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

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

The equilibrium structures for the ground and transition states of $C_7H_7^+$ 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-, m-and 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, ${\Delta}H^{\circ}_{f0}$, 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.