Band Structure Calculations for the Heavy Transition Metals: Parametrisation Methods, Band Structures and Problems with Iteration Techniques

Abstract

This paper discusses a parametrisation method developed by the author as a technique for the determination of band structures for the 4d transition metals and their compounds. It is suggested that some of the earlier work that has been published may not have found all the roots. Re-examination of the earlier work of the author reveals systematic discrepancies from benchmark band structure calculations. It is suggested that these results are an example of the unreliability of the earlier parametric band structure calculations, in which iteration techniques were used to determine the roots. Examples presented exhibit well known repeller behaviour, and so provide an early example where variation of initial conditions could have led to the discovery of bifurcation behaviour associated with the onset of chaos. The paper concludes with an application of the method to the calculation of electron-phonon interaction elements in the nonrelativistic limit.