Electronic energy calculation of C60 clusters

78 Materials Chemistry and Physics, 34 (1993) 78-80 Electronic energy calculation of CeO clusters !$. Katn-clo@u, 8. Erkog and T. Halmoglu” Depament of Physics, Middle East Technical University, 06531 Ankara (Turkey) (Received May 25, 1992; accepted August 21, 1992) Abstract The ground-state total electronic energy of the Buckminsterfullerene (BF) and truncated dodecahedron (TD) models of C, has been calculated using the empirical tight-binding (ETB) method. It was found that the BF model was energetically more stable than the TD model of Cm In recent years, after the special place of carbon and the truncated dodecahedron (TD), were found to among the elements was realized, many studies were be almost isoenergetic. The BF structure contains 12 conducted on carbon clusters. Among the carbon clus- regular pentagons and 20 regular hexagons. The TD ters, intense interest was focused on the C,, cluster, structure comprises triangular surfaces surrounded by owing to its special structure. The idea that C,, might larger decagons. In this empirical calculation [6], the form a stable soccerball molecule had first been con- potential energy of C,, was defined by a potential ceived in the imaginations of chemists. Later, a C,, energy function having two- and three-body interactions. cluster with a remarkably stable Buckminsterfullerene After a full energy minimization of the BF structure, structure was observed during laser vaporization of a C-C bond length of 1.351 A was calculated for the graphite in a high-pressure supersonic nozzle [l]. The edge between two hexagonal faces, and a C-C bond possibility of the existence of such a highly symmetric length of 1.413 %, was calculated for the edge between carbon molecule has generated a great deal of interest hexagonal and pentagonal faces. These calculated bond among both experimentalists [l-5] and theoreticians lengths are close to the X-ray diffraction values of 1.388 [6-111. %,and 1.432 A [12]. In the same full energy minimization The theoretical calculations of the properties of C,,, work, the C-C bond lengths were calculated to be have progressed from empirical and semi-empirical to 1.349 8, for the edge of an equilateral triangle, and ab initio methods. The limited ab initio studies helped 1.245 A for the edge between two decagons of the TD enable values of the energy and structure-related prop- structure. These C-C bond distances have been used erties of C,, cluster to be obtained, which are all based as the nearest-neighbor distances of C atoms in the on the ground-state geometry proposed by Larsson et present band-structure calculations. al. [7]. A systematic understanding of the dynamic and In this study, the total electronic energy of the BF thermal properties of C, cluster is aided by the empirical and TD structures has been calculated using the em- and semi-empirical calculations, which are based on a pirical tight-binding (ETB) method. The s and p atomic model that employs a many-body interaction potential orbitals are chosen to form the basis functions of the function [ 111. ETB method, and only the self-, the first- and the In the present work the electronic energy and the second-nearest-neighbor interactions have been taken band structure of C,, were investigated for the two into account. The necessary energy parameters cor- different structures given in [6]. In the empirical po- responding to four types of ETB interactions, namely tential energy function calculation of Hahclo@u [6], ssa, spa, ppu and ppr, were taken from [13]; they are the configurations corresponding to local energy minima given in Table 1. The optimized coordinates of C atoms were calculated for various shells of an icosahedron for BF and TD structures were taken from [6]. containing different numbers of carbon atoms. For C6,,, The total density of states (TDOS) profiles for the the two low-lying isomers, Buckminsterfullerene (BF) BF and TD C,, clusters have been calculated at the symmetry point r and are shown in Figs. 1 and 2, *Present address: Department of Materials Science and En- respectively. It was found that, because of the symmetric gineering, Stanford University, Stanford, CA 94305, USA. structure of the BF model of Cso, in this model the 0254-0584/93/$6.00 0 1993 - Elsevier Sequoia. All rights reserved  79 TABLE 1. Interaction energy (in eV) parameters used in the Figures 1 and 2 also show the s- and p-orbital calculations for carbon atomsa contributions to the TDOS of the two C, models. It was found that in the BF structure the contributions Interaction SSU spa PP* PPn of the s and p orbitals to the states at energies lower than - 25 eV were the same. The s-orbital contribution self -5.16 0.0 2.29 0.0 1st nearest neighbor - 4.43 3.79 5.66 - 1.83 to the states seen between -21 eV and - 25 eV was 2nd nearest neighbor 0.14 - 0.02 0.63 - 0.24 lower than the p-orbital contribution. The peaks seen between - 18 and -21 eV may be considered pure “Ref. 13. p-states. The state at about - 13 eV is the result of strong s-p interactions. The states above - 10 eV are dominantly formed by p orbitals. 40 TWS BF In the TDOS of the TD model, the two peaks seen 30 A at about - 18 eV obviously contain a strong s-orbital contribution. The separate peak at - 10 eV indicates strong s- and p-orbital interactions. As was observed in the TDOS of the BF model, the higher energy states (> -5 eV) are dominantly formed by p orbitals. The ground-state total electronic energy of the BF and TD models of C,, clusters has been calculated to be - 2486.46 eV and - 1587.78 eV, respectively. The total energy calculation was based on the charge transfer between the carbon atoms. It was found that the charge transfer between the atoms of BF was two orders of magnitude greater than the charge transfer in the TD structure. Although the BF and TD models of C,, were almost isoenergetic in the empirical potential calculation [6], the present electronic energy calculations show Fig. 1. DOS (in arbitrary units) for the BF structure of Cm. Arrow shows the position of the Fermi level. clearly that the BF structure is energetically more stable than the TD model of CeO,as was previously determined experimentally [l-5] and predicted theoretically [7-l 11. References H. W. Kroto, .I. R. Heath, S. C. O’Brien, R. F. Curl and R. E. SmalIey,Narure (London), 318 (1985) 162; W. Kratshmer, L. D. Lamb, K. Fostiropoulos and D. R. Huffman, Nature (London), 347 (1990) 354. D. M. Cox, D. J. Trevor, R. C. Reichmann and A. Kaldor, J. Am Chem. Sot., 108 (1986) 2457; M. Y. Hahn, E. C. Honea, A. J. 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