Theoretical studies of carbocations in ion pairs. 4. The interconversion of the 1-propyl cation and protonated cyclopropane

The structure of the l-propyl cation in the ion pair with the model anion t rihydrofluoroborate, proven in earlier work to be appropriate for such stud ies, was investigated by ab initio calculations at the level previously rep orted to give the definitive structure of carbocations. In previous work, i t was shown that the carbocation structure does not change with the nature of the anion, The cation structure is determined, however, by the distance between the cation and anion, d, and their relative orientation. At infinit e interionic distance the only stable chemical species (energy minimum) is the protonated cyclopropane, 1. As the ions move toward each other, the cyc lopropane bond opposite to the anion becomes progressively longer and event ually it breaks up in the contact ion pair. Three domains of cation stabili ty are identified as a function of d: at long distances, ion 1 is the only energy minimum; at intermediate distances 1 and the l-propyl cation 2 are b oth energy minima; at short distances, ion 2 is the only energy minimum. Th us, ionization of l-propyl precursors forms the tight ion pair of 2 as the first intermediate. Isomers 1 and 2 differ in both the C1-C2-C3 angle and t he conformation of the C2-C3 bond; the transition structure for their inter conversion has been determined by calculations, At the MP4(FC)/6-311 G**//M P2/6-311G** level, the two isomers have the same energy content for d = 2.4 0 Angstrom, but correction for the zero-point energies obtained from the vi brational frequencies calculated at the MP2/6-311G** level reduces the ener gy of 2 relative to 1, thus requiring a slight upward correction in the val ue of d for equal stability of isomers. The interconversion of 1 and 2 is o bserved for a position of the anion essentially in the same plane as the th ree carbon atoms. Movement of the anion above the same plane results in hyd rogen shift with the formation of the 2-propyl cation, 3, Some literature r esults in which primary carbocations could intervene as intermediates are d iscussed. In particular, the data on carbon and hydrogen scrambling in 3 in superacid solution are better accounted for by the results of calculations for ion pairs, with both 1 and 2 as intermediates, than by the results of calculations for isolated ions.