Envelope Functions and Structure Constants
The implementation of state-of-the-art first principles methods requires a lot of mathematical tools and numerical algorithms, some of which are of a more general nature but some of which are closely related to a particular method. This chapter introduces the most important mathematical functions entering the various augmented spherical wave methods and sketches the basic ideas of their efficient calculations. Among these are well-known functions such as spherical Bessel functions and functions specific to spherical-wave based methods such as the structure constants, which are usually evaluated with the help of the Ewald method.
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