J. Phys.: Condens. Matter 8 (1996) 287–302. Printed in the UK Transferability of a local pseudopotential based on solid-state electron density Fernando Nogueira†, Carlos Fiolhais†, Jingsong He‡, John P Perdew‡ and Angel Rubio§ † Department of Physics, University of Coimbra, P3000 Coimbra, Portugal ‡ Department of Physics, Tulane University, New Orleans, LA 70118, USA § Department of Theoretical Physics, University of Valladolid, E-47011 Valladolid, Spain Received 3 July 1995, in final form 14 November 1995 Abstract. Local electron–ion pseudopotentials fitted to dominant density parameters of the solid state (valence, equilibrium average electron density and interstitial electron density) have been constructed and tested for sixteen simple metals. Calculated solid-state properties present little evidence of the need for pseudopotential non-locality, but this need is increasingly evident as the pseudopotentials are transferred further from their solid-state origins. Transferability is high for Na, useful for ten other simple metals (K, Rb, Cs, Mg, Al, Ga, In, Tl, Sn, and Pb), and poor for Li, Be, Ca, Sr and Ba. In the bulk solid, we define a predictor of transferability and check the convergence of second-order pseudopotential perturbation theory for bcc Na. For six- atom octahedral clusters, we find that the pseudopotential correctly predicts self-compressions or self-expansions of bond length with respect to the bulk for Li, Na, Mg, and Al, in comparison with all-electron results; dimers of these elements are also considered. For the free atom, we examine the bulk cohesive energy (which straddles the atomic and solid-state limits), the atomic excitation energies and the atomic density. For the cohesive energy, we also present the results of the simpler stabilized jellium and universal-binding-energy-curve models. The needed non- locality or angular-momentum dependence of the pseudopotential has the conventional character, and is most strongly evident in the excitation energies. 1. Introduction and a summary of conclusions The pseudopotential [1, 2, 3, 4], a weak effective interaction between a valence electron and an ion core, brings a useful simplification to condensed-matter physics and quantum chemistry, at some cost in accuracy. The simplest and least accurate pseudopotentials are local or multiplication operators w(r), the same for all components of the electron’s angular momentum. This locality is required for fair tests of density functional approx- imations [5] against more accurate many-body methods, and has a number of other practical advantages [6, 7]. Two of us have recently proposed a local pseudopotential (the individual ‘evanescent-core pseudopotential’ of [7]) fitted to three dominant density parameters of a simple metal: the valence z , the equilibrium average valence electron density ¯ n = 3 4πr 3 s (1) and ¯ n int , the electron density averaged over the interstitial region between the surface of the polyhedral Wigner–Seitz cell and the inscribed sphere. Thus we have refined the ‘stabilized jellium’ [8, 9] and ‘ideal metal’ [10] models through the introduction of atomic structure. 0953-8984/96/030287+16$19.50 c  1996 IOP Publishing Ltd 287