Chromium-Doped Germanium Clusters CrGe n (n ) 1-5): Geometry, Electronic Structure, and Topology of Chemical Bonding Xin-Juan Hou, ² G. Gopakumar, ² Peter Lievens, ‡ and Minh Tho Nguyen* ,² Department of Chemistry and Institute for Nanoscale Physics and Chemistry, UniVersity of LeuVen, Celestijnenlaan 200F, B-3001 LeuVen, Belgium, and Laboratory of Solid State Physics and Magnetism and Institute for Nanoscale Physics and Chemistry, UniVersity of LeuVen, Celestijnenlaan 200D, B-3001 LeuVen, Belgium ReceiVed: September 12, 2007 The structure and properties of small neutral and cationic CrGe n 0,+ clusters, with n from 1 to 5, were investigated using quantum chemical calculations at the CASSCF/CASPT2 and DFT/B3LYP levels. Smaller clusters prefer planar geometries, whereas the lowest-lying electronic states of the neutral CrGe 4 , CrGe 5 , and cationic CrGe 5 + forms exhibit nonplanar geometries. Most of the clusters considered prefer structures with high-spin ground state and large magnetic moments. Relative to the values obtained for the pure Ge n clusters, fragmentation energies of doped CrGe n clusters are smaller when n is 3 and 4 and larger when n ) 5. The averaged binding energy tends to increase with the increasing number of Ge atoms. For n ) 5, the binding energies for Ge 5 , CrGe 5 , and CrGe 5 + are similar to each other, amounting to ∼2.5 eV. The Cr atom acts as a general electron donor in neutral CrGe n clusters. Electron localization function (ELF) analyses suggest that the chemical bonding in chromium-doped germanium clusters differs from that of their pure or Li-doped counterparts and allow the origin of the inherent high-spin ground state to be understood. The differential ΔELF picture, obtained in separating both R and  electron components, is consistent with that derived from spin density calculations. For CrGe n , n ) 2 and 3, a small amount of d-π back-donation is anticipated within the framework of the proposed bonding model. Introduction Silicon clusters have widely been studied because they are important for the fine processing of semiconductors and the synthesis of novel materials. The encapsulation of transition metals in the silicon clusters has been demonstrated to change the structures and properties of Si n clusters. 1 For the heavier congeners in group IV, relatively little attention has been paid on the preparation and properties of metal-doped M m Ge n clusters. The pure germanium clusters are chemically reactive and thus not suitable as a building block of self-assembly materials. 2 By an appropriate choice of the metal dopant, it is possible to design metallic as well as semiconducting nanotubes using Ge n as building blocks. 3 Metal-encapsulated caged clusters of Ge were investigated using the ab initio pseudopotential plane-wave method. 4 Their results revealed that metal-doped M m Ge n clusters possess large HOMO-LUMO gaps. Electronic properties of silicon- and germanium-doped indium clusters were investigated by photoionization spectroscopy and photoelectron spectroscopy. 5 The geometries, stability, and electronic proper- ties of Ge n and TMGe n (TM ) Zn, W, and Cu) clusters have also been systematically investigated by using a density functional approach. 6-8 The remarkable features of W-doped Ge n clusters were distinctly different from those of Cu- and Ni-Ge n clusters, indicating that the growth pattern of the TM- Ge n depends on the kind of doped TM impurity. Recently, quantum chemical calculations on the structure and energies of lithiated diatomic germanium clusters and their cations (Li n - Ge 2 and Li n Ge 2 + ) revealed that they all have low-spin ground state. 9 Small elemental and molecular clusters provide a bridge toward the understanding of how matter evolves from atoms to bulk. 10,11 The available experimental 12-18 and theoretical 19-26 studies on small Ge clusters focused mostly on the lowest energy electronic structure. Chromium has the largest magnetic moment among the 3d transition metal elements with half-filled 3d and 4s orbitals. In view of the recent experimental observations on the Cr-doped germanium clusters, 27 we set out to investigate the magnetic properties of these clusters employing various theoretical methodologies. As far as we are aware, there were no previous theoretical investigations on the CrGe n clusters. In the present paper, a detailed investigation on equilibrium geometries, stabilities, electronic structure, and bonding proper- ties, in particular the topology of the electron densities, of Cr- doped germanium clusters are reported. Computational Methods Calculations were performed for all possible spin multiplici- ties M ) 2S + 1 for each cluster considered. All investigated clusters were fully optimized making use of the density functional theory with the popular hybrid B3LYP functional, 28 in conjunction with a 6-311+G(d) basis set for chromium and the LANL2DZdp basis set with an effective core potential (ECP) for germanium (denoted hereafter as B3LYP/Gen). The ECP 29 has been selected in view of the large number of structures investigated. For each spin manifold, the geometry optimization was carried out without any symmetry constraint at different * Corresponding author. E-mail: minh.nguyen@chem.kuleuven.be. ² Department of Chemistry and Institute for Nanoscale Physics and Chemistry. ‡ Laboratory of Solid State Physics and Magnetism and Institute for Nanoscale Physics and Chemistry. 13544 J. Phys. Chem. A 2007, 111, 13544-13553 10.1021/jp0773233 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/04/2007