Experiments and calculations for determination of the stabilities of benzyl, benzhydryl, and fluorenyl carbocations: Antiaromaticity revisited

Article abstract of DOI:10.1021/ja00047a010

The following pK_R values for the formation of benzyl, benzhydryl, and fluorenyl carbocations in 50:50 (v:v) trifluoroethanol/water at I = 0.50 (NaClO₄) were determined as pK_R = -log (k_HOH[H₂O]/k_H), where k_H is the second-order rate constant for acid-catalyzed reaction of the alcohol to form the carbocation and k_HOH is the second-order rate constant for capture of the carbocation by water: (R⁺, pK_R); PhCH₂⁺, ≤-20; PhCH(Me)⁺, -15.4; PhC(Me)₂⁺, -12.3; Ph₂CH⁺, -11.7; Ph₂C(Me)⁺, -9.3; 9-fluorenyl carbocation (9-Fl⁺), -15.9; 9-methyl-9-fluorenyl carbocation (9-Me-9-Fl⁺), -11.1. The pK_R for Ph₂CH⁺ is in fair agreement with the value estimated using acidity functions,^1a but the pK_R for 9-Me-9-Fl⁺ is ca. 4 units more positive than that from the acidity function method,^1a so that the difference in the acidity of benzhydryl and fluorenyl carbocations is smaller than estimated in earlier work. The 12 π-electron cyclic fluorenyl system in 9-Fl⁺ and 9-Me-9-Fl⁺ causes only 5.7 kcal/mol and 2.4 kcal/mol, respectively, destabilization of the corresponding acyclic carbocations Ph₂CH⁺ and Ph₂C(Me)⁺. The pK_R values show that "antiaromatic" destabilization of the 9-fluorenyl carbocations must be small. Ab initio calculations of the structures and energies of 9-Fl⁺ and Ph₂CH⁺ and of the corresponding alcohols at the 3-21G//3-21G and 6-31G*//3-21G levels indicate that Ph₂CH⁺ is ca. 8-10 kcal/mol more stable than 9-F1⁺, which is in good agreement with the stability difference calculated from the pK_R data. This indicates that electronic factors play the major role in determining the relative energies of these carbocations. Force field calculations were performed to estimate the contribution of van der Waals and ring strains to the difference in the pK_R values for Ph₂CH⁺ and 9-Fl⁺. Assuming hypothetical structures for Ph₂CH⁺ and 9-Fl⁺ which are free of van der Waals and ring strains, it is then estimated that there is an 8-11 kcal/mol decrease in π-electron stabilization on moving from Ph₂CH⁺ (C_2v) and 9-F1OH to 9-Fl⁺ and Ph₂CHOH. It is concluded that 9-fluorenyl carbocations are not antiaromatic. The difference in the energy of the 9-fluorenyl and benzhydryl carbanions relative to the alcohols was calculated to be -13.2 kcal/mol at the 6-31G*//3-21G level. This difference is attributed to the difference in the energies of the HOMOs for the two carbanions.