Statistical reactivity

A reactive species in liquid solution is subject to pemianent random collisions with solvent molecules that lead to statistical fluctuations of position, momentum and internal energy of the solute. The situation can be described by a reaction coordinate X coupled to a huge number of solvent bath modes. If there is a reaction... 

A 3.13.6 STATISTICAL MECHANICAL MASTER EQUATION TREATMENT OF INTRAMOLECULAR ENERGY REDISTRIBUTION IN REACTIVE MOLECULES... 

Quack M and Troe J 1975 Complex formation in reactive and inelastic scattering statistical adiabatic channel model of unimolecular processes III Ber. Bunsenges. Phys. Chem. 79 170-83... 

The selectivity of an electrophile, measured by the extent to which it discriminated either between benzene and toluene, or between the meta- and ara-positions in toluene, was considered to be related to its reactivity. Thus, powerful electrophiles, of which the species operating in Friedel-Crafts alkylation reactions were considered to be examples, would be less able to distinguish between compounds and positions than a weakly electrophilic reagent. The ultimate electrophilic species would be entirely insensitive to the differences between compounds and positions, and would bring about reaction in the statistical ratio of the various sites for substitution available to it. The idea has gained wide acceptance that the electrophiles operative in reactions which have low selectivity factors Sf) or reaction constants (p+), are intrinsically more reactive than the effective electrophiles in reactions which have higher values of these parameters. However, there are several aspects of this supposed relationship which merit discussion. 

Under the conditions (1.1) the rate constant is determined by the statistically averaged reactive flux from the initial to the final state. 

When reaction is carried out homogeneously in solution this state of affairs more or less exists and it is possible to achieve a statistically random degree of substitution. (It is to be noted that the primary hydroxyl groups will be more reactive than the secondary hydroxyl groups.)... 

The value of k /k can be determined by measuring the ratio of the products 1-chlorobutane 2-chlorobutane during the course of the reaction. A statistical correction must be made to take account of the fact that the primary hydrogens outnumber the secondaiy ones by 3 2. This calculation provides the relative reactivity of chlorine atoms toward the primary and secondary hydrogens in butane ... 

Although anti-TNFa agents are well tolerated and have a good overall safety profile, pitfalls to the use of these drugs apparent with increasing clinical experience include infective complications and, in particular, reactivation of tuberculosis. To date, no statistically significant increased rate of tumour occurrence over that expected has been noted although cases of lymphoma have rarely been reported in patients treated with TNFa blockade. 

The copolymer composition equation only provides the average composition. Not all chains have the same composition. There is a statistical distribution of monomers determined by the reactivity ratios. When chains are short, compositional heterogeneity can mean that not all chains will contain all monomers. 

The isomer distribution is normal even when the low relative reactivity of substrates is observed. If reaction occurred at every collision then the statistical isomer distribution (40 % ortho, 40 % meta, and 20 % para for monoalkylbenzenes for example) would be expected, but this is not the case. 

Optoelectronics is a relatively new and fast-growing industry with many applications. Thin-film processes, such as reactive sputtering, molecular-beam epitaxy (MBE), and particularly MOCVD, play a major part in their production. Equipment and materials are similar to those used in the semiconductor industry and many companies manufacture both types of products. In fact the distinction between the two areas is often blurred. Statistics generally do not single out optoelectronics as such and, for that reason, it is difficult to define the scope of the industry accurately. 

Experience has shown that correlations of good precision are those for which SD/RMS. 1, where SD is the root mean square of the deviations and RMS is the root mean square of the data Pfs. SD is a measure equal to, or approaching in the limit, the standard deviation in parameter predetermined statistics, where a large number of data points determine a small number of parameters. In a few series, RMS is so small that even though SD appears acceptable, / values do exceed. 1. Such sets are of little significance pro or con. Evidence has been presented (2p) that this simple / measure of statistical precision is more trustworthy in measuring the precision of structure-reactivity correlations than is the more conventional correlation coefficient. 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

Such relationships were in fact found empirically (168, 169, 231) however, they should be confirmed by use of correct statistics. The whole treatment with temperature-dependent parameters has to be completed with appropriate statistical methods and tested on selected reactivity data (236) before one can judge whether it is worth the effort. Few data available at present fulfil the high demands on accuracy and extent. 

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