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Theoretical electronic structure studies on Mn n (nϭ2 -8) clusters have been carried out using a linearcombination-of-atomic-orbitals-molecular-orbital approach within the density-functional formalism. It is shown that Mn 2 and Mn 3 have energetically close ferromagnetic and antiferromagnetic or frustrated antiferromagnetic solutions. Mn 4 , Mn 5 , Mn 6 , Mn 7 , and Mn 8 are all ferromagnetic with moments of 20, 23, 26, 29, and 32 B . The appearance of ferromagnetic character is shown to be accompanied by bonding between minority d states. The relation between geometry and multiplicity and the possibility of closely spaced multiplet states are discussed.

Theoretical ab initio studies of neutral, cationic and anionic Cr 2 , Mn 2 , and CrMn dimers have been carried out to explore the progression of magnetic coupling with the number of electrons. It is shown that while Cr 2 and Cr 2 Ϫ have antiferromagnetically coupled atomic spins, Cr 2 ϩ has a ferromagnetic ground state closely followed by an antiferromagnetic state. On the other hand, all Mn 2 dimers are ferromagnetic, irrespective of the charge. The neutral CrMn is ferrimagnetic while the charged CrMn are antiferromagnetic. In all cases, the charged dimers are found to be more stable than the neutral ones. The results are compared with available calculations and experiments and the difficulties associated with theoretical description and the experimental interpretations are discussed.

Electronic-structure studies on a Ni&3 cluster have been carried out using a linear-combination-of-atomicorbitals -molecular-orbital approach within the density-functional formalism. The ground state is shown to be a distorted D3d icosahedron. The cluster has a magnetic moment per atom close to the bulk and is marked by a number of higher spin states close to the ground state. Their effect on the observed magnetic behavior is discussed.Small atomic clusters are now known to display geometrical arrangements and physical, chemical, electronic, and magnetic properties that are different from the bulk. The properties evolve with size and composition and this has provided hope of generating new materials with tailored properties using suitably designed clusters. The recent interest in clusters has been on transition-metal clusters, mainly due to their interesting magnetic behaviors. For example, Stern-Gerlach experiments ' on small clusters of Fe, Co, and Ni, which are itinerant ferromagnets in bulk, show that the clusters exhibit a variety of behaviors depending on their temperature. At high temperatures, the clusters show behaviors reminiscent of superparamagnetism, while at low rotational temperatures they show effects assigned to magnetic resonance. What is surprising is that the magnetization of certain clusters increases with temperature.There are also indications that the magnetic moment depends on the site and that the surface atoms have higher moments than the interior atoms. ' Since the magnetic moment is determined by electronic structure, which in turn depends on the geometry, a detailed study of these quantities is crucial for an understanding of these clusters.In this paper we present a detailed study of the groundstate geometry, its electronic structure, and the nature of lowlying spin states of an Ni&3 cluster. Recent experiments using molecular absorption of N2 on Ni"clusters as a way to determine their geometry indicate that Ni&3 has an icosahedral structure. Earlier theoretical studies are also based on such a geometry. While our studies carried out on icosahedral and cuboctahedral clusters do find the icosahedral geometry to be more stable, in agreement with experiment, we show that the resulting electronic structure is not compatible with the icosahedral symmetry. The perfect icosahedron is shown to undergo distortion. Further, the ground state is marked by several low-lying high spin states. It is shown that this could lead to an abnormal temperature dependence of the magnetic moment. We finally discuss the local moments and study the variation in moment between the central and outer atoms. The nature of orbitals contributing to the moment is examined via a decomposition of the charge density into different angular-momentum states. The theoretical studies were carried out using a linearcombination-of-atomic-orbitals -molecular-orbital (LCAO-MO) approach. ' The molecular orbitals were made out of a linear gombination of atomic orbitals taken as Gaussian functions centered at the atomic sites. The ...

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We present self-consistent local-spin-density calculations of the static electric dipole polarizability tensor for several isomers of sodium clusters with up to nine atoms. We show how the comparison of the calculated polarizabilities with the experimental data can be used to identify which isomer is observed in the experiments. Our results indicate that sodium clusters with six atoms or less are planar and that the drop in the polarizability of Na7 is related to the change from two-dimensional to three-dimensional geometries. We also present an analysis of recent measurements of photoabsorption resonance frequencies.PACS numbers: 31.20.Sy, 36.40.+d The determination of the atomic geometrical arrangement is a fundamental problem in the study of very small metallic clusters, because a deep understanding of their electronic and chemical properties requires the knowledge of their atomic structure. Unfortunately, direct experimental evidence on the geometrical structure of small metal clusters is scarce and it is very difficult to obtain for unsupported clusters. Quantum calculations of the total energy of clusters can suggest plausible structures, but they often find isomers with similar energies, and therefore cannot predict with confidence which structure is the most stable because the accuracy of the calculations is limited. In this context, the measurements of the average static electric polarizability of clusters x are very interesting since the polarizability depends on both cluster shape and size. Furthermore, recent measurements of the total photoabsorption cross section of alkali clusters 2 " 4 have been fitted to a collective resonance model, which uses the principal values of the static polarizability tensor as fit parameters. The anisotropy of the polarizability tensor provides additional information on the shape of the cluster.The rotationally averaged static electric polarizabilities a of sodium clusters with less than forty atoms were measured by Knight et al. l using a mclecular-beam deflection technique. The experimental results indicate that the general trend of the average polarizability per atom normalized to the atomic value a/na\ is a slow decrease with increasing cluster size from the atomic value of unity to the bulk value of 0.4. They also found that clusters with a "magic number" of atoms corresponding to the closed electronic shells of spherical models have smaller relative polarizabilities. Finally, they observed a "fine structure" of the polarizability between two shell closings which was attributed to the deviation from sphericity of the geometry of the sodium clusters. 5 The classical electrostatic polarizability of a perfect conducting sphere of radius R is a -Ane^R 3 . Using a conducting sphere of radius R=n x^r s , where r s is the Wigner-Seitz radius, as a model for a Na" cluster, the predicted normalized polarizability a/n is 40% of the measured atomic value a\, a good ballpark figure. Including the effect of the charge "spill out" present at the surface leads to the predictio...