E x a c t A n a l y t i c a l F o r m u l a e for M e a n C o o r d i n a t i o n N u m b e r s in ClustersH a n s -G e r h a r d Fritsche 1 ~z R o b e r t E. Benfield ~ 1Fakult~t ffir Chemic, Friedrich-Schiller UniversitY.t, Am SteigeI 3, A b s t r a c t .Rigorous analytical formulae for mean nearest-neighbour coordination numbers in clusters as a function of cluster size have been derived for a range of geometries: the tetrahedron, octahedron, cuboctahedron, icosahedron and bcc rhombic dodecahedron. Formulae for outer-neighbour coordination numbers are also reported, including a complete analysis of interatomic distances and mean coordination numbers in icosahedra. The formulae will find application in studies of electronic structure and interpretation of EXAFS data.

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+ + +To examine this transition, binding energies of icosahedra and cuboctahedra will be compared. Letbe the energy of a homonuclear cluster, having N differently coordinated atoms (18i -sjl distance between atoms i and j). Only pair potentials V.. between nearest -neighbowing a toms a r e considered . 11, if I 8i -8. I = R, nearest neighbour distance,

a), and V. HEERA (c)The interaction of hydrogen with palladium and platinum is studied on the basis of cluster calculations using the SW-Xa method in a semirelativistic variant. Energy level spectra, density-ofstates curves, and charge distributions arc represented and discussed w t h respect to other theoretical and experimental investigations. The dominant role of covalent bond between hydrogon and palladium/platinum is illustrated. The results of the calculations show that for a heavy element as platinum relativistic effects can influence the bonding between atoms in a qualitative way. The less stability of the hydrogen-platinum Bystemcompared with the Pd-H systemis explained as a relativistic effect. Die Wechselwjrkung von Wasserstoff mit Pallndium und Platin wird auf der Grundlage v mCluster-Rechnungen mit der SW-Xa-Methode in einer scmirelativistischen Variante untersucht. Die Energicniveauschemata, Zustandedichtekurven und Ladungsdichteverteilungen werden dargestellt und hinsichtlich anderer theoretischcr und cxperimenteller Untersuehungen diskutiert. Die dominicrcnde Rolle der kovalentcn Bindung zwischen Wasserstoff und Palladium/Platin wird illustriert. Die Ergebnisse der Berechnungen zcigen, da13 fiir ein schweres Element wie Platin die relativistischen Effekte die Bindung zwischen Atomen in qualitativer Weise beeinflussen konncn. Die geringero Stabilitat des Platin-Wasscrstoff-Systemsverglichen mit dem Pd-H-Systemwird als ein relativistischer Effckt erkliirt. ~-I) Mommsenstr. 13, DDR-8027 Dresden, GDR. 2, Am Steiger 3, DDR-6900 Jenct, GDR.