Multiple coordination

The conceptually simplest approach to solve for the -matrix elements is to require the wavefimction to have the fonn of equation (B3.4.4). supplemented by a bound function which vanishes in the asymptote [32, 33, 34 and 35] This approach is analogous to the fiill configuration-mteraction (Cl) expansion in electronic structure calculations, except that now one is expanding the nuclear wavefimction. While successfiti for intennediate size problems, the resulting matrices are not very sparse because of the use of multiple coordinate systems, so that this type of method is prohibitively expensive for diatom-diatom reactions at high energies. 

Metal deactivators—Organic compounds capable of forming coordination complexes with metals are known to be useful in inhibiting metal-activated oxidation. These compounds have multiple coordination sites and are capable of forming cyclic strucmres, which cage the pro-oxidant metal ions. EDTA and its various salts are examples of this type of metal chelating compounds. 

Complexation is a phenomenon that involves a coordinate bond between a central atom (the metal) and a ligand (the anions). In a coordinate bond, the electron pair is shared between the metal and the ligand. A complex containing one coordinate bond is referred to as a monodentate complex. Multiple coordinate bonds are characteristic of polydentate complexes. Polydentate complexes are also referred to as chelates. An example of a monodentate-forming ligand is ammonia. Examples of chelates are oxylates (bidentates) and EDTA (hexadentates). 

The deadly terrorist bombings of July 7, 2005 in London again demonstrated that even sophisticated terrorists capable of planning and executing multiple, coordinated attacks continue to rely on traditional weapons rather than risk the technical and political uncertainty of chemical, biological, radiological or nuclear (CBRN) weapons. While terrorists have the motivations and capabilities to conduct large (and small) attacks worldwide, we have not yet witnessed the use of so called weapons of mass destruction (WMD) foreshadowed by the 1995 Sarin attacks in... 

The complexation of anionic species by tetra-bridged phosphorylated cavitands concerns mainly the work of Puddephatt et al. who described the selective complexation of halides by the tetra-copper and tetra-silver complexes of 2 (see Scheme 17). The complexes are size selective hosts for halide anions and it was demonstrated that in the copper complex, iodide is preferred over chloride. Iodide is large enough to bridge the four copper atoms but chloride is too small and can coordinate only to three of them to form the [2-Cu4(yU-Cl)4(yU3-Cl)] complex so that in a mixed iodide-chloride complex, iodide is preferentially encapsulated inside the cavity. In the [2-Ag4(//-Cl)4(yU4-Cl)] silver complex, the larger size of the Ag(I) atom allowed the inner chloride atom to bind with the four silver atoms. The X-ray crystal structure of the complexes revealed that one Y halide ion is encapsulated in the center of the cavity and bound to 3 copper atoms in [2-Cu4(//-Cl)4(//3-Cl)] (Y=C1) [45] or to 4 copper atoms in [2-Cu4(/U-Cl)4(/U4-I)] (Y=I) and to 4 silver atoms in [2-Ag4(/i-Cl)4(/i4-Cl)] [47]. NMR studies in solution of the inclusion process showed that multiple coordination types take place in the supramolecular complexes. 

Polyether containing 2,2 -bipyridil units 8 spontaneously forms a double helicate 9 by multiple coordination with Cu+ ions [13]. This process of self-organization is enforced by the proper orientation of coordinated bipyridyl units analogous to that shown in Figure 1.2. It is characterized by a positive cooperativity yielding no partly assembled species. 

Dendrimers based on 1,4,7-triazacyclononane macrocycle (capable of multiple coordination of Cu(II) and Ni(II) metal cations) like 317 have been synthesized by Beer and Gao [8]. 

Warning physicists use the word tensor to describe objects that arise in the theory of general relativity (such as the metric tensor or the curvature tensor), among other places. Although these objects are indeed tensors in the sense we will define below, they are also more complicated they involve multiple coordinate systems. We warn the reader that this section will not address the issues raised by multiple coordinate systems. Thus a reader who has been confused by such physicists tensors may not be fiilly satisfied by our discussion here." ... 

