Advertisement

Barriers to Rotation and Inversion

  • Philip W. Payne
  • Leland C. Allen
Part of the Modern Theoretical Chemistry book series (MTC, volume 4)

Abstract

Approximately two-thirds of the chapters in these two companion volumes are devoted to methods of obtaining high-accuracy electronic wave functions for molecules and solids. The remaining third are concerned with particular chemical species or properties, and our chapter fits the latter category. Within this category the extensive literature on barriers offers two special opportunities of general interest to chemical theorists. First, it is possible to make rather definitive statements on the quality of wave functions required to yield quantitative predictions. Second, methods for analyzing ab initio wave functions to ascertain the physical origin of the barrier and provide a quantum mechanically well-defined, but simple picture of the mechanism have been more extensively developed for this topic than any other.

Keywords

Barrier Height Internal Rotation Rigid Rotation Rotational Barrier Inversion Barrier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. A. Pople, Molecular orbital studies of conformation, Tetrahedron 30, 1605–1615 (1974).Google Scholar
  2. 2.
    A. Golebiewski and A. Parczewski, Theoretical conformational analysis of organic molecules, Chem. Rev. 74, 519–530 (1974).Google Scholar
  3. 3.
    D. T. Clark, Theoretical organic chemistry and ESCA, Annu. Rep. Prog. Chem., 69(B), 40–83 (1973).Google Scholar
  4. 4.
    A. Veillard, Ab initio calculations of barrier heights, in : Internal Rotation in Molecules (W. J. Orville-Thomas, ed.), pp. 385–421, John Wiley and Sons, New York (1974).Google Scholar
  5. 5.
    W. Orville-Thomas, Internal rotation in molecules, in : Internal Rotation in Molecules (W. J. Orville-Thomas, ed.), pp. 1–18, John Wiley and Sons, New York (1974).Google Scholar
  6. 6.
    W. H. Fink and L. C. Allen, Origin of rotational barriers. I. Many-electron molecular orbital wavefunctions for ethane, methyl alcohol, and hydrogen peroxide, J. Chem. Phys. 46, 2261–2275 (1967).Google Scholar
  7. 7.
    K. S. Pitzer, Thermodynamic functions for molecules having restricted internal rotations, J. Chem. Phys. 5, 469–472 (1937);Google Scholar
  8. 7a.
    K. S. Pitzer, Thermodynamic functions for molecules having restricted internal rotations, J. Chem. Phys. 5, 473–479 (1937).Google Scholar
  9. 8.
    R. M. Pitzer, A Calculation of the Barrier to Internal Rotation in Ethane, Ph.D. dissertation, Harvard University, 1964, University Microfilms, Ann Arbor, Order No. 63–7842; Diss. Abstr. 25(2), 870 (1964).Google Scholar
  10. 9.
    S. Epstein, The Variational Method in Quantum Chemistry, Academic Press, New York (1974).Google Scholar
  11. 10.
    J. Goodisman and W. Klemperer, On error in Hartree-Fock calculations, J. Chem. Phys. 38, 721–725 (1963).Google Scholar
  12. 11.
    K. F. Freed, Geometry and barriers to internal rotation in Hartree-Fock theory, Chem. Phys. Lett. 2, 255–256 (1968).Google Scholar
  13. 12.
    L. C. Allen and J. Arents, Adequacy of the molecular orbital approximation for predicting rotation and inversion barriers, J. Chem. Phys. 57, 1818–1821 (1972).Google Scholar
  14. 13.
    R. E. Stanton, Hellmann-Feynman theorem and correlation energies, J. Chem. Phys. 36, 1298–1300. (1962).Google Scholar
  15. 14.
    B. Levy and M. C. Moireau, Correlation effect in the rotation barrier of ethane, J. Chem. Phys. 54, 3316–3321 (1971).Google Scholar
  16. 15.
    E. Clementi and H. Popkie, Analysis of the formation of the acetylene, ethylene, and ethane molecules in the Hartree-Fock model, J. Chem. Phys. 57, 4870–4883 (1972).Google Scholar
  17. 16.
    B. Zurawski and W. Kutzelnigg, Correlation energy of the internal rotation barrier in ethane, Bull. Acad. Pol. Sci., Ser. Soc. Chim. 22, 363–366 (1974).Google Scholar
  18. 17.
    R. Ahlrichs and F. Keil, Structure and bonding in dinitrogen tetroxide (N2O4), J. Am. Chem. Soc. 96, 7615–7620 (1974).Google Scholar
  19. 18.
    B. Dumbacker, Ab initio SCF and CI calculations on the barrier to internal rotation in 1,3-butadiene, Theor. Chim. Acta 23, 346–359 (1972).Google Scholar
  20. 19.
    U. Pincelli, B. Cadioli, and B. Levy, On the internal rotation in 1,3-butadiene, Chem. Phys. Lett. 13, 249–252 (1972).Google Scholar
  21. 20.
