Geometric complexity associated with

When a nucleophilic reagent, Nu X+ (or Nu—X), is reacted with a ketone, com-plexation of oxygen by X+ may precede attack at carbon. Geometric changes associated with such complexation have been calculated for a series of 4-substituted cyclohexanones. The results allow the facial selectivity of the subsequent nucleophilic attack to be predicted, and without the need to calculate the transition-state geometry. 

Thus, it seemed worthwhile to compare photoinitiated reaction probabilities for linear and broadside structures. Such a steric or regiospecific effect, i.e., based on the geometric differences associated with the weak inter-molecular forces, might be present in many different environments such as liquids, surfaces, and larger complexes. 

Chaotic attractors are complicated objects with intrinsically unpredictable dynamics. It is therefore useful to have some dynamical measure of the strength of the chaos associated with motion on the attractor and some geometrical measure of the stmctural complexity of the attractor. These two measures, the Lyapunov exponent or number [1] for the dynamics, and the fractal dimension [10] for the geometry, are related. To simplify the discussion we consider tliree-dimensional flows in phase space, but the ideas can be generalized to higher dimension. 

The physical and chemical properties of complex ions and of the coordination compounds they form depend on the spatial orientation of ligands around the central metal atom. Here we consider the geometries associated with the coordination numbers 2,4, and 6. With that background, we then examine the phenomenon of geometric isomerism, in which two or more complex ions have the same chemical formula but different properties because of their different geometries. 

Fig. 9a-c. Relative positions of LS and HS potential energy surfaces for complexes showing spin-state equilibria associated with different amounts of geometric reorganization a no intersection of potential surfaces b intersection accompanied by moderate displacement of the minima of potential surfaces c (avoided) interseetion accompanied by sizeable displacement of the minima of potential surfaces. AEq = AG° is the difference of zero-point energies of LS and HS states, E = AG h and jlj... 

An enormous variety of solvates associated with many different kinds of compounds is reported in the literature. In most cases this aspect of the structure deserved little attention as it had no effect on other properties of the compound under investigation. Suitable examples include a dihydrate of a diphosphabieyclo[3.3.1]nonane derivative 29), benzene and chloroform solvates of crown ether complexes with alkyl-ammonium ions 30 54>, and acetonitrile (Fig. 4) and toluene (Fig. 5) solvates of organo-metallic derivatives of cyclotetraphosphazene 31. In most of these structures the solvent entities are rather loosely held in the lattice (as is reflected in relatively high thermal parameters of the corresponding atoms), and are classified as solvent of crystallization or a space filler 31a). However, if the geometric definition set at the outset is used to describe clathrates as crystalline solids in which guest molecules... 

The fundamental reason for the uneven distribution of reactions is that the rate of electrochemical reactions on a semiconductor is sensitive to the radius of curvature of the surface. This sensitivity can either be associated with the thickness of the space charge layer or the resistance of the substrate. Thus, when the rate of the dissolution reactions depends on the thickness of the space charge layer, formation of pores can in principle occur on a semiconductor electrode. The specific porous structures are determined by the spatial and temporal distributions of reactions and their rates which are affected by the geometric elements in the system. Because of the intricate relations among the kinetic factors and geometric elements, the detail features of PS morphology and the mechanisms for their formation are complex and greatly vary with experimental conditions. 

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