plane wave sum or transforming the plane-wave coefficients into coefficients for a localized basis set. Either way, a given location then only depends on a small fixed number of polynomials as opposed to a large number of plane waves that grows with the number of particles simulated.
William Parker
Department of Physics
the Ohio State University
Created by: wparker at mps dot ohio dash state dot edu
Last Modified: November 27, 2006