    R. Ahlrichs, F. Driessler, H. Lischka, V. Staemmler, and W. Kutzelnigg, PNO-CI (pair natural orbital configuration interaction) and CEPA-PNO (coupled electron pair approximation with pair natural orbitals) calculation of molecular systems. II. The molecules BeH2, BH, BH3, CH4, CH- 3, NH3 (planar and pyramidal, H2O, OH+ 3, HF, and the Ne atom), J. Chem. Phys. 62, 1235–1247 (1975).Google Scholar
  22. 21.
    R. E. Kari and I. G. Csizmadia, Configuration interaction wavefunctions and computed inversion barriers for NH3 and CH- 3, J. Chem. Phys. 56, 4337–4344 (1972).Google Scholar
  23. 22.
    A. Pipano, P. R. Gilman, C. F. Bender, and I. Shavitt, Ab initio calculations of the inversion barrier in ammonia, Chem. Phys. Lett. 4, 583–584 (1970).Google Scholar
  24. 23.
    R. M. Stevens, CI calculations for the inversion barrier of ammonia, J. Chem. Phys. 61, 2086–2090 (1974).Google Scholar
  25. 24.
    N. C. Dutta and M. Karplus, Correlation contribution to the ammonia inversion barrier, Chem. Phys. Lett. 31(3), 455–461 (1975).Google Scholar
  26. 25.
    G. H. F. Diercksen, W. P. Kraemer, and B. O. Roos, SCF-CI studies of correlation effects on hydrogen bonding and ion hydration. The systems: H2O, H+ H2O, Li+·H2O, F- H2O, and H2O·H2O, Theor. Chim. Acta 36, 249–274 (1975).Google Scholar
  27. 26.
    J. D. Swalen and J. A. Ibers, A potential function for the inversion of ammonia, J. Chem. Phys. 36, 1914–1918 (1962).Google Scholar
  28. 27.
    A. Rauk, L. C. Allen, and E. Clementi, Electronic structure and inversion barrier of ammonia, J. Chem. Phys. 52, 4133–4144 (1970).Google Scholar
  29. 28.
    L. Radom, W. J. Hehre, and J. A. Pople, A systematic study of energies, conformations, and bond interactions, J. Am. Chem. Soc. 93, 289–300 (1971).Google Scholar
  30. 29.
    L. Radom, W. A. Lathan, W. J. Hehre, and J. A. Pople, Internal rotation in 1,2-disubstituted ethanes, J. Am. Chem. Soc. 95, 693–698 (1973).Google Scholar
  31. 30.
    B. Kirtman, Interactions between ordinary vibrations and hindered internal rotation. I. Rotational energies, J. Chem. Phys. 37, 2516–2539 (1962).Google Scholar
  32. 31.
    B. Kirtman, Interactions between ordinary vibrations and hindered internal rotation. II. Theory of internal rotation fine structure in some perpendicular bonds of ethane-type molecules, J. Chem. Phys. 41(3), 775–788 (1964).Google Scholar
  33. 32.
    D. Papousek, High resolution infrared spectra of ethane-like molecules and the barrier to internal rotation, J. Mol. Spectrosc. 28, 161–190 (1968).Google Scholar
  34. 33.
    J. Susskind, Theory of torsion-vibration-rotation interaction in ethane and analysis of the bond ν 11 = ν 4, J. Mol. Spectrosc. 49, 1–17 (1974).Google Scholar
  35. 34.
    J. Susskind, Torsion-vibration-rotation interaction in ethane: the bonds ν 12 = ν 4, ν 8 and ν 6, J. Mol. Spectrosc. 49, 331–342 (1974).Google Scholar
  36. 35.
    D. R. Woods, High-Resolution Infrared Spectra of Normal and Deuterated Methanol between 400 cm-1 and 1300 cm-1, Ph.D. dissertation, University of Michigan, 1970, University Microfilms, Ann Arbor, Order No. 70–21, 819.Google Scholar
  37. 36.
    C. S. Ewig, W. E. Palke, B. Kirtman, Dependence of the CH3SiH3 barrier to internal rotation on vibrational coordinates: testing of models and effect of vibrations on the observed barrier height, J. Chem. Phys. 60, 2749–2758 (1974).Google Scholar
  38. 37.
    B. Kirtman, W. E. Palke, and C. S. Ewig, private communication, 1975.Google Scholar
  39. 38.
    D. R. Herschbach, Calculation of energy levels for internal torsion and over-all rotation. III, J. Chem. Phys. 31, 91–108 (1959).Google Scholar
  40. 39.
    A. Veillard, Relaxation during internal rotation in ethane and hydrogen peroxide, Theor. Chim. Acta 18, 21–33 (1970).Google Scholar
  41. 40.
    A. Veillard, Distortional effects on the ethane internal rotation barrier and rotation barriers in borazane and methylsilane, Chem. Phys. Lett. 3, 128–130 (1969).Google Scholar
  42. 41.
    P. H. Blustin and J. W. Linnett, Application of a simple molecular wavefunction. Part 2. The torsional barrier in ethane, J. Chem. Soc., Faraday Trans. 2 70, 290–296 (1974).Google Scholar
  43. 42.
    A. A. Frost and Robert A. Rouse, A floating spherical Gaussian orbital model of molecular structure. Hydrocarbons, J. Am. Chem. Soc. 90, 1965–1969 (1968).Google Scholar
  44. 43.
