Numerical tests of high-precision multiple-scattering band theory

Calculations done on the empty lattice test the convergence properties of high-precision non-muffin-tin band theories based on multiple scattering. The results at $l_{\max =6\mathrm{}}$ in the scattered wave show that two methods of this type are still strongly converging to the correct band energies. The dominant source of error in both seems to be the truncation error; the near-field error present in one of the theories is extremely small. We conclude that the exact theory developed by the authors is probably correct.