Carbocation bonding theory

Problem 8.28 (a) Apply the MO theory to the allyl system (cf. Problem 8.26). Indicate the relative energies of the molecular orbitals and state if they are bonding, nonbonding, or antibonding, (b) Insert the electrons for the carbocation C,H, the free radical C,H, and the carbanion CjH, and compare the relative energies of these three species. 

These theoretical considerations reveal that the empirical r values are intimately related to the theoretical indices of the structures of benzylic carbocations derived from resonance theory. The coefficient r in the Y-T equation can thus be replaced as a first approximation by a set of theoretical quantities, e.g. increment of bond orders (PAr,a)H as in (35) or sum of charge populations in the aryl ring (2 for the parent carbocations (X = H) as... 

Over the past few years, the debate over the origin of the p-silicon effect on carbocations has narrowed to one of the relative magnitudes of inductive and hyperconjugative factors. Theory and experiment are finally in agreement that hyperconjugation is by far the dominant factor—29 kcal/mol calculated to be from P-stabilization ( ) versus 9 kcal/mol from induction and polarization. The realization of these effects is dramatically revealed in the SnI solvolyses of the conformationally locked cyclohexyl trifluoroacetates (OTFA) (3-5), The relative solvolysis rates at 25 °C for compounds 3-5 are 1, 4 X 10, and 2.4 X 10, respectively. Compound 4 cannot attain the necessary anti-coplanar relationship of the Si-C and C-O bonds, which is present in 5 and required for full hyperconjugative interaction with the cation formed as the C-O bond suffers heterolysis. 

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