Statistics ratio

If, on the other hand, the encounter pair were an oriented structure, positional selectivity could be retained for a different reason and in a different quantitative sense. Thus, a monosubstituted benzene derivative in which the substituent was sufficiently powerfully activating would react with the electrophile to give three different encounter pairs two of these would more readily proceed to the substitution products than to the starting materials, whilst the third might more readily break up than go to products. In the limit the first two would be giving substitution at the encounter rate and, in the absence of steric effects, products in the statistical ratio whilst the third would not. If we consider particular cases, there is nothing in the rather inadequate data available to discourage the view that, for example, in the cases of toluene or phenol, which in sulphuric acid are nitrated at or near the encounter rate, the... 

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. 

Any given molecule has only one of the three possible alignments of -CH2Br spins, but in a large collection of molecules, all three spin states are represented in a 1 2 1 statistical ratio. We therefore find that the neighboring -CFIj protons come into resonance at three slightly different values of the applied field, and we see a 1 2 1 triplet in the NMR spectrum. One resonance is a little above where it... 

Three products were obtained in a statistical ratio of 1 2 1. 

After what we have seen to date, it surely comes as no great surprise to find that the ratio of o- to p-product obtained from substitution of C6H5Y, where Y is o-/p-directing, is seldom, if ever, the statistical ratio of 2 1. There is found to be very close agreement between calculation and n.m.r. data for the distribution of +ve charge—p-> o- m—around the ring in the cyclohexadienyl cation (57), which is the Wheland intermediate for proton exchange in benzene (cf. p. 133) ... 

The difference is clearly seen for a spur initially containing two dissociations of AB molecules into radicals A and B (Pimblott and Green, 1995). Considering the same reaction radii for the reactions A + A, A + B, and B + B and the same initial distributions of radicals, the statistical ratio of the products should be 1 4 1 for A2 AB B2, since there is one each of A-A and B-B distances but there are four A-B distances. For n dissociations in the spur, this combinatorial ratio is n(n - l)/2 n2 n(n - l)/2, whereas deterministic kinetics gives this ratio always as 1 2 1. Thus, deterministic kinetics seriously underestimates cross-recombination and overestimates molecular products, although the difference tends to diminish for bigger spurs. Since smaller spurs dominate water radiolysis (Pimblott and Mozumder, 1991), many authors stress the importance of stochastic kinetics in principle. Stochasticity enters in another form in... 

The formation of HCO+ and DCO+ must be in the statistical ratio of 3 1, so the observed HCO+/DCO+ ratio in an astrochemical environment is a measure of the deuterium chemistry. All of the reverse reactions are possible in the reaction scheme but at 10 K, for example, the increased bond energy of DCO+ prevents the reverse reaction from occurring and the DCO+ becomes enriched. The H/D ratio is... 

Statistical analysis is important and relatively easy. Suppose we have a fully atactic polymer which we analyse for the triad content for isotactic polymer. Only three methyl resonances due to triads are observed, and the statistical ratio of mm, rr, and mr is 1 1 2. Thus even in the atactic polymer our isotactic content is 25% Pentad analysis, however, would give only 8% mmmm isotactic content Especially for catalysts with low enantiospecificity it is worthwhile keeping this in mind. 

Subsequent reports showed that a wide range of arene substrates could be borylated, with regioselectivity predominantly dictated by steric factors [77]. In the case of monosubstituted arenes, borylation generally occurs predominantly at the meta and para positions, with a near-statistical ratio while substitution at the ortho position is minor (Scheme 4). In the case of 1,3-disubstituted arenes, borylation occurs exclusively at 5-position. The selectivity was reversed in favor of the ortho position in the case of diethylbenzamide, presumably due to chelation [77]. 

The reaction of dibutyldidecyl tellurium with phenylacetylenes yields nearly statistical ratios of products. 

The liver enzyme exists in two forms, E and S, which differ only by some six residues in their amino acid sequence.13 Only the S is active toward 3-/3-hydroxysteroids, but both forms are active toward ethanol. None of the known amino acid differences is located in the subunit interfaces. Accordingly, E and S chains combine in statistical ratios to form EE, SS, and ES dimers. These different species are termed isozymes, which means that they are multiple molecular forms of the same enzyme. When it is isolated from liver, the enzyme consists of about 40 to 60% of the EE dimer, the remainder being SS and ES. 

