Use of energy derivative of the radial solution in an augmented plane wave method: application to copper

Abstract

By a suitable combination inside the muffin-tin sphere of a radial solution to the Schrodinger equation and its energy derivative, the dependence of the APW matrix elements on the energy E used to construct the basis functions can be greatly reduced. This has a number of advantages. The authors present an application of the method, previously suggested by Marcus (1967) and analysed by Andersen to the Chodorow copper potential and examine its precision and its convergence properties. It was found the method converges about equally well or somewhat more slowly than the standard APW method in number of basis functions. The eigenvalue error of the method is proportional to (E-E₀)⁴. The error of the wavefunction is proportional to (E-E_o)². The d states limit the range of mod E-E₀ mod <0.1 Ryd for acceptable wavefunctions. The limit for non-d states is larger than 1 Ryd.