Abstract
Calculations on one-dimensional differential equations and simplified threedimensional tight-binding models have proved helpful in the development of a theory for the electronic states of macroscopic solids that do not have translational symmetry.1 Using modern order-N methods, it is now possible to calculate the electronic states of large clusters f atoms with realistic self-consistent density functional theory local density approximation (DFT-LDA) potentials. It has been proposed by Anderson,2 quite correctly, that certain aspects of the electronic structure of macroscopic solids must be qualitatively different from those of finite clusters of atoms, and this argument holds even if the clusters are periodically reproduced to fill all space. When coupled with other theoretical insights, however, results for large finite systems can be extrapolated to give a reliable picture of the electronic states of macroscopic disordered systems.
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