Cluster symmetry

The polyhedra in Fig. 1 thus represent suitable shapes for cluster species with n skeletal atoms (each of which can furnish three AO s for use in skeletal bonding) and with (n + 1) skeletal bond pairs. Since it is the cluster symmetry that determines the number of bonding MO s, the same polyhedra can serve as the basis for the structures of a whole range of isoelectronic species, including neutral carboranes of formula C2B 2Hn, bismuth clusters, such as the trigonal-bipyramidal Bis " ",... 

Resonance Raman spectra Cluster symmetry, ligand types, and oxidation states Extended X-ray absorption fine structure (EXAFS) spectra Metal ligand distances number and types of liganded atom... 

The calculation of free-space clusters while giving insight into supported clusters is also computationally easier (no support atoms, higher cluster symmetries). 

This lowering of effective cluster symmetry from has recently gained further support. Thus, Reedijk et al. (283) observed a typical antiferromagnetic x vs temperature plot, with a maximum at ca. 80 K, for the complex [Cu40(Cl)e(3-phenyl, 4,5-dimethyl-pyrazole)4]. They used a number of Heisenberg models to fit the data, the best being a D4 (square) distortion yielding = 2.11, Jj = -36 cm" J2 = -23 cm" ... 

The values of 5 and g depend upon the structure of the complex. If it is assumed that the cluster is made up of a central core consisting of (COj) [i-e., (C02) J+i = (C02)J(CQ2) i] surrounded by loosely held COj units, then any of the loosely held CO2 units can evaporate. Thus it is assumed that the cluster symmetry number is n — 1 while the transition state has a symmetry of 1, so that g = n-1. Because the intramolecular CO2 modes are assumed too high to contribute to the density of states at the low energies involved in the metastable ion dissociation, the total number of vibrational modes is just 5 = 5 n— 1). (With the loss of each linear CO2 unit, the cluster looses five van der Waals modes.) With these assumptions and the measured (Stace and Shukla, 1982) average kinetic energy releases, the binding energies for CO2 monomers... 

The practical cyclic-cluster calculations for crystals were made by EHT, MR and different ZDO methods. In these calculations one has to take into account the mul-tipbcation law of the cyclic-cluster symmetry group. This requires the modifications (compared with molecules) of Fock matrix elements in the LCAO approximation. 

However, a comment on the expected clustering of two different types of phases is first necessary. In Chem. 24, two clusters are obvious. The upper cluster. Symmetry Shield to Nucleosil Nautilus, contains embedded phases. The lower cluster, XTerra MS to Chromolith Performance, contains phases with a classical coverage. 

Since the number of bonding molecular orbitals is determined by the cluster symmetry, the same polyhedron can serve as the basis for the structures of an ample range of isoelectronic species as neutral carboranes with formula C2B -2H or the naked clusters as Ge that will be dealt with in Chapter 4. 

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