Such a reader might find relief in differential geometry, the mathematical study of multiple coordinate systems. There are many excellent standard texts, such as Isham s book [I] for a gentle introduction to some basic concepts of differential geometry, try [Si]. A text that discusses covariant and contravariant tensors is Spivak s introduction to differential geometry [Sp, Volume I, Chapter 4]. For a quick introduction aimed at physical calculations, try Joshi s book [Jos]. 

Again, we remind physicists that tensor products of vector spaces are neither as general nor as powerful as the objects called tensors appearing in general relativity. Issues of covariance and contravariance have to do with multiple coordinate systems. Because quantum mechanics is Unear, we do not need the more general notion of tensor in this book, so we do not stop to introduce it. We do, however, offer our condolences and a few references to physicists searching for clarification. See Footnote 4 in this chapter. 

In this space-group the general positions have fourfold multiplicity. (Coordinates xyz, xyz, ( + )( —y)( +z)> ( — )( + )( —z).) The only special positions have twofold multiplicity these are pairs of symmetry centres. There are four such pairs (a) 00 , (b) 00, ... 

Thus, for both the terminal diammonium and dicarboxylate substrates, selective binding by the appropriate receptors describes a linear recognition process based on length complementarity in a ditopic binding mode. Important biological species, such as polyamines, amino acid and peptide diamines, and dicarboxylates [4.18] may also be bound selectively. Recognition is achieved by multiple coordination to metal ions in dinuclear bis-macrocyclic coreceptors that complex selectively complementary bis-imidazole substrates of compatible length [4.21]. 

Wedge, T. J. and Hawthorne, M. F., Multidentate carborane-containing Lewis acids and their chemistry mercuracarborands , Coord. Chem. Rev. 2003, 240, 111-128 Wuest, J. D., Multiple coordination and activation of Lewis bases by multidentate Lewis acids , Acc. Chem. Res., 1999, 32, 81-89. 

The sensitivity of EPR to multiple coordination environments has been demonstrated in studies of Mn2+-doped CdS nanocrystals (63). In Mn2+ CdS nanocrystalline powders prepared by inverted micelle synthesis, four distinct resonances were observed and deconvoluted by varying experimental parameters including microwave power, microwave frequency, and temperature. The deconvoluted signals are shown in Fig. 18. Four distinct manganese species were detected through this experiment. A six line spectrum characteristic of isolated paramagnetic Mn2+ was observed at 300 K and below [multiline... 

Remark 3.4. In the context of the present chapter (and of the remainder of the book), the term hierarchical control structure reflects the use of two (or multiple) coordinated tiers of control action, and should not be confused with hierarchical plant-wide controller design strategies (see, e.g. Ponton and Laing 1993, Luyben et al. 1997, Zheng et al. 1999, Antelo et al. 2007, Scattolini 2009, and references therein), which use the term hierarchy to denote a set of guidelines, to be followed in sequence, for designing the control system for a chemical plant. 

SFG toward multiple-coordinated CO. The spectra agree with those reported by Somorjai et al. (46,396) for CO chemisorption at pressures below 900 mbar and indicate a (2 x 2)-3CO saturation structure (0.75 ML) (219). 

Equation (65) is an example of a process that may be readily promoted by a cluster but not necessarily with a mononuclear complex. Scheme 8 shows how the multiple-coordination capabilities of a trinuclear cluster could reduce the N—C bond and eventually cleave it. To date, examples of the NCO ligand bridging more than two metals in either a mono- or polyhapto fashion are unknown. The reverse process represents a unique method for forming carbon-nitrogen bonds. Although the above chemis-... 

Dendrimers containing coordination sites (e.g., amine, amide groups) in their structure can act as ligands of metal ions. We can distinguish dendrimers containing a single coordination site, for example, in the core (Fig. 2c), or multiple coordination sites in the branches (Fig. 2d). 

A. Dendrimers with Multiple Coordination Sites A.I. Amide coordinating units... 

This bimolecular coupling is a structure-sensitive reaction, and it illustrates a key characteristic of metal oxides multiple coordinative unsaturation of surface metal cations may facilitate coupling of ligands in a manner similar to that for unsaturated metal complexes in solution. Examples of other coupling reactions... 

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