Asymptotic behaviour of the Fourier coefficients of MAPW wave functions

In contrast to the conventional APW method the MAPW method imposes continuity conditions on the trial wave functions which guarantee that the wave functions and their first derivatives are continuous throughout the whole atomic polyhedron. It is shown that as a consequence of this fact the Fourier coefficients of the MAPW wave functions approach zero as 1/p ⁴ whereas conventional APW functions decay as 1/p ² only. For the MAPW Fourier coefficients asymptotic formulas are derived that may be useful in numerical calculations. Numerical results are given for metallic Li and Cu.