Product geometry

The emissive power of a fireball, however, will depend on the actual distribution of flame temperatures, partial pressure of combustion products, geometry of the combustion zone, and absorption of radiation in the fireball itself. The emissive power ( ) is therefore lower than the maximum emissive power (E ) of the black body radiation ... 

These methods assume that the reactant and product geometries are known, and that a TS is located somewhere between these two end-points. They differ in how the interpolation is perfonned. It should be noted that many of the methods in this group do not actually locate the TS, they only locate a point close to it. The geometry can then be further refined by some of the local methods given in Section 14.5.9. 

In the Self Penalty Walk (SPW) method the whole reaction path is approximated by minimizing the average energy along the path, given as a line integral between the reactant and product geometries (R and P). 

Metliods of the local type propagate the geometry by using only information about the function and its derivatives at the current point, i.e. they require no knowledge of the reactant and/or product geometries. 

Under certain conditions, it will be impossible for the metal and the melt to come to equilibrium and continuous corrosion will occur (case 2) this is often the case when metals are in contact with molten salts in practice. There are two main possibilities first, the redox potential of the melt may be prevented from falling, either because it is in contact with an external oxidising environment (such as an air atmosphere) or because the conditions cause the products of its reduction to be continually removed (e.g. distillation of metallic sodium and condensation on to a colder part of the system) second, the electrode potential of the metal may be prevented from rising (for instance, if the corrosion product of the metal is volatile). In addition, equilibrium may not be possible when there is a temperature gradient in the system or when alloys are involved, but these cases will be considered in detail later. Rates of corrosion under conditions where equilibrium cannot be reached are controlled by diffusion and interphase mass transfer of oxidising species and/or corrosion products geometry of the system will be a determining factor. 

Substrate Alkylating Agent Major Product Geometry d.r. Yield Ref... 

Phosphorylation of enolate ions by dialkyl or diaryl phosphorochlori-dates gives exclusive O-phosphorylation and it appears that the product geometry in acyclic systems is determined by the polarity of the solvent and... 

The foregoing treatment assumes that at least one of the reactants is a single crystal and the reactant/product geometry is well-defined. Many technologically important ceramic reactions, on the other hand, are usually carried out between polycrystalline powders. The reaction kinetics in these cases depend on several physical factors such as particle size, packing density, porosity, and so on. Jander (1927) and Carter (1961) have proposed models for powder reactions making several simplifying assumptions. 

Figure 6.12 The anti-SN2 reaction of chloride with allyl chloride. While RHF theory does well with the reactant/product geometries, it significantly overestimates the C-Cl bond lengths in the C2 symmetric TS structure based on calculations at more reliable levels of theory...

I n the latter two examples the EM values calculated from rate data are higher than the actual concentration of encapsulated reactants. This result indicates a favorable directional correlation of functionalities in the complex, but it is apparent that Rebek s capsule is less efficient than cucurbit[6]uril in promoting the productive geometry or stabilizing the TS. The molecular capsules not only concentrate reactants but also increase the time that the reacting function reside within critical distance (productive geometry) - both factors are determinant in achieving effective catalysis [24]. 

Today, it is known that Cram was wrong about this preferred conformation (he assumed that the bulkiest Ca carbon bond was oriented anti to the C=0 double bond actually this Ca carbon bond prefers a syn-orientation). If Cram had known this conformation at that time, he would certainly not have based his explanation of Cram selectivity upon a reaction with the most stable conformer of the aldehyde. This is because, in order to establish the experimentally found product geometry, the nucleophile would have been required to approach the C=0 double bond of the truly favored conformer from the sterically more hindered side. However, even at that time this error could have been avoided (see below). 

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