    J. D. Dill, P. v. R. Schleyer, and J. A. Pople, Geometries and energies of small boron compounds. Comparisons with carbocations, J. Am. Chem. Soc. 97, 3402–3409 (1975).Google Scholar
  45. 44.
    W. E. Palke, Calculation of the internal rotation barrier and its derivatives in BH3NH3, J. Chem. Phys. 56, 5308–5311 (1972).Google Scholar
  46. 45.
    J. O. Jarvie and A. Rauk, A theoretical study of the conformational changes in hydrazine, Can. J. Chem. 52, 2785–2791 (1974).Google Scholar
  47. 46.
    A. Veillard, Distortional effects on the internal rotation in hydrogen peroxide, Chem. Phys. Lett. 4, 51–52 (1969).Google Scholar
  48. 47.
    R. B. Davidson and L. C. Allen, Rotational barriers in hydrogen peroxide, J. Chem. Phys. 55, 519–527(1971).Google Scholar
  49. 48.
    T. H. Dunning, Jr. and N. W. Winter, private communication.Google Scholar
  50. 49.
    T. H. Dunning Jr. and N. W. Winter, Hartree-Fock calculation of the barrier to internal rotation in hydrogen peroxide, Chem. Phys. Lett. 11, 194–195 (1971).Google Scholar
  51. 50.
    J. P. Ranck and H. Johansen, Polarization functions and geometry optimization in ab initio calculations of the rotational barrier in hydrogen peroxide, Theor. Chim. Acta 24, 334–345 (1972).Google Scholar
  52. 51.
    L. Radom and J. A. Pople, Internal rotation in hydrocarbons using a minimal Slater-type basis, J. Am. Chem. Soc. 92, 4786–4795 (1970).Google Scholar
  53. 52.
    P. N. Skancke and J. E. Boggs, Molecular orbital studies of conformers and the barrier to internal rotation in 1,3-butadiene, J. Mol. Struct. 16, 179–185 (1973).Google Scholar
  54. 53.
    K. R. Sundberg and L. M. Cheung, Potential energy curve in the trans-cis isomerization of glyoxal, Chem. Phys. Lett. 29, 93–97 (1974).Google Scholar
  55. 54.
    D. H. Christensen, R. N. Kortzeborn, B. Bak, and J. J. Led, Results of ab initio calculations on formamide, J. Chem. Phys. 53, 3912–3922 (1970).Google Scholar
  56. 55.
    P. A. Kollman and C. F. Bender, The structure of the H3O+ (hydronium) ion, Chem. Phys. Lett 21, 271–273 (1973).Google Scholar
  57. 56.
    F. Driessler, R. Ahlrichs, V. Staemmler, and W. Kutzelnigg, Ab initio calculations on small hydrides including correlation. XI. Equilibrium geometries and other properties of CH3, CH+ 3, and CH- 3, and inversion barrier of CH- 3, Theor. Chim. Acta 30, 315–326 (1973).Google Scholar
  58. 57.
    J. M. Lehn and B. Munsch, An ab initio SCF-LCAO-MO study of the phosphorous pyramidal inversion process in phosphine, Mol. Phys. 23, 91–107 (1972).Google Scholar
  59. 58.
    E. Zeeck, Ab initio calculation of the barrier to free rotation of the methyl group in propylene (in German), Theor. Chim. Acta 16, 155–162 (1970).Google Scholar
  60. 59.
    U. Wahlgren and K. H. Johnson, Determination of the internal rotation barrier in ethane by the SCF-Xα scattered wave method, J. Chem. Phys. 56, 3715–3716 (1972).Google Scholar
  61. 60.
    U. Wahlgren, Calculations of potential barriers using the SCF-Xa method, Chem. Phys. Lett. 20, 246–249 (1973).Google Scholar
  62. 61.
    S. Weiss and G. Leroi, Direct observations of the infrared torsional spectrum of C2H6, CH3CD3, and C2D6, J. Chem. Phys. 48, 962–967 (1968).Google Scholar
  63. 62.
    P. A. Christiansen and W. E. Palke, Ethane internal rotation barrier, Chem. Phys. Lett. 31, 462–466 (1975).Google Scholar
  64. 63.
    W. E. Palke, Calculations of the barrier to internal rotation in ethyl fluoride: a comparison with ethane, Chem. Phys. Lett. 15, 244–247 (1972).Google Scholar
  65. 64.
    L. C. Allen and H. Basch, Theory of the rotational barriers in ethyl fluoride and ethane, J. Am. Chem. Soc. 93, 6373–6377 (1971).Google Scholar
  66. 65.
    L. Radom, W. A. Lathan, W. J. Hehre, and J. A. Pople, Internal rotation in some organic molecules containing methyl, amino, hydroxyl, and formyl groups, Aust. J. Chem. 25, 1601–1612 (1972).Google Scholar
  67. 66.
    R. M. Stevens, Geometry optimization in the computation of barriers to internal rotation, J. Chem. Phys. 52, 1397–1402 (1970).Google Scholar
  68. 67.
    G. F. Musso and V. Magnasco, Localized orbitals and short-range molecular interactions. III. Rotational barriers in C2H6 and H2O2, J. Chem. Phys. 60, 3754–3759 (1974).Google Scholar
  69. 68.
