Theoretical Treatment of Proton Addition Complexes

When a proton addition complex is formed, the particular even-numbered hydrocarbon is converted to an odd hydrocarbon ion. The TT-electron number remains even, but is reduced by two as a result of the formation of the u-bond. Thus we are dealing with a diamagnetic positive hydrocarbon ion. The theoretical treatment of this 7r-electron system has to reflect the following  

Questions concerned with the energy can in the first instance be treated to a good approximation by means of the HMO theory if the effect of substituents is neglected. If HMO theory is used it must be specified to which C-atom the proton is added. In the case of anthracene, for example, three positions of the molecule must be considered. A decision as to which of these three positions is energetically the most favoured can easily be reached by means of the HMO theory. 

From the known starting points of HMO theory, the 7r-electron energy of the neutral w-electron system (E )f and the corresponding energy of the protonated system (E ) may be calculated. The difference of the two energies 

The requisite relation between the basicity constants and the localization energy can easily be obtained. The following relation exists between the thermodynamic quantities  

Since TA8 is practically independent of the structure of the aromatic substances (cf. IV, C), one obtains the simple relation 

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