Extended Hückel Theory. IV. Carbonium Ions

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Abstract
The conformations, relative stabilities, and electronic distribution of a sample of the more important carbonium ions and positively charged hypothetical transition states are examined. The species studied include the methyl, ethyl, isopropyl, tertiary butyl, and higher alkyl carbonium ions; protonated ethylene, acetylene, benzene, cyclopropane; the cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl carbinyl, allyl, and benzyl cations; the carbonium ions based on norbornane, norbornene, norbornadiene. Significant charge delocalization for a classical carbonium ion geometry is observed—the extent of this phenomenon is wider than anticipated. For the alkyl carbonium ions it is shown that the order of stabilities may be obtained from a calculation in which the polarity of the C–H bond is C—–H+. Protonated ethylene and acetylene show local minima for a symmetrical complex, but with rearrangement to an unsymmetrical cation favored. Protonated cyclopropane prefers an unsymmetrical three‐center bonded structure, protonated benzene stabilizes in the familiar benzenium. The orientation of the empty carbonium p orbital with respect to other π‐type orbitals determines the conformation in cyclopropyl carbinyl, benzyl, and allyl. The peculiar nature of the cyclopropane electron distribution is studied. The carbonium ions based on the bicyclo[2.2.1]‐heptane structure show some nonclassical features; confirming experimental conclusions, the unusual 7‐norbornadienyl cation is calculated to prefer an unsymmetrical geometry. Difficulties in applying the extended Hückel theory to charged species make some of the conclusions from the calculations less certain.

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