Computational study of Jahn-Teller type distortions in radical cations of methyl-substituted cyclopropanes

We have studied Jahn-Teller (JT) type distortions in a series of methyl-substituted cyclopropane cations with ab initio molecular orbital techniques. Two sets of cyclopropane cation structures are considered for the parent (1a) and the 1-methyl-substituted (1b), 1,1-dimethyl-substituted (1c), 2,3-dimethyl-substituted (1d (trans), 1e (cis)), and 2,2,3,3-tetramethyl-substituted (1f) species. These structures reflect the first-order JT distortions occurring in the parent cation (1a) from a doubly degenerate 2E' (D3h symmetry) ground state to nondegenerate states of 2A1 and B-2(2) symmetry (C2v point group). States of the "2A1 type" possess one long and two short ring C-C bonds, are always structural minima on their respective potential energy surfaces, and represent the minimum energy structures for 1a, 1d, 1e, and 1f. The "B-2(2)-type" states are structurally characterized by two tong and one short ring C-C bonds and are always transition states, although they are the preferred first-order JT type distorted structures for both 1-methylated cations (1b,c). Unsymmetrical (scalene) triangular structures actually represent the absolute minima for 1b and 1c. These structures may be viewed as distorted from the "B-2(2)-type" geometries via a second-order JT type mechanism or, alternatively, as "2A1-type" with the substituents at the "wrong" carbon atom. The predicted fine-tuning of cation state preference and substantial differences in spin density distributions should be verifiable by spectroscopic means (ESR). The qualitative charge density distributions might be probed by chemical means (nucleophilic capture); an unequivocal interpretation is questionable, however.