Convergence properties of APW wavefunctions and matrix elements

The convergence properties of both APW wavefunctions and various matrix elements calculated from these wavefunctions have been studied using Cu and Gd metals as examples. The authors find that s-p-like states converge much faster than d-like states in local properties (e.g. the discontinuity in slope at the muffin-tin sphere radius); surprisingly however, even the d-like states converge rapidly for integrated properties (e.g. the charge density and optical matrix elements). The authors conclude that for the materials and matrix elements studied, there is no need to utilize methods involving the matching of basis function derivatives at the APW sphere boundary; and that matrix elements can converge faster than the energy eigenvalue using the wavefunctions from the standard APW method.