Applications of the Additivity Rule

The additivity rule governing the proton affinity of various multiply substituted aromatics may be useful in rationalizing many closely related properties of this family of compounds. For instance. Brown and Brady [47] determined the relative basicities of a number of aromatic compounds including methylbenzenes. Unfortunately, experimental PA values related to methylbenzenes are scarce. Hence, proton affinities obtained by the additivity rule may prove very useful here in predicting the missing experimental data 

Proton affinities of compounds 25-40 as obtained by the MP2(I) model and the additivity formula (22) (in kcal/mol) 

We have conclusively shown that the ISA model was very useful in predicting and interpreting proton affinities in polysubstituted benzenes and naphthalenes. A compelling evidence is provided which documents that the PA values obtained by the additivity rule of thumb are in very good accordance with available experimental data and/or the accurate theoretical results offerred by the ab initio models at the MP2 level of sophistication. Analogous formulas should work in larger aromatic systems too. If there are some 

Bamford and C.F.H. Tipper (eds.). Comprehensive Chemical Kinetics, Vol.8, Proton Transfer, Elsevier, Amsterdam, 1977. 

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Davies and Warren have investigated the nitration of naphthalene, ace-naphthene and eight dimethylnaphthalenes in acetic anhydride at o °C. Rates relative to naphthalene were determined by the competition method, and the nitro-isomers formed were separated by chromatographic and identified by spectrophotometric means. The results, which are summarised in the table, were discussed in terms of various steric effects, and the applicability of the additivity rule was examined. For the latter purpose use was made of the data of Alcorn and Wells (table 10.2) relating to the nitration of monomethyl-naphthalenes at 25 °C. The additivity rule was found to have only limited utility, and it was suggested that the discrepancies might be due in part to the... 

One of the values that is often determined is the value equaled or exceeded. The probability of a value equaled or exceeded may be calculated by the application of the addition rule of probability. The phrase equaled or exceeded denotes an element equaling a value and elements exceeding the value. Therefore, the probability that a value is equaled or exceeded is by the addition rule,... 

Two synthetic bridged nitrogen heterocycles are also prepared on a commercial scale. The pentazocine synthesis consists of a reductive alkylation of a pyridinium ring, a remarkable and puzzling addition to the most hindered position, hydrogenation of an enamine, and acid-catalyzed substitution of a phenol derivative. The synthesis is an application of the reactivity rules discussed in the alkaloid section. The same applies for clidinium bromide. 

In synthetic work, amidyl radicals, prepared by BusSnH/AIBN-mediated homolysis of O-benzoylhydroxamic acid derivatives, have been shown to cyclize in a A-exo fashion to give -lactams (Scheme 10). In addition, radicals generated in this way have also been reported to undergo 5-exo cyclization to give mixtures of cis- and Iranx-pyrrolidinones with the steric nature of the Al-substituent having little effect on the stereochemical outcome (Scheme 11). The major products detected were those predicted by application of the Beckwith rule. ... 

For applications to more complex macromolecules and the use of the additional rules, not cited herein, associated with the fractal notation, one should consult the Mendenhall article.181... 

Bearing in mind the outlined peculiarities of condensation polymer blends, and particularly when they consist of one component and one phase (this case is more the exception rather than the general rule since block copolymers usually consist of two, three, or more phases), the application of the additivity law for the evaluation of their characteristics does not seem to be completely justified. The observed good agreement between the measured microhardness values and the calculated ones (Fig. 5.7) allows one to make an important conclusion in this respect. 

View factors are not always as easy to find as for the simple geometry present in the example we have just looked at. Then the multiple integral in (5.130) has to be evaluated. However, not all the view factors have to be calculated in this manner. In an enclosure bounded by n surfaces there are n2 view factors in total. From these, n view factors can be found by the application of the summation rule (5.133) on each of the n surfaces. In addition to this, n(n — l)/2 view factors can be determined using the reciprocity rule (5.132). Therefore the number of view factors that have to be calculated from (5.130) is only... 

From a systematic study focused on fhe tt-A isofherm of protein-LMWE mixed monolayers (including fhe application of fhe additivity rule on miscibility and the quantification of inferacfions between monolayer components by excess free energy ( if has been concluded that, at a macroscopic level, these compounds form a pracfically immiscible monolayer at the air-water interface, af tt < Tlf At higher tt the collapsed protein is displaced from the interface by LMWE (monoglycerides, phospholipids, etc.). The existence of low profein interactions in disordered proteins ((3-casein and caseinate) facilitates the protein displacement by LMWE from fhe air-water interface. However, the lower surface acfivify of unsafurafed-LMWE explains the fact that this lipid has a lower capacity than saturated-LMWE for protein displacement. 

We consider first a diamagnetic d complex. In the structure with 9 = 90 , three nonbonding orbitals (xy, xz, and yz) are doubly occupied (Figure 2.8). An increase in the value of 9 above 90° leads to a destabilization of two of these orbitals (xz and yz), which is energetically unfavourable (Figure 2.8). We may therefore predict that these complexes will adopt a structure in which the metal stays in the basal plane (9 = 90°). Experimental values for these complexes are indeed close to 90° (91-94° for the [M(CO)5] complexes if M=Cr, W). But in a d diamagnetic complex, the two additional electrons occupy the z orbital, which is stabilized when 9 increases above 90° (Figure 2.8). Application of the HOMO rule leads to the prediction that in these complexes, the... 

The deshielding of protons and carbon by substituents has given rise to attempts to predict the chemical shift by application of empirical additivity rules. While these can be useful, they are, at best, only approximate. Thus, as shown in Table 5.3 for the chlorinated derivatives of methane, there is not a simple incremental value to... 

By application of Cram s rule or a more recent model on the reactivity of a-chiral aldehydes or ketones, a prediction can be made, which stereoisomer will be formed predominantly, if the reaction generates an additional chiral center. 

Additions to cyclopropanes can take place by any of the four mechanisms already discussed in this chapter, but the most important type involves electrophilic attack. For substituted cyclopropanes, these reactions usually follow Markovnikov s rule, though exceptions are known and the degree of regioselectivity is often small. The application of Markovnikov s rule to these substrates can be illustrated by the reaction of 1,1,2-trimethylcyclopropane with The rule predicts that the... 

The application of n additional thermodynamic potentials (of electric, magnetic or other origin) implies that the Gibbs phase rule must be rewritten to take these new potentials into account ... 

The Council and the Commission must adopt positive fists of additives, authorised to the exclusion of all others, fists of foods in which the additives may be used with conditions of use, and rules on carrier solvents. The Standing Committee on Foodstuffs must approve adoption of purity criteria for listed additives and, if necessary, methods of analysis to verily these purity criteria, sampling procedures and methods of analysis for food additives in food. The directive includes provisions that a member state may temporarily suspend or restrict application of an authorisation if it has detailed grounds for considering that the use of the additive in food, although permitted, endangers health. The... 

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