Bonding and topology

Boranes are usually named by indicating the number of B atoms with a latin prefix and the number of H atoms by an arable number in parentheses, e.g. B5H9, pentaborane(9) B5H11, pentaborane( 11). Names for anions end in ate rather than ane and specify both the number of H and B atoms and the charge, e.g. BsHg-octahydropentaborate(I—). Further information can be provided by the optional inclusion of the italicized descriptors closo-, nido-, arachno-, hypho- and conjuncto-, e.g.  

The detailed numbering schemes are necessarily somewhat complicated but, in all other respects, standard nomenclature practices are followed.  

Derivatives of the boranes include not only simple substituted compounds in which H has been replaced by halogen, OH, alkyl or aryl groups, etc., but also the much more diverse and numerous class of compounds in which one or more B atom in the cluster is replaced by another main-group element such as C, P or S, or by a wide range of metal atoms or coordinated metal groups. These will be considered in later sections. 

Localized 3-centre bond formalism can readily be used to rationalize the structure and bonding in most of the non-c/o5o-boranes. This is illustrated for some typical nido- and arachno-hor nes in the following plane-projection diagrams which use an obvious symbolism for normal 2-centre bonds B-B O—O, B-H( O— , (t = terminal). 

Electron counting and orbital bookkeeping can easily be checked in these diagrams as each B has 4 valency orbitals (s 4- 3p) there should be 4 lines emanating from each open circle likewise, as each B atom contributes 3 electrons in all and each H atom contributes 1 electron, the total 

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Iversen, B.B., Larsen, F.K., Figgis, B.N. and Reynolds, P.A. (1997) X-N study ofthe electron density distribution in tra s-tetraammine-dinitronickel(II) at 9K transition metal bonding and topological analysis, J. Chem. Soc., Dalton Trans. 2227-2240. 

From the active site topology it seems that there is room for substrate flexibility. Indeed, experiments with the closely related P450eryF have demonstrated that some substitutions within the macrolactone ring of the substrate are possible [28] for example, reduction of the C9 oxo to the hydroxy group is well tolerated. However, any changes with impact on the overall confonnation of the substrate, thus changing the trajectory between the reactive C-H bond and the iron-bound oxy-... 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

For over a decade, the topological analysis of the ELF has been extensively used for the analysis of chemical bonding and chemical reactivity. Indeed, the Lewis pair concept can be interpreted using the Pauli Exclusion Principle which introduces an effective repulsion between same spin electrons in the wavefunction. Consequently, bonds and lone pairs correspond to area of space where the electron density generated by valence electrons is associated to a weak Pauli repulsion. Such a property was noticed by Becke and Edgecombe [28] who proposed an expression of ELF based on the laplacian of conditional probability of finding one electron of spin a at t2, knowing that another reference same spin electron is present at ri. Such a function... 

Of course, the empirical point charges of an SPC-type model can always be chosen to make one or a few selected H-bonded clusters come out right. We therefore emphasize the overall quality of the description of H-bonded clusters of various sizes and topologies. 

The theory as presented so far is clearly incomplete. The topology of the density, while recovering the concepts of atoms, bonds and structure, gives no indication of the localized bonded and non-bonded pairs of electrons of the Lewis model of structure and reactivity, a model secondary in importance only to the atomic model. The Lewis model is concerned with the pairing of electrons, information contained in the electron pair density and not in the density itself. Remarkably enough however, the essential information about the spatial pairing of electrons is contained in the Laplacian of the electron density, the sum of the three second derivatives of the density at each point in space, the quantity V2p(r) [44]. 

Under the conditions of maximum localization of the Fermi hole, one finds that the conditional pair density reduces to the electron density p. Under these conditions the Laplacian distribution of the conditional pair density reduces to the Laplacian of the electron density [48]. Thus the CCs of L(r) denote the number and preferred positions of the electron pairs for a fixed position of a reference pair, and the resulting patterns of localization recover the bonded and nonbonded pairs of the Lewis model. The topology of L(r) provides a mapping of the essential pairing information from six- to three-dimensional space and the mapping of the topology of L(r) on to the Lewis and VSEPR models is grounded in the physics of the pair density. 

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