Accuracy and convergence properties of the extended linear augmented-plane-wave method

A detailed analysis of the accuracy of linear augmented-plane-wave (LAPW) methods is presented. A number of known APW-like formalisms are reviewed and their properties are related to the flexibility of the radial basis set used for the augmentation. The accuracy of the wave functions produced by the standard LAPW and by the extended LAPW method is numerically tested using Nb metal as an example. It is shown that the methods employing an extended set of radial basis functions yield better accuracy and acquire convergence properties similar to those of Slater's APW method. In contrast to the previous analyses of the accuracy of linear methods, we take into account the matching constraints at the muffin-tin sphere and focus on the problem of fitting the radial function to an exact solution with a different logarithmic derivative. Based on this approach, we deduce a value that characterizes the closeness of the linear APW-like method to Slater's APW method. A possibility to improve presently used extended LAPW techniques further is discussed.