Clusters valence molecular orbital

The N electrons will fill the N/2 energetically low-lying metal cluster valence molecular orbitals (CVMO) so that the number of CVMOs can be obtained as... 

In this cluster, which has C2, symmetry, the calculated molecular-orbital energy levels should be compcu-ed with those of the FeO cluster in Fig. 4.26(a). As for the latter cluster, the molecular orbitals can be grouped into sets in relation to their atomic-orbital character, with the dominantly Fe 3d (crystal-field-type) orbitals being at the top of the valence band. Now, however, as shown in Fig. 4.29, the orbitals below these in energy fall into four groups O 2p nonbonding orbitals, Fe-(9... 

Table 3.10. Number of Valence Molecular Orbitals (CVMO) for Various Atoms in Clusters of Transition Metals...

Lauher [220, 221] proposed that the metal derived MO s of a carbonylated cluster can be derived from an extended Hiickel calculation on the bare metal duster and then divided into sets of filled duster valence molecular orbitals, CVMO, and... 

A schematic molecular orbital diagram for the Fe-Fe interaction in an S = I valence-delocalized Fe Fe pair based on effective C v symmetry at the Fe sites and the observed electronic transitions for the valance-delocalized [Fe2S2l cluster is shown in Fig. 15. The dominant interaction (responsible for the S = ground state) is the a overlap between the pair of orbitals, with progressively smaller tt interactions between pairs of d z and dyz orbitals and S interactions between pairs of d y amd / orbitals. The three highest energy tran-... 

The location of electrons linking more than three atoms cannot be illustrated as easily. The simple, descriptive models must give way to the theoretical treatment by molecular orbital theory. With its aid, however, certain electron counting rules have been deduced for cluster compounds that set up relations between the structure and the number of valence electrons. A bridge between molecular-orbital theory and vividness is offered by the electron-localization function (cf p. 89). 

Quantum-chemical cluster models, 34 131-202 computer programs, 34 134 methods, 34 135-138 for chemisorption, 34 135 the local approach, 34 132 molecular orbital methods, 34 135 for surface structures, 34 135 valence bond method, 34 135 Quantum chemistry, heat of chemisorption determination, 37 151-154 Quantum conversion, in chloroplasts, 14 1 Quantum mechanical simulations bond activation, 42 2, 84—107 Quasi-elastic neutron scattering benzene... 

In bridged metal-metal bonded dimeric complexes, the relative importance of metal-metal and bridging ligand effects are more difficult to unravel. Dahl and his co-workers have elegantly exploited systematic crystallographic analyses to detail the stereochemical consequences of valence-electron addition or removal in dimeric metal complexes (46, 47, 65, 230) and clusters (66, 88, 204, 205, 213, 216, 222). Their experimental work has been neatly underpinned by nonparameterized approximate Hartree-Fock molecular orbital calculations (217) on the phosphido-bridged dimers [Cr2(CO)80ti-PR2)2]n"2 and [Mn2(CO)g(/i.-PR2)2]n (rt = 0, + 1, or +2) ... 

We discuss here two examples of vibronic effects in polynuclear highly symmetrical transition metal clusters. The existence of degenerate and quasi-degenerate molecular orbitals in their energy spectra results in the Jahn-Teller effect or in the vibronic mixing of different electronic states. We show that both quantum-chemical methods and model approaches can provide valuable information about these vibronic effects. In the case of the hexanuclear rhenium tri-anion, the Jahn-Teller effect is responsible for the experimentally observed tetragonal distortion of the cluster. The vibronic model of mixed-valence compounds allows to explain the nature of a transient in the photo-catalytic reaction of the decatungstate cluster. 

Figure 12. Molecular orbital diagram for an FegOjg cluster used to understand the orbitals involved in Fe Fe3 charge transfer. The absorption band observed near 13,000 cm 1 in the spectra of mixed-valence silicates is due to the transition from the Fe2 (t2g)- Fe3+(t2g) orbitals. A transition state calculation for that energy in the cluster presented here gives 10,570 cm"1 in fair agreement with experiment.

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