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Molecular Orbital Calculations on Carbonium Ions. 11. The Methyl, Ethyl, and Vinyl Cations. The Series C,H,+ R. Sustmann, J. E.
M . J. S. Dewar, L. C. Allen, and P. von R. Schleyer Contribution from the Departments of Chemistry, Princeton University, Princeton, New Jersey 08540, and the University of Texas, Austin, Texas 78712. Received April 26, 1969 Abstract: Semiempirical NDDO and ab initio Hartree-Fock-Roothaan SCF calculations are reported and compared for the isomeric structures of formulae CzH3+ and CzHs+. The NDDO (neglect of diatomic differential overlap) scheme is described. It is found that NDDO and all less complete schemes overestimate the stability of bridged ions, relative to the much more rigorous ab initio method. Thus NDDO favors the protonated acetylene over the vinyl cation structure by 32.0 kcal/mole, and the protonated ethylene over the ethyl cation structure by 33.2 kcal/mole. Ab initio calculations show the unbridged species to be more stable: the vinyl cation is favored by 25.1 kcal/mole, and the ethyl cation by 9.0 kcal/mole. NDDO calculations predict that an a-methyl substituent on a vinyl cation stabilizes the ion by 1.0-1.5 eV (ca. 20-35 kcal/mde) more than the methane-ethane or ethylene-propene energy differences. However, methyl substitution on protonated acetylene gives no such "extra" stabilization. NDDO calculations show the 2-propyl cation to be 18 kcal/mole more stable than the 1-propyl cation, in good agreement with experimental values. Edge-protonated cyclopropane is calculated to be 81 kcal/mole more stable than 2-propyl cation, but the validity of this result is considered dubious on theoretical grounds. Edge-protonated cyclopropane is computed to be 137 kcal/mole more stable than the face-protonated isomer by NDDO, in good agreement with the ab initio result of 125 kcal/mole. NDDO predicts corner-protonatedcyclopropane to be some 20 kcal/mole less stable than the edge-protonated isomer.
T
he widespread occurrence of carbonium ions as reaction intermediates, and their more recent preparation in strong acid media, have stimulated investigations of their structure by molecular orbital methods. Early extended Hiickel (EHT) calculations4 showed promise, but are not satisfactory for charged species or for calculating bond lengths. The use of more refined treatments, including electron-electron interactions and capable of predicting molecular geometries, was clearly indicated if meaningful results are to be obtained with both classical and nonclassical (bridged) structures. While ab initio calculations have been performed on small cations6v6 (and further results are reported in this paper) the need for semiempirical methods still prevails for most systems of chemical interest. Several approximate schemes have been applied to the calculation of carbonium ion~.~-lO A disadvantage of most of these procedures is that they do not account correctly for bond lengths. The most successful semiempirical treatment to date'" uses the INDO procedure" for calculations on the C3H7+series. In the present paper we apply a semiempirical method based on the neglect of diatomic differential overlap (1) Paper I [J. E. Williams, R. Sustmann, L. C. Allen, and P. von R. Schleyer, J . Am. Chem. SOC.,91, 1037 (1969)l presented a preliminary account of part of this work. (2) National Science Predoctoral Fellow, 1965-1969, Ph.D. Thesis, Princeton University, 1969. (3) N. Muller and R. S . Mulliken, J. Am. Chem. SOC.,80, 3489 ( 195 8). (4) R.Hoffmann, J . Chem. Phys., 40, 2480 (1964). (5) R. E. Kari and I . G. Csizmadia, ibid., 46, 1817 (1967); 50, 1443 (1969); G. von Bunau, G. Diercksen, and H. Preuss, Intern. J . Quant. Chem., 1, 645 (1967); S. D. Peyerimhoff, R. J. Buenker, and L. C. Allen, J . Chem. Phys., 45, 734 (1966). (6) J. D. Petke and J. L. Whitten, J. Am. Chem. SOC.,90, 3338 (1968). (7) K.B. Wiberg, Tetrahedron, 24, 1083 (1968). (8) T. Yonezawa, H. Hakatsuji, and H. Kato, J . Am. Chem. SOC.,90, 1239 (1968). (9) G.Klopman, ibid., 91, 89 (1969). (10) H.Fischer, H. Kollmar, H. 0. Smith, and I
