An ab initio investigation of the stabilization of selected .beta.-substituted ethyl cations and .alpha.-substituted methyl cations

In this study, we calculate the stabilization of /3-substituted ethyl cations (R = H, Li, BeH, BH,. CH,, NH,, OH, F, Na, MgH, A1H2, SiH,, PH2, SH, CI) and a-substituted methyl cations (R = H, Li, CH,, NH,, OH, F, Na, SiH,, PH,, SH, CI) in order to obtain a relationship between the nature of the substituent and the degree of stabilization of the cation. Results show that the stabilization energy is related to the electronegativity of the @ substituents, but not the CY substituents. The rotational barrier of the @-substituted ethyl cation is linearly related to the Mulliken population of the 2p(C+) orbital. We found that the stabilization energy is linearly related to the ionization potential of the aand PLA @-substituted radicals, and the HOMO energies of the PLA /3-substituted radical are linearly related to the corresponding ionization potentials. Trends in the stabilization by secondand third-row substituents are discussed. A wide variety of theoretical results have been presented which examine substituent effects in carbocation sy~tems.I-’~ Simple theoretical models have been studied as a means of interpreting and a-acceptors. For the case of carbocations the a-acceptor function is of less importance than for radicals or carbanions.I2 experimental results obtained for larger, more complex-carbocations. As a result, a relatively clear qualitative picture has emerged of the factors that can affect the stability of carbocations.‘, 99. 1291. (1) Hoffmann, R.; Radom, L.; Pople, J. A,; Schleyer, P. v. R.; Hehre, W. (2) Apeloig, Y.; Schleyer, P. v. R.; Pople, J . A. J . Am. Chem. SOC. 1977, J , ; Salem, L. J , Am. Chem, sot, 1972, 94, 6221, One way of assessing the stability of a carbocation is to use an isodesmic reaction such as eq 1, where SE+ (SE+ is the SE+ RCH2CH2’ + HCH2CH3 RCHZCH, + HCH2CH2’ (1) “stabilization” energy of the cation) is defined as AE.IZ (Here we use a @-substituted ethyl cation as an example; an analogous equation would be used for methyl cations.) When SE+ is greater than zero the cation RCH2CH2+ is more stable than the corresponding unsubstituted one, HCH2CH2+. It has been determined that two distinct types of substituents are capable of stabilizing the cation center. The first consists of substituents more electropositive than H (e.g., BeH, BH,, AIH,) that can act as cr-donors *Author to whom correspondence should be addressed. (3) Apeloig, Y.; Schleyer, P. v. R.; Pople, J. A. J . Am. Chem. SOC. 1977, (4) Pross, A.; Radom, L. Aust. J . Chem. 1980, 33, 241. ( 5 ) Radom, L.; Pople, J . A,; Schleyer, P. v. R. J . Am. Chem. SOC. 1972, ( 6 ) Creary, X.; Merhrsheikh-Mohammadi, M. E.; Eggers, M. D. 1. Am. (7 ) Pople, J . A.; Apeloig, Y.; Schleyer, P. v. R. Chem. Phys. Lett. 1982, (8) Hopkinson, A. C.; Lien, M. H. Can. J . Chem. 1985, 63, 3582. (9) Lien, M. H.; Hopkinson, A. C. J . Mol. Struct. (Theochem) 1985, 121, (10) Dorado, M.; M6,O.; YBRez, M. J . Am. Chem. SOC. 1980, 102,947. ( I 1 ) Radom, L.; Poppinger, D.; Haddon, R. C. Carbonium Ions; Olah, G . (12) Hehre, W. J . ; Radom, L.; Schleyer, P. v. R.; Pople, J . A. Ab Initio ( 1 3) Rdriquez, C. F.; Hopkinson, A. C. J . Mol. Struct. (Theochem) 1987, 99, 5901.