Theoretical study of stable carbocations and their interactions with anions

The relative stabilities of ion-pair and biradical (or covalent) electron configurations are studied with respect to a simple system, CH₃^--C₃H₃⁺, in a C_3v symmetrical structure with a view of clarifying the basic feature of hydrocarbon ion pairs. As a possible source of stabilizing cations, the effect of hyperconjugation is analyzed on cyclopropenium ions by representing the interaction between the ring and the substituent groups in terms of paired interacting orbitals. The ability of carbon atoms in cyclopropenium and tropylium ions for electron acceptance is also discussed by projecting out the reactive unoccupied orbitals each of which has the maximum amplitude on the 2p_π atomic orbital of one of the carbon atoms in the three-membered or seven-membered ring. A tropylium ion with an interesting reactivity trend is suggested. Other factors that should stabilize hydrocarbon ion pairs are discussed.