Molecular orbital study of internal rotation

Abstract

The CND0/2 molecular orbital method is used to predict and explain the barriers to internal rotation in a number of molecules. The observed 3: 2: 1 ratio of the barriers in ethane, methylamine, and methyl alcohol is approximately reproduced as are most trends in the barriers of fluoro-substituted propenes; however, the calculated trends for fluoro-substituted ethanes are incorrect. The barriers in H202, F202, N2H4, N 2F4, and NH20H and the effect of geometry optimization on these barriers are also discussed. The major source of the barriers in the first group of molecules is predicted to be due primarily to nonbonded interactions across the axial bonds, while interactions between the lone pairs on the axial bonds are found to be important in the latter group. It is concluded that CNDO will be applicable to further barrier studies only if nonbonded interactions involving highly electronegative atoms (e.g., F) are unimportant. T he nature of the forces which give rise to barriers to internal rotation has been an important and intriguing problem for quite some time. In recent years accurate SCF molecular orbital calculations have been used with increasing frequency in an attempt to reproduce and explain the origin of these barriers. 210 However, owing to the complexity of the calculation of accurate molecular wave functions, ab initio results for internal rotation barriers have been limited to rather small molecules. The method of complete neglect of differential overlap (CNDO) developed by Pople, Santry, and Segal 1113 is much reduced in complexity with respect to ab initio calculations and is therefore applicable to a much wider range of molecules. Since CNDO has proved to be quite successful in predicting and explaining many molecular properties, 1320 the present work was undertaken to determine the applicability of the method to the problem of internal rotation. Method of Calculation The coordinates of all molecules investigated were obtained using the Model-Builder program (MBLD) described elsewhere. 21 The approximations involved in CNDO have been described in detaiP 113 and will not be repeated here; however, the energy expressions derived in ref 11 are pertinent to the discussion of bar(1) Department of Chemistry, Iowa State University, Ames, Iowa. (2) R. M. Pitzer and W. N. Lipscomb, J. Chern. Phys., 39, 1995 (1963). (3) R. M. Pitzer, ibid., 47, 965 (1967). (4) E. Clementi and D. R. Davis, ibid., 45, 2593 (1966). (5) L. Pedersen and K. Morokuma, ibid., 46, 3941 (1967). (6) W. H. Fink and L. C. Allen, ibid., 46,2261, 2276 (1967). (7) U. Kaldor and I. Shavitt, ibid., 44,1823 (1966). (8) W. Palke and R. M. Pitzer, ibid., 46, 3948 (1967). (9) A. Veillard, Theoret. Chim. Acta, 5, 413 (1966). (10) W. H. Fink, D. C. Pan, and L. C. Allen, J. Chern. Phys., 47, 895 (1967). (11) J. A. Pople, D. P. Santry, and G. A. Segal, ibid., 43, S129 (1965). (12) J. A. Pople and G. A. Segal, ibid., 43, S136 (1965). (13) J. A. Pople and G. A. Segal, ibid., 44, 3289 (1966). (14) D.P. Santry and G. A. Segal, ibid., 47, 158 (1967). (15) H. W. Kroto and D.P. Santry, ibid., 47,792, 2736 (1967). (16) J. A. Pople and M. Gordon, J. Am. Chern. Soc., 89,4253 (1967). (17) G. A. Segal, J. Chern. Phys., 47, 1876 (1967). (18) G. A. Segal and M. L. Klein, ibid., 47,4236 (1967). (19) K. B. Wiberg, J. Am. Chern. Soc., 90, 59 (1968). (20) C. Giessner-Prettre and A. Pullman, Theoret. Chim. Acta, 9, 279 (1968). (21) M. S. Gordon and J. A. Pople, Quantum Chemistry Program Exchange, Program No. 135. Journal of the American Chemical Society I 91:12 I June 4, 1969 riers and will be described briefly. If one writes a molecular orbital ¢ 1 as a linear combination of atomic orbitals x~'