Abstract
The recent methods to calculate the electronic structure of solids generate a more or less limited number of Bloch states which does not make a complete set. As a consequence for example the sum rule of Thomas-Reiche-Kuhn is not fulfilled. To overcome this deficiency a new method to solve the Schrödinger equation is proposed which uses far more trial functions than other methods. Similar to the APW-scheme the wave-functions are superpositions of plane waves and, within the APW-sphere, of spherical waves. Contrary to the APW-scheme the radial dependence of the spherical waves is expressed in a basis of localized spline functions determined for each k using the variational scheme. The new method is expected to be especially appropriate for non-warpedmuffin-tin potentials. Our tests showed that the method is very accurate and the sum rule involving the momentum operator is now well satisfied.
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Bross, H., Fehrenbach, G.M. The spline augmented plane wave method. Z. Physik B - Condensed Matter 81, 233–243 (1990). https://doi.org/10.1007/BF01309354
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DOI: https://doi.org/10.1007/BF01309354