Abstract
Nuclear permutation-inversion (PI) group theory and the linear combination of localized wavefunctions (LCLW) method are applied to the proton “ring-walk” tunneling problem in C 6D 6H + and the benzenium ion ( C 6 H 7 + ) . For C 6D 6H + and C 6 H 7 + , the rigid and non-rigid MS groups are developed, and their corresponding correlation tables constructed. The reverse correlation relationship is combined with spin statistical restrictions to determine the number of allowed tunneling split levels for both ions. Through the use of the LCLW method and the WKB approximation, the qualitative pattern of the tunneling splitting is presented for C 6D 6H +. Application of the LCLW problem for the benzenium ion is presented, but the complete treatment to obtain the structure of the tunneling split levels is limited by the computational expense of obtaining the eigenvectors from the diagonalization of the 15 120 × 15 120 connectivity matrix.
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