Z. Phys. D 41, 69–72 (1997) ZEITSCHRIFT F ¨ UR PHYSIK D c  Springer-Verlag 1997 Electronic structure of Lanthanum-carbon clusters A. Ayuela, G. Seifert, R. Schmidt Institut f¨ ur Theoretische Physik, Technische Universit¨ at Dresden, D-01062 Dresden, Germany Received: 27 November 1996 / Final version: 14 February 1997 Abstract. As the attachment of a metal change the molecu- lar and electronic structure of carbon clusters, the electronic properties as ionization potentials (IP) and electron affinities (EA) for small Lanthanum-carbon clusters LaC n with n=1– 6 have been investigated theoretically. They were studied by density-functional-theory (DFT) within LDA and consider- ing Gradient corrections (GC) for the exchange-correlation potential ( Becke-Perdew). The results for both quantities were obtained in good agreement with the experimental data: odd-even alternating IP’s, and no alternations for the EA’s. The different charge location in the carbon chains or at the La atom can explain the different trends of both quantities, respectively. PACS: 36.40.+d 1 Introduction The carbon-metal compounds are largely known in the bulk phase as carbides [1]. Carbon metal clusters in nearly stoi- chiometric composition with transition metals are known as metcars [2]. While with few atoms per fullerene cage the atoms are generally sited in or out the fullerene structure, they are described as endo- or exo-fullerenes, respectively. In this last case there is a long treatment with metals rang- ing from those alkalines, to transition metals, and elements from the rare earths. From the latter group the La had par- ticularly attracted the interest from the very beginning [3]. While a wide variety of physical and chemical properties for larger sizes can be proved, the small cluster sizes have only recently received a considerable amount of attention. To gain experimental information about the electronic structure of clusters, e.g., the ionization energies and elec- tron affinities, photoelectron spectroscopy (PES) is a power- ful tool. For small sizes of LaC n the appearance potentials (AP) have been measured for some of these clusters [4]. They showed even-odd alternations for the AP’s with max- ima for a odd number of carbon atoms n. On the other hand measurements of the PES have been performed recently for the corresponding cluster anions: Suzuki et al. [5] reported the vertical detachment energies (VDE) for LaC − n (2 ≤ n ≤ 8 ). While Arnold et al. measured also the VDE’s for pure carbon clusters C − n [6]. The VDE’s for C − n showed odd-even alternations, with maxima for n even. However, the odd-even alternation in VDE’s of the clusters for LaC − n disappears, and the VDE’s increase slightly as the size n of carbon atoms increase. While some experimental work has been done [4–6], lit- tle systematic theoretical investigations have been performed to understand these experimental results. The purpose of this study is to clarify the trends in VDE’s for LaC n − and in AP’s for the LaC n clusters. Some results for C − n clusters are also given for comparison. The paper is organized as follows. In Sect. 2 the com- putational method is sketched briefly, and the geometries of the clusters are described. In Sect. 3 the results of the calculations for the LaC n (n=1–6) and the corresponding anions are discussed; as well as the results for some C − n clusters have been considered. Finally, Sect. 4 summarizes our results. 2 Methodology The calculations were performed using Density-Functional- Theory (DFT) within the Local Density Approximation (LDA) plus the consideration of gradient corrections (GC). We applied the Amsterdam density functional (“adf”) pro- gram of Baerends et al. [7]: The Kohn-Sham equations are solved within a LCAO ansatz for the one-particle wave function; all integrals are evaluated numerically with Gauss- Legendre based integration algorithms [8], where the space is separated in a special manner. The densities are fitted to a sum of Slater-type functions to simplify the numerical calcu- lations of the multicenter Couloumb integrals. The orbitals are given as expansion of Slater-type orbitals considered as basis functions. An extended basis: triple-zeta with two po- larization functions is used as basis set for carbon C. While for Lanthanum atom triple -zeta basis set is chosen. The elec- tronic occupation of the atoms are 2s 2 2p 2 and 5d 1 6s 2 for C and La respectively. The functions of the core that remained fixed are 1s for C, and up to 5p for La. The exponents for the valence functions are: i) C: 2s 1.28 2.10 4.60 2p.82 1.48