    R. M. Pitzer, Calculation of the barrier to internal rotation in ethane with improved exponential wavefunctions, J. Chem. Phys. 47, 965–967 (1967).Google Scholar
  70. 69.
    W. von Niessen, A theory of molecules in molecules. II. The theory and its application to the molecules Be-Be, Li2-Li2, and to the internal rotation in C2H6, Theor. Chim. Acta 31, 111–135 (1973).Google Scholar
  71. 70.
    O. J. Sovers, C. W. Kern, R. M. Pitzer, and M. Karplus, Bond-function analysis of rotational barriers: ethane, J. Chem. Phys. 49, 2592–2599 (1968).Google Scholar
  72. 71.
    A. Liberies, B. O’Leary, J. E. Eilers, and D. R. Whitman, Methyl rotation barriers and hyperconjugation, J. Am. Chem. Soc. 94, 6894–6898 (1972).Google Scholar
  73. 72.
    J. R. Hoyland, Ab initio bond-orbital calculations. I. Application to methane, ethane, propane, and propylene, J. Am. Chem. Soc. 90, 2227–2232 (1968).Google Scholar
  74. 73.
    L. Pedersen and K. Morokuma, Ab initio calculations of the barriers to internal rotation of CH3CH3, CH3NH2, CH3OH, N2H4, H2O2, and NH2OH, J. Chem. Phys. 46, 3941–3947 (1967).Google Scholar
  75. 74.
    E. Clementi, H. Kistenmacher, and H. Popkie, On the SCF-LCAO-MO and the SCH-Xα-SW approximations: Computation of the barrier to internal rotation for ethane, J. Chem. Phys. 58, 4699–4700 (1973).Google Scholar
  76. 75.
    J. L. Nelson and A. A. Frost, Local orbitals for bonding in ethane, Theor. Chim. Acta 29, 75–83 (1973).Google Scholar
  77. 76.
    R. E. Christoffersen, D. W. Gensen, and G. M. Maggiora, Ab initio calculations on large molecules using molecular fragments. Hydrocarbon characterization, J. Chem. Phys. 54, 239–252 (1971).Google Scholar
  78. 77.
    R. H. Hunt, R. A. Leacock, C. W. Peters, and K. T. Hecht, Internal rotation in hydrogen peroxide: the far infrared spectrum and the determination of the hindering potential, J. Chem. Phys. 42, 1931–1946 (1965).Google Scholar
  79. 78.
    C. Guidotti, U. Lamanna, M. Maestro, and R. Moccia, Barriers to the internal rotation and observables of the ground state for hydrogen peroxide, Theor. Chim. Acta 27, 55–62 (1972).Google Scholar
  80. 79.
    W. H. Fink and L. C. Allen, Origin of rotational barriers. I. Methylamine and improved wavefunctions for hydrogen peroxide, J. Chem. Phys. 46, 2276–2284 (1967).Google Scholar
  81. 80.
    L. Radom, W. H. Hehre, and J. A. Pople, Fourier component analysis of internal rotation potential functions in saturated molecules, J. Am. Chem. Soc. 94, 2371–2381 (1972).Google Scholar
  82. 81.
    W. E. Palke and R. M. Pitzer, On the internal rotation potential in H2O2, J. Chem. Phys. 46, 3948–3950 (1967).Google Scholar
  83. 82.
    P. F. Franchini and C. Vergani, SCF calculation with minimal and extended bases sets for H2O, NH3, CH4, and H2O2, Theor. Chim. Acta 13, 46–55 (1969).Google Scholar
  84. 83.
    U. Kaldor and I. Shavitt, LCAO-SCF computations for hydrogen peroxide, J. Chem. Phys. 44, 1823–1829 (1966).Google Scholar
  85. 84.
    I. H. Hillier, V. R. Saunders, and J. F. Wyatt, Theoretical study of the electronic structure and barriers to rotation in H2O2 and H2S2, Trans. Faraday Soc. 66, 2665–2670 (1970).Google Scholar
  86. 85.
    B. V. Cheney and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Oxygen-containing molecules, J. Chem. Phys. 56, 3503–3518 (1972).Google Scholar
  87. 86.
    G. Winnewisser, M. Winnewisser, and W. Gordy, Bull. Am. Phys. Soc. 2, 312 (1966).Google Scholar
  88. 87.
    A. Veillard and J. Demuynck, Barrier to internal rotation in hydrogen persulfide, Chem. Phys. Lett. 4, 476–478 (1970).Google Scholar
  89. 88.
    E. V. Ivash and D. M. Dennison, The methyl alcohol molecule and its microwave spectrum, J. Chem. Phys. 21, 1804–1816 (1953).Google Scholar
  90. 89.
    L. M. Tel, S. Wolfe, and I. G. Csizmadia, Near-molecular-Hartree-Fock wavefunctions for CH3O-, CH3OH, and CH3OH+ 2, J. Chem. Phys. 59, 4047–4060 (1973).Google Scholar
  91. 90.
    C. W. Kern, R. M. Pitzer, and O. J. Sovers, Bond-function analysis of rotational barriers: methanol, J. Chem. Phys. 60, 3583–3587 (1974).Google Scholar
  92. 91.
