Theoretically optimized structures of carbocations

The identity of the empirical r value for the solvolysis transition state with that for the corresponding gas-phase cation indicates that the structures of the transition states in benzylic solvolyses should be essentially constant and that 

The characteristic change of the r value in the solvolysis reaction of benzylic precursors and for the corresponding carbocations should provide important information concerning the solvolysis transition state. The r value, reflecting the TT-delocalization within the cationic species, appears to remain essentially the same in solution as in the gas phase, and the charge delocalization in the transition state of the solvolytic ionization should be close to that in the carbocation intermediate. Advanced ab initio molecular orbital calculations can be used to find the underlying relationship between quantum chemical quantities and experimental r values, and the relation between r values and theoretical indices provides a basis for the physical meaning of the r parameter (Nakata et al, 1996,1998,1999). 

These theoretical considerations reveal that the empirical r values are intimately related to the theoretical indices of the structures of benzyhc 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 for the parent carbocations (X = H) as 

This provides theoretical support for the concept of varying resonance demand, which reflects the varying degree of ir-overlap interaction between the benzylic p-orbital and the benzene ir-system. 

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Structure-reactivity relationship in polyarylcarbocation systems 334 Conformations of carbocations 334 Reactivity-conformation relationship 337 Stabilities of carbocations in the gas phase 343 Structural effects 343 Tlie resonance demand parameter 355 Theoretically optimized structures of carbocations 362 Reaction mechanisms and transition-state shifts 365 Extended selectivity-stability relationships 365 Ground-state electrophilic reactivity of carbocations 366 Sn2 reactions of 1-arylethyl and benzyl precursors 372 Concluding remarks 378 Acknowledgements 379 References 379... 

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