Localized electron count

We briefly report here a few definitions coneerning global and local electron counting procedures, remembering also that the number of cluster valence electrons (CVE) strongly determines the stoichiometry and the cluster shape, while the correct local valence electrons (LVE) distribution influences the ligand conformation. For a BMCC ... 

This cluster has a monocapped trigonal bipyramidal structure in which the 18-electron rule is obeyed for only two of the six Os atoms. The situation is worse for the localized electron count and for the 18-electron rale that do not work at all in the very stable octahedral 86-electron dianion (see below). On the other hand, Wade s theory that uses the polyhedral skeleton electron pairs very well rationalizes the electron counts in large organometallic clusters. - ... 

Determine the number of electrons (NCE) of the clusters [Re4H4(CO)i2], [Fe6 C(CO)i6 ] and [NiCpJe by adding the metal valence electrons and the electrons provided by the ligands on one hand and by the localized electron count on the other hand. Do these clusters follow the localized electron count ... 

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). 

Table 4.52. A synopsis of localized electronic structures for simple metallocenes in terms of MLX formulation, spin-state multiplicity, nonbonding d electrons (d count) and orbitals (nd), ordinary (2c/2e) and tu (3c/4e) bonds, and nominal sd" hybridization...

In the spirit of the Anderson model, we separate electrons into two subsystems delocalized electrons for which the LDA is assumed to give reasonable results and localized electrons for which it is well known that the LDA can lead to unphysical results. To treat these states in a better way, and to avoid double counting, we exclude the interaction between localized electrons (/ or d) already taken into account in an average way in the LDA-on-site energy... 

The tuning of electron counts is one of the strategies of the solid state chemists. Elements can be substituted, atoms intercalated, nonstoichiometries enhanced. Oxidation and reduction, in solid state chemistry as in ordinary molecular solution chemistry, are about as characteristic (but experimentally not always trivial) chemical activities as one can conceive. The conclusions we reached for the Pt-Pt chain were simple, easily anticipated. Other cases are guaranteed to be more complicated. The COOP curves allow one, at a glance, to reach conclusions about the local effects on bond length (will bonds be weaker, stronger) upon oxidation or reduction. 

The electronic structures of borane clusters were first successfully described using localized three-center- and two-center-two-electron bonds. These treatments have been replaced by the cluster electron-counting rule based on MO methods hence, why bother with the three-center bond model in a book about clusters Let s consider why there is value in a more localized approach. 

Y3+ or La3+ cations. Consequently, the additional electron populates an antibonding Trg orbital thereby reducing the bond order and increasing the C-C distance. Reality is a little more complicated since there are low-lying d orbitals on these metals. Consequently a metallic d band overlaps with the C2 TTg band as shown below. For this reason, the electron is partly localized in the metal d band and partly localized in the C2 band. Nevertheless the C-C distance in these materials is chiefly governed by the electron count of the metal. 

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