    S. Rothenberg, Localized orbitals for polyatomic molecules. I. The transferability of the C-H bond in saturated molecules, J. Chem. Phys. 51, 3389–3396 (1969).Google Scholar
  93. 92.
    D. R. Lide, Jr., Structure of the methylamine molecule. I. Microwave spectrum of CD3ND2, J. Chem. Phys. 27, 343–352 (1941).Google Scholar
  94. 93.
    D. R. Armstrong and P. G. Perkins, Calculation of the electronic structures and the gas-phase heats of formation of BH3NH3 and BH3CO, J. Chem. Soc. A 1969, 1044–1048 (1969).Google Scholar
  95. 94.
    J. R. Hoyland, Internal rotation in propane. Reanalysis of the microwave spectrum and quantum-mechanical calculations, J. Chem. Phys. 49, 1908–1912 (1968).Google Scholar
  96. 95.
    P. W. Payne and L. C. Allen, Charge density difference analysis. Comparison of rotational barriers in ethane and propane, submitted to J. Am. Chem. Soc. (1977).Google Scholar
  97. 96.
    J. R. Hoyland, Barriers to internal rotation in propane, Chem. Phys. Lett. 1, 247–248 (1967).Google Scholar
  98. 97.
    P. H. Blustin and J. W. Linnett, Applications of a simple molecular wavefunction. I. Floating spherical Gaussian orbital calculations for propylene and propane, J. Chem. Soc., Faraday Trans. 2 70, 274–289 (1974).Google Scholar
  99. 98.
    T. Kasuya and T. Kojima, Internal motions of hydrazine, J. Phys. Soc. Japan 18, 364–368 (1963).Google Scholar
  100. 99.
    W. H. Fink, D. C. Pan, and L. C. Allen, Internal rotation barriers for hydrazine and hydroxylamine from ab initio LCAO-MO-SCF wavefunctions, J. Chem. Phys. 47, 895–905 (1967).Google Scholar
  101. 100.
    A. Veillard, Quantum mechanical calculations on barriers to internal rotation. I. Self-consistent field wavefunctions and theoretical potential energy curves for the hydrazine molecule in the Gaussian approximation, Theor. Chim. Acta 5, 413–421 (1966).Google Scholar
  102. 101.
    J. O. Jarvie, A. Rauk, and C. Edmiston, The effect of bond function polarization on the LCAO-MO-SCF calculation of bond angles and energy barriers, Can. J. Chem. 52, 2778–2784 (1974).Google Scholar
  103. 102.
    E. L. Wagner, Ab initio versus CNDO barrier calculations. I. N2H4 and N2F4, Theor. Chim. Acta 23, 115–126 (1971).Google Scholar
  104. 103.
    R. G. Snyder and I. C. Hisatsune, Infrared spectrum of dinitrogen tetroxide, J. Mol. Spectrosc. 1, 139–150(1957).Google Scholar
  105. 104.
    J. M. Howell and J. R. Van Wazer, Electronic structure of dinitrogen tetroxide and diboron tetrafluoride and an analysis of their conformational stabilities, J. Am. Chem. Soc. 96, 7902–7910 (1974).Google Scholar
  106. 105.
    D. R. Lide, Jr., and D. E. Mann, Microwave spectra of molecules exhibiting internal rotation. I. Propylene, J. Chem. Phys. 27, 868–876 (1957).Google Scholar
  107. 106.
    D. R. Lide, Jr., and D. Christiansen, Microwave structure of propylene, J. Chem. Phys. 35, 1374–1378 (1962).Google Scholar
  108. 107.
    A. D. English and W. E. Palke, Calculation of barriers to internal rotation in propene and monofiuoropropenes, J. Am. Chem. Soc. 95, 8536–8538 (1973).Google Scholar
  109. 108.
    E. Scarzafaza and L. C. Allen, Rotational barriers in propene and its fluoro derivatives, J. Am. Chem. Soc. 93, 311–314 (1971).Google Scholar
  110. 109.
    M. L. Unland, J. R. Van Wazer, and J. H. Letcher, Ab initio calculation of the barrier to internal rotation in propylene using a Gaussian basis self-consistent field wavefunction, J. Am. Chem. Soc. 91, 1045–1052 (1969).Google Scholar
  111. 110.
    R. W. Kilb, C. C. Lin, and E. B. Wilson, Jr., Calculation of energy levels for internal torsion and over-all rotation. II. CH3CHO type molecules; acetaldehyde spectra, J. Chem. Phys. 26, 1695–1704 (1957).Google Scholar
  112. 111.
    R. B. Davidson and L. C. Allen, Attractive nature of the rotational barrier in acetaldehyde, J. Chem. Phys. 54, 2828–2830 (1971).Google Scholar
  113. 112.
    N. L. Allinger and Sister M. J. Hickey, Acetone, ab initio calculations, Tetrahedron 28, 2157–2161 (1972).Google Scholar
  114. 113.
    W. G. Fately and F. A. Miller, Torsional frequencies in the far infrared. II. Molecules with two or three methyl rotors, Spectrochim. Acta 18, 977–993 (1962).Google Scholar
  115. 114.
