Theoretical Approach for the Equilibrium Structures and Relative Energies of C₇H₇⁺Isomers and the Transition States between o-, m-, and p-Tolyl Cations

Abstract

The equilibrium structures for the ground and transition states of C 7 H 7 + isomers have been investigated using sophisticated ab initio quantum mechanical techniques with various basis sets. The structures of tropyrium and benzyl cations have been fully optimized at the DZP CCSD(T) levels of theory. And the structures of o-, mand p-tolyl cations are optimized fully up to the DZ CCSD(T) levels of theory. The geometries for the transition states between three isomers of tolyl cations have been optimized up to DZP CISD level of theory. The SCF harmonic vibrational frequencies for tropylium, benzyl, and three isomers of tolyl cations are all real numbers, which confirm the potential minima and each unique imaginary vibrational frequencies for TS1 and TS2 confirm the true transition states. The relative energy of the benzyl cation with respect to the tropyrium cation is predicted to be 28.5 kJ/mol and is in good agreement with the previous theoretical predictions. The 0 K heats of formation, ∆H°f 0 , have been predicted to be 890, 1095, 1101, and 1110 kJ/mol for tropylium, ortho-, meta-, and para-tolyl cations by taking the experimental value of 919 kJ/mol for the benzyl cation as the base level. The relative stability between tolyl cations is in the order of ortho < meta < para and is in good agreement with previous theoretical predictions both in magnitude and in order. The energy barriers are predicted to be 51.2 kcal/mol for the rearrangement from o-tolyl to m-tolyl cation and 53.1 kcal/mol for conversion of m-tolyl cation to p-toly.

Structure and Dissociation Pathways of Protonated Tetralin (1,2,3,4-Tetrahydronaphthalene)

“…The formation and isomerization of the C 7 H 7 + ion from a large number of alkylbenzene precursors has been the subject of extensive study. − In a 1994 review, Lifshitz pointed out that the first studies on the C 7 H 7 + ion, which utilized appearance potentials, hydrogen scrambling in deuterated precursors, and other thermochemical data, concluded that the tropylium ion was the final product . Later work, however, presented evidence for the benzylium structure. − Very recent studies on the “thermometer” ion, benzylpyridinium ion, have inferred that the benzylium structure is formed first but later rearranges to form the tropylium structure. , …”

Vacuum Ultraviolet Fingerprints as a New Way of Disentangling Tropylium/Benzylium Isomers

“…The formation of the various isomers has perhaps been the most studied problem in gas-phase physical organic chemistry . Particular emphasis was placed on understanding the formation routes of the two most stable isomers, Tr + and Bz + , as well as their interconversion pathways, as evidenced by this nonexhaustive list of references, refs − , contributing to this topic.…”