Exchange reaction between heteroatom ligands of A3-iodanes probably occurs [Eq. (9)] 13C NMR spectra of a mixture of 4 and (dichloroiodo)benzene 15 in CDC13 showed a rapid ligand exchange and formation of a new A3-iodane, presumably 16, was detected as a major component in a nearly statistical ratio 1 1 2 of 4 15 16 [30]. 

The formation of lignin proceeds by the uncontrolled coupling of the radical species, which leads to an irregular structure (Figure 2). The structure of lignin can be represented by the statistic ratio of each monomer, the frequency of each coupling mode, and the steric hindrance of substituents. This reaction mechanism has been successfully simulated [22],... 

One can define diastereoselectivity as the formation of diastereoisomers in a non-statistical ratio in any chemical transformation (formation of transition states included). Such a definition concerns equilibrium as well as nonreversible reactions. An asymmetric synthesis in a restricted sense can be considered as a reaction leading to a product containing at least one new stable dissymmetric center with a definite chirality. Such a reaction may take place in the coordination sphere of a metal ion. First of all the following question has to be answered which are the structural properties in the architecture of the coordination sphere that lead to the following phenomenona ... 

A dimeric capsule can also be formed by two different tetra-urea molecules, and in aprotic solvents a mixture of two tetra-urea derivatives usually contains not only the two homodimers but also the heterodimer in a more or less statistical ratio. This formation of heterodimers is an additional proof of the dimerization [39], which is also valid when other indications (e.g. m-coupled doublets for aryl protons) fail. As an example, sections of the spectra of tetra-tolylurea (1), tetra-hexylurea (3), and of a mixture of the two are shown in Figure 5.3a-c [37a],... 

The synthesis of fourfold [2]rotaxanes by clipping requires the efficient formation of heterodimers between a tetra-urea substituted by bulky stopper groups and an octaalk-enyl urea 6. We initially hoped that the steric crowding in homodimers of a tetra-tritylphenylurea calix[4]arene would be sufficient to shift the equilibrium toward the heterodimers in a mixture with 6. However, the distribution of the dimers was close to the statistical ratio and the desired rotaxane could be obtained in only 5% yield [59]. 

A pairwise mechanism involving a quasi-cyclobutane structure was suggested first, Eq. (3) [18], but cross metathesis between cyclopentene and 2-pentene produced a statistical ratio of cross-products 1-3 (1 2 3 = 1 2 1), Eq. (4) [19]... 

In a two-phase system similar to that used by Price, Stamatoff (29) obtained from 2,6-dichloro-4-bromophenol a branched polymer having approximately the statistical ratio of ortho and para ether linkages. When the reaction was carried out using the anhydrous salt of the phenol in the presence of highly polar aprotic solvents, such as dimethyl sulfoxide, the product was the linear poly(2,6-dichlorophenylene oxide) (Reaction 23). 

An insertion-type mechanism for the S( Z)) atom reaction is further supported by the indiscriminative nature of the attack on the various paraffinic C—H bonds. For the propane and isobutane molecules it was found that the two possible isomeric mercaptans were formed in a statistical ratio, i.e., n-PrSH/iso-PrSH 5 3.0, and iso-BuSH/f-BuSH iii 9.0. From methylene chemistry it is well known that singlet CH2 in its insertion reactions may be completely indiscriminative, but the abstractive attack of free radicals upon C—H bonds is known to be very sensitive to bond order and strongly increases in the sequence 0° < 1° < 2° < 3°. Insertive interactions with C—H bonds have also been postulated for singlet and triplet carbon atoms, NH, C2O radicals, and recently for the reactions of 0( Z)) atoms with alkanes. ... 

Photolysis of diazirine in the presence of a large excess of propane yielded n- and isobutane and in the presence of n-butane yielded n- and isopentane. From the relative rates of attack on the primaiy and secondary carbon-hydrogen bonds in these compounds, it was concluded that methylene derived from diazirine showed approximately the same discrimination as methylene formed by the photolysis of ketene. The results obtained, using methylene derived from the photolysis of diazomethane, gave a product ratio closer to the simple statistical ratio of the number of carbon-hydrogen bonds without correction factors for the type involved and indicated almost no differentiation between the types. 

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