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The rare-earth metals have high magnetic moments and a diverse range of magnetic structures 1 . Their magnetic properties are determined by the occupancy of the strongly localized 4f electronic shells, while the outer s±d electrons determine the bonding and other electronic properties 2 . Most of the rare-earth atoms are divalent, but generally become trivalent in the metallic state. In some materials, the energy difference between these valence states is small and, by changing some external parameter (such as pressure), a transition from one to the other occurs. But the mechanism underlying this transition and the reason for the differing valence states are not well understood. Here we report ®rst-principles electronic-structure calculations that enable us to determine both the valency and the lattice size as a function of atomic number, and hence understand the valence transitions. We ®nd that there are two types of f electrons: localized core-like f electrons that determine the valency, and delocalized band-like f electrons that are formed through hybridization with the s±d bands and which participate in bonding. The latter are found only in the trivalent systems; if their number exceeds a certain threshold, it becomes energetically favourable for these electrons to localize, causing a transition to a divalent ground state.Here we report a systematic theoretical investigation of the rareearth elements and their sulphides using ab initio electronicstructure methods. These go well beyond standard calculations in which the 4f shell is described by an atomic model, while an itinerant picture for the s±d electrons is implemented 3,4 . We include a self-interaction correction (SIC) which removes the spurious interaction of each electron with itself that occurs in conventional band-structure theory 5 . Our approach has the advantage of describing both the bonding s±d electrons and the f electrons on an equal footing. The SIC has a negligible effect on the bonding s±d electrons, but is substantial for the f electrons 6 . Application of the SIC to the f electrons provides a de®nition of valency of the metallic rare-earth materials. Here we associate the valency with the number of states available for the electron to propagate through the solid, namely N valency Z 2 N core 2 N SIC where Z is the atomic number of the rare earth and N core is the number of atomic core electrons. The quantity N SIC is the number of letters to nature 756 NATURE | VOL 399 | 24 JUNE 1999 | www.nature.com Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb -2 0 2 4 E II -E III (eV) Figure 1 The energy difference (in eV) between the divalent and trivalent state of rare-earth materials. The dashed line shows the`experimental' values for the rare-earth metals 3 . The open circles and the crosses show the calculated values for the rare-earth metals and the rare-earth sulphides, respectively. We see that the divalent and trivalent energy difference is large and positive at the beginning of the series, indicating that the trivalent state is well favoured. The en...

The electronic structure of the rare-earth nitrides is studied systematically using the ab initio self-interaction corrected local-spin-density approximation. This approach allows both a localized description of the rare-earth f electrons and an itinerant description of the valence electrons. Localizing different numbers of f electrons on the rare-earth atom corresponds to different valencies, and the total energies can be compared, providing a first-principles description of valence. We show that these materials have a broad range of electronic properties including forming a different class of half-metallic magnets with high magnetic moments, and are strong candidates for applications in spin-filtering devices.

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We report density functional theory (DFT) calculations for gold atoms and dimers on the surface of graphene. The calculations were performed using the plane wave pseudopotential method. Calculations were performed for a variety of geometries, and both the graphene surface and gold atoms were allowed to fully relax. In agreement with experiment, our results show that the gold-gold interaction is considerably stronger than the gold-graphene interaction, implying that uniform coverage could not be attained. The minimum energy configuration for a single gold atom is found to be directly above a carbon atom, while for the dimer it is perpendicular to the surface and directly above a carbon-carbon bond. Our results are consistent with previous similar calculations.

The electronic structure of some europium chalcogenides and pnictides is calculated using the abinitio self-interaction corrected local-spin-density approximation (SIC-LSD). This approach allows both a localised description of the rare earth f −electrons and an itinerant description of s, p and delectrons. Localising different numbers of f -electrons on the rare earth atom corresponds to different nominal valencies, and the total energies can be compared, providing a first-principles description of valency. All the chalcogenides are found to be insulators in the ferromagnetic state and to have a divalent configuration. For the pnictides we find that EuN is half-metallic and the rest are normal metals. However a valence change occurs as we go down the pnictide column of the Periodic Table. EuN and EuP are trivalent, EuAs is only just trivalent and EuSb is found to be divalent. Our results suggest that these materials may find application in spintronic and spin filtering devices.

The crystal structure of CuS has been confirmed experimentally using the powder diffraction method on the high-resolution powder diffractometer at the Rutherford-Appleton laboratory. The observed crystal structure is P63/mmc. Standard density functional calculations on CuS on a variety of crystal structures are also reported. The calculations also predict P63/mmc as the stable crystal structure. On the basis of the agreement between theory and experiment the authors are able to discuss the details of the bonding in this material.

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