INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 13 (2001) 8697–8706 PII: S0953-8984(01)24875-9 Simple rules for determining valencies of f-electron systems L Petit 1 , A Svane 1 , Z Szotek 2 , P Strange 3 , H Winter 4 and W M Temmerman 2 1 Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark 2 Daresbury Laboratory, Daresbury, Warrington WA4 4AD, UK 3 Department of Physics, Keele University, Keele, Staffordshire ST5 5DY, UK 4 INFP, Forschungszentrum Karlsruhe, Postfach 3640, Karlsruhe D-76021, Germany Received 18 May 2001 Published 7 September 2001 Online at stacks.iop.org/JPhysCM/13/8697 Abstract The electronic structure of f-electron systems is calculated with the self- interaction-corrected local-spin-density (LSD) approximation. This scheme allows for a splitting of the f-electron manifold into an integral number of localized electrons and self-consistently determined fractional number of band electrons. Therefore, in comparison with the LSD approximation, where all f states are pinned at the Fermi energy, only a maximum of one f band is left at the Fermi energy. We show that this band is partially occupied with occupancy n f , and the f-electron fluctuations are reduced compared with the LSD approximation. When n f exceeds a critical value of approximately 0.6, it becomes energetically more favourable to localize this state, and the number of valence bands is reduced by one. 1. Introduction The classification of the rare earths and their compounds in terms of their valencies provides an elementary explanation of their physical properties. In particular, dramatic changes in the lattice parameters of the rare earths can be related to valency changes [1]. Most of the rare earths in the solid state are trivalent; this is in contrast to the atomic state, where the rare earths are divalent. However, some compounds involving Eu, Sm, Tm and Yb can become divalent. Ce compounds, on the other hand, can be either trivalent or tetravalent. Not all rare-earth compounds can be classified in this simple manner and some of the materials with the most interesting magnetic and superconducting properties are of intermediate-valence character, i.e. no integer valency can be associated with the system. In this article we will show how to calculate the valency of f-electron systems and from this derive a simple physical picture of valencies in the solid state [2]. Valency is a chemical concept but is also very effective in describing the rare earths in the solid state. The valency of a rare earth can vary from divalent to trivalent and tetravalent. This 0953-8984/01/388697+10$30.00 © 2001 IOP Publishing Ltd Printed in the UK 8697