Theory of energy bands and related properties of 4d transition metals. I. Band parameters and their volume dependence

The energy bands of the 4d transition metal series are computed self-consistently within the atomic sphere approximation (ASA) over a range where the volume changes by nearly an order of magnitude about the equilibrium atomic volume. The parameters defining the position and width of the s and d bands are tabulated across the series and as a function of volume. A theoretical interpretation of the trends gives a more detailed understanding of the electronic structure of transition metals. The bottom of the conduction band is accurately described by an Ashcroft empty core pseudopotential. The centre of the d band is fitted very well by an exponential, and the width approximately satisfies Heine's inverse five-thirds volume dependence. The d band occupancy to the left of the series is very sensitive to the relative ion core volume which Duthie and Pettifor show as explaining the rare earth crystal structure trend. The ASA includes explicitly the very important bonding d charge in addition to the usual renormalized atom contribution.