Isomorphous geometry

Figure 1.66 Illustrations of the specific Watson-Crick base pairings, dG.dC and dA.dT involving complementary deoxynucleoside residues. Overlay structure provides visual demonstration of the dG.dC/dA.dT isomorphous geometry.

Cobalt(i).— Anhydrous CoX (X - Cl,Br. or I) can be reduced by BH in the presence of MeC(CH2PPh2)3 to form [CoXL], which are non-electrolytes and isomorphous with the analogous Cu complexes. Pseudo-tetrahedral geometry is proposed. ... 

The analogous homoaryl complex, tetrakis(tetrahydrofuran)Hthium tetrakis-(2,6-dimethylphenyl)lutetiate, has been prepared and its structure determined [130). The ytterbium homologue is isomorphous. The molecular geometry of the anion is shown in Fig. 12 and the molecular parameters are summarized in Table 6. 

Among the chelated species, octacoordination is often encountered. The tetrakis-acetylacetonate complex of U(IV) (a-form) and Ce(IV) are isostructural. A two-dimensional X-ray analysis showed a slightly distorted square antiprismatic geometry [109—111) for Ce(acac)4 belonging to space group P2i/c [Ctn] with an average Ce—O (acac) bond length of 2.40 A and an <0—Ce—0 of 72°. The a-form of Th(acac)4 is found to be isomorphous (770) with Ce(acac)4 (Th—0=2.41 A)... 

Th(PhCOCHCOPh)4 has been reported as being isomorphous with the corresponding protactinium(IV), uraniumflV) and cerium(IV) complexes the coordination geometry in the last is a triangular faced dodecahedron, but a more recent publication73 reports the coordination geometry of the uranium(IV) compound as square antiprismatic. 

The coordination geometry in anhydrous Th(CF3COCHCOMe)4 is a 1111 ( )4-422) antiprism 74 the structure of the monohydrate has been discussed earlier (p. 1144). Th[CF3COCHCO(2-C4H3S)]4 is isostructural with the cerium(IV), uranium(IV) and plutonium(IV) analogues. The coordination polyhedron is a distorted dodecahedron in which the four ligands span the two perpendicular trapezoids of the dodecahedron.75 In the complexes M(n-C3F7COCHCOBut)4, the thorium(IV), uranium(IV) and neptunium(IV) compounds are isomorphous, but the plutonium compound is not. 

U(Et2NCS2)4 is a monomer in benzene and is very sensitive to air oxidation in solution. It is isomorphous with Th(Et2NCS2)4, in which the coordination geometry is close to an ideal dodecahedron.134 The XH NMR spectra of Th(R2NCS2)4 (R = Me, Et) indicate that the two alkyl groups are equivalent. 

KsIMofCN H jO is isomorphous with K3[W(CN)8]-H20, which has square antiprismatic geometry, although a full structure was not determined for the molybdenum analogue as it decomposed under X-ray irradiation,312 The ESR spectrum of K3[Mo(CN)8] in glycerine solution indicates that all the cyanides are equivalent, consistent with a square antiprismatic structure, or with stereochemical non-rigidity on the ESR timescale.313... 

It is a remarkable fact that properties (13.4a-c) are necessary and sufficient to give Euclidean geometry. In other words, if any rule can be found that associates a number (say, (X Y)) with each pair of abstract objects ( vectors X), Y)) of the manifold in a way that satisfies (13.4a-c), then the manifold is isomorphic to a corresponding Euclidean vector space. We introduced a rather unconventional rule for the scalar products (X Y) [recognizing that (13.4a-c) are guaranteed by the laws of thermodynamics] to construct the abstract Euclidean metric space Ms for an equilibrium state of a system S, characterized by a metric matrix M. This geometry allows the thermodynamic state description to be considerably simplified, as demonstrated in Chapters 9-12. 

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