Rearrangement pathways of five-membered ring enlargement in carbocations: quantum chemical calculations and deuterium kinetic isotope effects.

Three plausible routes for the five-membered ring expansion in the equilibrating 2-cyclopentyl-2-propyl and 1-(2-propyl)cyclopentyl cations 1A/1B were located on the PES, all calculated at the MP4/6-31G(d)//MP2/6-31G(d) level of theory. In pathway I, the six-membered transition structure (TS-I) connects the less stable cyclopentyl cation 1A and the 1,2-dimethylcyclohexyl carbocation (2) via a barrier of 16.4 kcal/mol. In pathway II, which has a barrier of 16.3 kcal/mol, the methyl migration occurs first in the more stable 1B via transition structure TS-II. Pathway III involves the uphill hydride shift and formation of the secondary cation 3, which undergoes Wagner-Meerwein 1,2-isopropyl shift via a transition structure TS-III and the protonated carbocation intermediate 4. The barrier pathway III is for 17.0 kcal/mol. Experimental secondary deuterium isotope effects of the rearrangement were measured for the hexadeuterated 1A-d6/1B-d6 (kH/kD = 2.40) and tetradeuterated 1A-d4/1B-d4 (kH/kD = 0.18) cations by means of 1H NMR. Comparison of the experimental data with the theoretical values (kH/kD = 2.40 for 1B-d6 and kH/kD = 0.24 for 1B-d4, respectively) obtained with QUIVER revealed that pathway II is a major reaction route.