    W. G. Fately, R. K. Harris, F. A. Miller, and R. E. Witkowski, Torsional frequencies in the far infrared. IV. Torsions around the C-C single bond in conjugated molecules, Spectrochim. Acta 21, 231–244 (1965).Google Scholar
  116. 115.
    G. N. Currie and D. A. Ramsay, The 4875 Å band system of cis glyoxal, Can. J. Phys. 49, 317–322 (1971).Google Scholar
  117. 116.
    U. Pincelli, B. Cadioli, and D. J. David, A theoretical study of the electronic structure and conformation of glyoxal, J. Mol. Struct. 9, 173–176 (1971).Google Scholar
  118. 117.
    T. K. Ha, Ab initio calculation of cis-trans isomerization in glyoxal, J. Mol. Struct. 12, 171–178 (1972).Google Scholar
  119. 118.
    B. Sunners, L. H. Piette, and W. G. Schneider, Proton magnetic resonance measurements of formamide, Can. J. Chem. 38, 681–688 (1960).Google Scholar
  120. 119.
    H. Kamei, Nuclear magnetic double-resonance study of the hindered internal rotation in formamide, Bull. Chem. Soc. Japan 41, 2269–2273 (1968).Google Scholar
  121. 120.
    M. Penicaudet and A. Pullman, An ab initio quantum-mechanical investigation on the rotational isomerism in amides and esters, Int. J. Pept. Protein Res. 5, 99–107 (1973).Google Scholar
  122. 121.
    L. A. Carreira, Determination of the torsional potential function of 1,3-butadiene, J. Chem. Phys. 62, 3851–3854 (1975).Google Scholar
  123. 122.
    P. Th. van Duijnen and D. B. Cook, Ab initio calculations with ellipsoidal Gaussian basis sets, Mol. Phys. 21, 475–483 (1971).Google Scholar
  124. 123.
    R. J. Buenker, Theoretical study of the rotational barriers of allene, ethylene, and related systems, J. Chem. Phys. 48, 1368–1379 (1968).Google Scholar
  125. 124.
    J. M. André, M. C. André, and G. Leroy, Barrier to internal rotation in allene, Chem. Phys. Lett. 3, 695–698 (1969).Google Scholar
  126. 125.
    L. J. Schaad, The internal rotation barrier in allene, Tetrahedron 26, 4115–4118 (1970).Google Scholar
  127. 126.
    L. J. Schaad, L. A. Burnelle, and K. P. Dressier, The excited states of allene, Theor. Chim. Acta 15, 91–99 (1969).Google Scholar
  128. 127.
    L. J. Weimann and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Cumulenes and related molecules, J. Am. Chem. Soc. 95, 2074–2083 (1973).Google Scholar
  129. 128.
    R. M. Stevens, Accurate SCF calculation for ammonia and its inversion motion, J. Chem. Phys. 55, 1725–1729 (1971).Google Scholar
  130. 129.
    A. J. Duke, A Hartree-Fock study of the methyl anion and its inversion potential surface : use of an augmented basis set for this species, Chem. Phys. Lett. 21, 275–282 (1973).Google Scholar
  131. 130.
    P. Millie and G. Berthier, SCF wavefunction in Gaussians for methyl and vinyl radicals, Int. J. Quantum Chem. 2, 67–73 (1968).Google Scholar
  132. 131.
    R. E. Kari and I. G. Csizmadia, Potential-energy surfaces of CH+ 3 and CH3– 11, J. Chem. Phys. 50, 1443–1448 (1969).Google Scholar
  133. 132.
    R. E. Kari and I. G. Csizmadia, Near molecular Hartree-Fock wavefunction for CH3– 11, J. Chem. Phys. 46, 4585–4590.Google Scholar
  134. 133.
    R. Grahn, A theoretical study of the H3O+ ion, Arkiv. Fys. 19, 1417 (1961).Google Scholar
  135. 134.
    M. Fournier, G. Mascherpa, D. Rousselet, and J. Potier, Assignment of the vibrational frequencies of the oxonium ion, C. R. Acad. Sci., Ser. C 269, 279–282 (1969).Google Scholar
  136. 135.
    J. Lischka, Ab initio calculations on small hydrides including electron correlation. IX. Equilibrium geometries and harmonic force constants of HF, OH-, H2F+, and H2O and proton affinities of F-, OH-, HF, and H2O, Theor. Chim. Acta 31, 39–48 (1973).Google Scholar
  137. 136.
    M. Allevena and E. Le Clech, A conformational study of the H3O+ ion by an MO-SCF ab initio calculation, J. Mol. Struct. 22, 265–272 (1974).Google Scholar
  138. 137.
    J. W. Moskowitz and M. C. Harrison, Gaussian wavefunctions for the 10-electron systems. III. OH-, H2O, H3O+, J. Chem. Phys. 43, 3550–3555 (1965).Google Scholar
  139. 138.
    P. A. Kollman and L. C. Allen, A theory of the strong hydrogen bond, ab initio calculations on HF- 2 and H5O2, J. Am. Chem. Soc. 92, 6101–6107 (1970).Google Scholar
  140. 139.
