Eur. Phys. J. D 24, 245–248 (2003) DOI: 10.1140/epjd/e2003-00151-4 T HE EUROPEAN P HYSICAL JOURNAL D Study of (Al 2 O 3 ) n (O x ) clusters with n ≤ 16 and x = 0, 1, 2 from first principles calculations E.M. Fern´ andez 1, a , G. Borstel 2 , J.M. Soler 3 , and L.C. Balb´ as 1 1 Dpto. de F´ ısica Te´orica, Universidad de Valladolid, 47011 Valladolid, Spain 2 Fachbereich Physik, Universit¨at Osnabr¨ uck, 49069 Osnabr¨ uck, Germany 3 Dpto. de F´ ısica de la Materia Condensada, C-III, Universidad Aut´onoma de Madrid, 28049 Madrid, Spain Received 10 September 2002 Published online 3 July 2003 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2003 Abstract. The ionic and electronic structure of (Al2O3)n(Ox) clusters with n ≤ 16 and x = 0, 1, 2 is studied by means of first principles density functional calculations, norm-conserving pseudopotentials and a numerical atomic basis set. The equilibrium geometries have been determined by total energy minimization, starting with several initial geometries for each cluster size. The trends obtained for the atomic arrangements (structural isomers, coordination numbers, “disordered” versus “ordered” structures, etc.) and the electronic properties (binding energies, Homo-Lumo gap and dipole moments) are discussed. For most of the oxidized clusters studied here we find that the Homo-Lumo gap and the magnitude of dipole moment of isomeric species can vary drastically. PACS. 36.40.-c Atomic and molecular clusters – 36.40.Cg Electronic and magnetic properties of clusters – 36.40.Jn Reactivity of clusters – 61.46.+w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals 1 Introduction Aluminum oxide (alumina, Al 2 O 3 ) in its various allotropi- cal forms play a vital role in an increasingly large number of industrial applications: heterogeneous catalysis, ther- mal barriers, corrosion protection, and metal processing are but a few representative examples. Amorphous alu- mina is present at most crystal alumina polymorphs and at the surface of aluminium in contact to air but the un- derstanding of the detailed mechanism of the oxidation and passivation process is still lacking. The alumina amor- phous state have been related directly to γ -alumina [1], and also molten alumina is recognized as one of the pre- cursors of the allotropic form γ -Al 2 O 3 [2]. Reactions of halomethanes with γ -alumina particles from rocket ex- haust has been implicated in stratospheric ozone deple- tion [3]. Simulations of the hydrated α-alumina (0001) surface have been performed considering both the bare surface [4] and small isolated clusters modelling that sur- face [5]. The results show large differences in the calcu- lated energetics and local structural relaxations. There are numerous recent calculations of the (0001) surface of α-alumina [6–9] and of the κ-Al 2 O 3 (001) and (00 ¯ 1) sur- faces [10] revealing strongly relaxed surface Al ions, which explain the abnormally-coordinated Al ions observed in bulk porous aluminas [11]. The reactivity of different non- conventional alumina surfaces to typical contaminants and radicals is largely unknown. a e-mail: eva@lcb.fam.cie.uva.es As a preliminary attempt to understand those process, we calculate in this paper the atomic and electronic struc- ture of fully relaxed alumina clusters (Al 2 O 3 ) n (O x ) with the bulk Al 2 O 3 stoichiometry (x = 0) and with an added oxygen atom (x = 1) or molecule (x = 2). The sizes 1 ≤ n ≤ 16 for stoichiometric clusters and 1 ≤ n ≤ 10 for oxidised clusters are considered, resulting in a variety of “surfaces” and atomic coordinations for both, Al and O atoms. In a previous paper we have presented prelimi- nary results for a smaller range of sizes [12]. Here we pay special attention to important electronic and geometric differences between isomeric species of some clusters. In particular, we point to the large Homo-Lumo gap vari- ation obtained for isomers of some cluster sizes, which could have experimental relevance [13,14]. A quantitative way to discriminate the geometry of these isomers for their utilization in different applications is the chirality index recently introduced by Garz´ on and coworkers [15]. In Section 2 a brief description of the method of cal- culation, as well as a first test case study of the smaller clusters, is given. In Section 3 the results are presented and discussed and in Section 4 we present some conclusions. 2 Method of calculation and first test case We use the first-principles density functional theory (DFT) in the local density approximation (LDA) [16]. The electronic structure code SIESTA [17] is used to solve the