Lebedev rule

Quite a considerable number of papers deal with the effect of structure of olefinic substrates on their reactivity in the catalytic hydrogenation 65). Lebedev 66) attempted a generalization of the problem. His conclusion that the rate of hydrogenation of olefins decreases in the order monosubstituted - symmetric disubstituted - asymmetric disubstituted - trisubstituted tet-rasubstituted ethylene derivatives is called the Lebedev rule. Campbell 67) supplemented it by demonstrating that the rate of hydrogenation decreases with the number and size of substituents on carbon atoms of the double bond, cis isomers are usually hydrogenated more quickly than trans isomers, and olefins containing the terminal double bond are more reactive than those with the double bond inside the chain. 

Angular quadrature is accomplished by an Af-point Lebedev rule where M =6, 38, 86 or 194. 

The works of Maurel and Tellier 82), Rhzicka and Cerveny 83, 84), Litvin, Freidlin, and Tilyaev (55) and Brown and Ahuja 86), who have used extensive series of alkenes, confirmed the Lebedev s rule. With 1-alkenes C -Cn) on palladium, platinum, and rhodium catalysts, the initial reaction rate decreased with the length of the chain, and with Pd and Pt a hnear dependence on the number of carbon atoms was obtained 83) (series 53). An example of the influence of the number of substituents on the carbon atoms of the double bond is shown in Fig. 4. It is evident that the mere presence of the substituent is more important than its nature. However, this secondary factor has been accounted for by using the sums of the Taft polar (7 or steric constants for all substituents on C=C. Cerveny and Rfizicka 84) have found excellent linear relationships between the initial hydrogenation rate of 15 alkenes on 3 different Pt catalysts and 2 (series 54), and... 

The hydrogenation rate of olefins on Pt falls as the extent of the hydrogen substitution at the double bond by alkyl groups increases [Lebedev s rule (418)-, as the number of phenyl radicals substituting the alkyl radicals at the double bond in olefins increases the rate of hydrogenation on Pt decreases 419)]. 

By construction, Lebedev quadrature rules exactly integrate all spherical harmonics up to a certain degree on the surface of a sphere. The 6, 38, 86 and 194 point rules are exact for all spherical harmonics up to 3rd, 9th, 15th and 23rd degree, respectively. 

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