    G. Alagona, R. Cimiraglia, and U. Lamanna, Theoretical investigations of the solvation process. III. STO double-Z SCF calculations on the hydrated H5O2, Theor. Chim. Acta 29, 93–96 (1973).Google Scholar
  141. 140.
    J. Almlöf and U. Wahlgren, Ab initio studies of the conformation of the oxonium ion in solids, Theor. Chim. Acta 28, 161–168 (1973).Google Scholar
  142. 141.
    M. D. Newton and S. Ehrenson, Ab initio studies on the structures and energetics of inner and outer-shell hydrates of the proton and the hydroxide ion, J. Am. Chem. Soc. 93, 4971–4990 (1971).Google Scholar
  143. 142.
    R. E. Weston, Vibrational energy level splitting and optical isomerism in pyramidal molecules of the type XY3, J. Am. Chem. Soc. 76, 2645–2648 (1954).Google Scholar
  144. 143.
    R. Moccia, One-center basis set SCF MO’s. II. NH3, NH+ 4, PH3, and PH+ 4, J. Chem. Phys. 40, 2176–2192 (1964).Google Scholar
  145. 144.
    L. J. Aarons, M. F. Guest, M. B. Hall, and I. H. Hillier, Theoretical study of the geometry of PH3, PF3, and their ground ionic states, J. Chem. Soc., Faraday Trans. 2 69, 643–647 (1973).Google Scholar
  146. 145.
    A. Rauk, L. C. Allen, and K. Mislow, Pyramidal inversion, Angew. Chem. 82, 453–468 (1970).Google Scholar
  147. 146.
    T. Kojima, E. L. Breig, and C. C. Lin, Microwave spectrum and internal barrier of methylphosphine, J. Chem. Phys. 35, 2139–2144 (1961).Google Scholar
  148. 147.
    I. Absar and J. R. Van Wazer, Rotational barrier and electronic structure of monomethylphosphine from ab initio LCAO-MO-SCF calculations, J. Chem. Phys. 56, 1284–1289 (1972).Google Scholar
  149. 148.
    J. R. Durig, Y. S. Li, L. A. Carreira, and J. D. Odom, Microwave spectrum, structure, dipole moment, and barrier to internal rotation of phosphine-borane, J. Am. Chem. Soc. 95, 2491–2496 (1973).Google Scholar
  150. 149.
    J. R. Sabin, On the barrier to internal rotation in phosphineborane, Chem. Phys. Lett. 20, 212–214 (1973).Google Scholar
  151. 150.
    D. R. Herschbach, Calculation of energy levels for internal torsion and over-all rotation. III, J. Chem. Phys. 31, 91–108 (1959).Google Scholar
  152. 151.
    C. S. Ewig, W. E. Palke, and B. Kirtman, Dependence of the CH3SiH3 barrier to internal rotation on vibrational coordinates: testing of models and effect of vibrations on the observed barrier height, J. Chem. Phys. 60, 2749–2758 (1974).Google Scholar
  153. 152.
    L. L. Shipman and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Characterization of the zwitterion of glycine, Theor. Chim. Acta 31, 75–82 (1973).Google Scholar
  154. 153.
    L. L. Shipman and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Polypeptides of glycine, J. Am. Chem. Soc. 95, 4733–4744 (1973).Google Scholar
  155. 154.
    L. L. Shipman and R. E. Christoffersen, Ab initio calculations on large molecules using molecular fragments. Model peptide studies, J. Am. Chem. Soc. 95, 1408–1416 (1973).Google Scholar
  156. 155.
    A. Pullman, G. Alagona, and J. Tomasi, Quantum mechanical studies of environmental effects on biomolecules. IV. Hydration of N-methylacetamide, Theor. Chim. Acta 33, 87–90 (1974).Google Scholar
  157. 156.
    L. L. Shipman, R. E. Christoffersen, and B. V. Cheney, Ab initio calculations on large molecules using molecular fragments. Lincomycin model studies, J. Med. Chem. 17, 583–589 (1974).Google Scholar
  158. 157.
    J. A. Pople and L. Radom, Internal rotation potentials in biological molecules, in: The Jerusalem Symposium on Quantum Chemistry and Biochemistry, Vol. 5, Conformation of Biological Molecules and Polymers (E. D. Bergmann and B. Pullman, eds.), Academic Press, New York (1973).Google Scholar
  159. 158.
    A. Pullman and G. N. J. Port, An ab initio SCF molecular orbital study of acetylcholine, Theor. Chim. Acta 32, 77–79 (1973).Google Scholar
  160. 159.
    G. N. J. Port and A. Pullman, Acetylcholine, gauche or trans? A standard ab initio SCF investigation, J. Am. Chem. Soc., 95, 4059–4060 (1973).Google Scholar
  161. 160.
    D. W. Genson and R. E. Christoffersen, Ab initio calculation on large molecules using molecular fragments, electronic and geometric characterization of acetylcholine, J. Am. Chem. Soc. 95, 362–368 (1973).Google Scholar
  162. 161.
    R. E. Christoffersen, D. Spangler, G. G. Hall, and G. M. Maggiora, Ab initio calculations on large molecules using molecular fragments. Evaluation and extension of initial procedures, J. Am. Chem. Soc. 95, 8526–8536 (1973).Google Scholar
  163. 162.
