Coordinate geometry

A familiar example of coordinates in two dimensions is a map reference, which gives a nnique identification of a point on the land. In order to set np snch a coordinate system, an origin O needs to be defined, and two directions x and y. A general point P is then described as having coordinates 

Suppose there are two points, one at (1,4) and the other at (3,9). The distance d between them will be 

The values of x and y can both take negative values, in which case it can be very easy to deal with the negative signs incorrectly. Suppose the distance d between (—2, —4) and (—5, 8) is required. Using the formula gives 

It is important to remember here that two negatives combine to make a positive, and that the square of a negative number is the same as the square of the corresponding positive number and is itself always positive. 

Most of the spatial problems encountered in chemistry are three dimensional, so a third direction, z, needs to be introduced to the previous coordinate scheme, as shown in Fig. 28.3. Calculating distances now requires inclusion of this third direction, so point P has coordinates (xi, yi, zi) and point Q has coordinates (X2, Ji, 22)- The distance d between them will be 

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Some of the other features of this program are the ability to compute transition states, coordinate driving, conformation searches, combinatorial tools, and built-in visualization. The builder includes atoms and fragments for organics, inorganics, peptides, nucleotides, chelates, high-coordination geometries, and... 

Copper(I) tends towards a tetrahedral coordination geometry in complexes. With 2,2 -bipyr-idine as a chelate ligand a distorted tetrahedral coordination with almost orthogonal ligands results. 2,2 -Bipyridine oligomers with flexible 6,6 -links therefore form double helices with two 2,2 -bipyridine units per copper(I) ion (J. M. Lehn, 1987,1988). J. M. Lehn (1990 U. Koert, 1990) has also prepared such helicates with nucleosides, e.g., thymidine, covalently attached to suitable spacers to obtain water-soluble double helix complexes, so-called inverted DNA , with internal positive charges and external nucleic bases. Cooperative effects lead preferentially to two identical strands in these helicates when copper(I) ions are added to a mixture of two different homooligomers. 

The most common oxidation states and the corresponding electronic configuration of mthenium are +2 and +3 (t5 ). Compounds are usually octahedral. Compounds in oxidations states from —2 and 0 (t5 ) to +8 have various coordination geometries. Important appHcations of mthenium compounds include oxidation of organic compounds and use in dimensionally stable anodes (DSA). 

The most common oxidation states and the corresponding electronic configurations of osmium ate +2 and + (t5 ), which ate usually octahedral. Stable oxidation states that have various coordination geometries include —2 and 0 to +8 (P] The single most important appHcation is OsO oxidation of olefins to diols. Enantioselective oxidations have also been demonstrated. 

The most common oxidation states, corresponding electronic configurations, and coordination geometries of iridium are +1 (t5 ) usually square plane although some five-coordinate complexes are known, and +3 (t7 ) and +4 (t5 ), both octahedral. Compounds ia every oxidation state between —1 and +6 (<5 ) are known. Iridium compounds are used primarily to model more active rhodium catalysts. 

Chlorides. The oHve-green trichloride [10025-93-1], UCl, has been synthesized by chlorination of UH [13598-56-6] with HCl. This reaction is driven by the formation of gaseous H2 as a reaction by-product. The stmcture of the trichloride has been deterrnined and the central uranium atom possesses a riine-coordinate tricapped trigonal prismatic coordination geometry. The solubiUty properties of UCl are as follows soluble in H2O, methanol, glacial acetic acid insoluble in ethers. 

Bromides and Iodides. The red-brown tribromide, UBr [13470-19-4], and the black tniodide, Ul [13775-18-3], may both be prepared by direct interaction of the elements, ie, uranium metal with X2 (X = Br, I). The tribromide has also been prepared by interaction of UH and HBr, producing H2 as a reaction product. The tribromide and tniodide complexes are both polymeric soflds with a local bicapped trigonal prismatic coordination geometry. The tribromide is soluble in H2O and decomposes in alcohols. 

Table 1. Polyhedral Symbols for Common Coordination Geometries ...

Figure 5.12 Coordination geometry about Ca in polymeric [Ca(C5H5)2l showing 2k rj -, and ij - bonding (see text).

In the vast majority of its compounds Si is tetrahedrally coordinated but sixfold coordination also occurs, and occasional examples of other coordination geometries are known as indicated in Table 9.2 (p. 335). Unstable 2-coordinate Si has been known for many years but in 1994 the stable, colourless, crystalline silylene [ SiNBu CH=CHNBu j, structure (1), p. 336, was... 

This latter complex also has a linearly coordinated NO group. The diagrams show only the coordination geometry around ihe metal (the phenyl groups being omitted for clarity). 

Figure 11.12 Comparison of the coordination geometries of [Co(diars)2(NO)] " and [IrCl2(NO)(PPh3)l diars = l,2-bis(di-methylarsino)benzene.

Figure 11.16 Coordination geometries of the nitrate group showing typical values for the interatomic distances and angles. Further structural details are in ref. 150.

The detailed coordination geometry about As, Sb or Bi in these clusters varies substantially, and is of considerable signilicancc in describing the nature of the bonding in these species. 

Figure 13.12 Schematic representation of the structure of the complex anion LSbjCIiiO] " showing the two different coordination geometries about Sb and the unique quadruply bridging Cl atom.

Chemical properties of dioxygen, O2 Table 14.3 Coordination geometry of oxygen... 

Figure 15.16 Coordination geometries of bis- and tris-l,2-dithiolene complexes (see text).

The known coordination geometries of Se, Te and Po are summarized in Table 16.3 together... 

Other less-symmetrical coordination geometries for Se and Te occur in the /t,-Se2 and /t-Te2 complexes and the polyatomic cluster cations Seio and Tee" " ", as mentioned below. 

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