    G. N. J. Port and B. Pullman, An ab initio SCF molecular orbital study on the conformation of serotonin and bufotenine, Theor. Chim. Acta 33, 275–278 (1974).Google Scholar
  164. 163.
    B. Pullman and H. Berthod, Molecular orbital studies on the conformation of GABA Cγ-aminobutyric acid. The isolated molecule and the solvent effect, Theor. Chim. Acta 36, 317–328(1975).Google Scholar
  165. 164.
    M. D. Newton, A model conformational study of nucleic acid phosphate ester bonds. The torsional potential of dimethyl phosphate monoanion, J. Am. Chem. Soc. 95, 256–258 (1973).Google Scholar
  166. 165.
    E. Clementi and H. Popkie, Study of the electronic structure of molecules. Barriers to internal rotation in polynucleotide chains, Chem. Phys. Lett. 20, 1–4 (1973).Google Scholar
  167. 166.
    G. C. Liu and E. Clementi, Additional ab initio computations for the barrier to internal rotation in polynucleotide chains, J. Chem. Phys. 60, 3005–3010 (1974).Google Scholar
  168. 167.
    J. Koller, S. Kaiser, and A. Azman, Ab initio calculation on 2-amino-ethylacetate ion, Z. Naturforsch. 28A, 1745 (1973).Google Scholar
  169. 168.
    J. Almlöf, Ab initio calculations on the equilibrium geometry and rotation barriers in biphenyl, Chem. Phys. 6, 135–139 (1974).Google Scholar
  170. 169.
    R. J. Kurland and W. B. Wise, The proton magnetic resonance spectra and rotational barriers of 4,4’-disubstituted biphenyls, J. Am. Chem. Soc. 86, 1877–1879 (1964).Google Scholar
  171. 170.
    L. Radom, W. J. Hehre, J. A. Pople, G. L. Carlson, and W. G. Fately, Torsional barriers in para-substituted phenols from ab initio molecular orbital theory and far infrared spectroscopy, J. Chem. Soc. D 1972, 308–309 (1972).Google Scholar
  172. 171.
    V. M. Guttins, W. Wyn-Jones, and R. F. M. White, Ring inversion in some six-membered heterocyclic compounds, in:Internal Rotation (W. Orville-Thomas, ed.), John Wiley and Sons, New York (1974).Google Scholar
  173. 172.
    D. Cremer and J. A. Pople, A general definition of ring puckering coordinates, J. Am. Chem. Soc. 97, 1354–1358 (1975).Google Scholar
  174. 173.
    D. Cremer and J. A. Pople, Pseudorotation in saturated five-membered ring compounds, J. Am. Chem. Soc. 97, 1358–1367 (1975).Google Scholar
  175. 174.
    R. M. Stevens and M. Karplus, A test of the closed-shell overlap-repulsion model for the ethane barrier, J. Am. Chem. Soc. 94, 5140–5141 (1972).Google Scholar
  176. 175.
    P. A. Christiansen and W. E. Palke, Ethane internal rotation barrier, Chem. Phys. Lett. 31, 462–466 (1975).Google Scholar
  177. 176.
    V. Magnasco and A. Perico, Uniform localization of atomic and molecular orbitals. I, J. Chem. Phys. 47, 971–981 (1967).Google Scholar
  178. 177.
    V. Magnasco and A. Perico, Uniform localization of atomic and molecular orbitals. II, J. Chem. Phys. 48, 800–808 (1968).Google Scholar
  179. 178.
    M. Levy, T. S. Nee, and R. G. Parr, Method for direct determination of localized orbitals, J. Chem. Phys. 63, 316–318 (1975).Google Scholar
  180. 179.
    R. M. Pitzer, Localized molecular orbitals for ethane, J. Chem. Phys. 41, 2216–2217 (1964).Google Scholar
  181. 180.
    C. Edmiston and K. Ruedenberg, Localized atomic and molecular orbitals, Rev. Mod. Phys. 35, 457–465 (1963).Google Scholar
  182. 181.
    R. M. Pitzer and W. N. Lipscomb, Calculation of the barrier to internal rotation in ethane, J. Chem. Phys. 39, 1995–2004 (1963).Google Scholar
  183. 182.
    G. L. Bendazzoli, F. Bernardi, and P. Palmieri, Group function analysis of the barriers to internal rotation on propargyl alcohol, and hydroxyacetonitrile, J. Chem. Soc. Faraday Trans. 2 69, 579–584 (1973).Google Scholar
  184. 183.
    V. Magnasco and G. F. Musso, Localized orbitals and short-range molecular interactions. I. Theory, J. Chem. Phys. 60, 3744–3748 (1974).Google Scholar
  185. 184.
    V. Magnasco and G. F. Musso, On factors contributing to rotational barriers, Chem. Phys. Lett. 9, 433–436 (1971).Google Scholar
  186. 185.
    V. Magnasco and G. F. Musso, Simple model of short-range interactions. III. Ethane, propane, and butane, J. Chem. Phys. 54, 2925–2935 (1971).Google Scholar
  187. 186.
    K. Ruedenberg, The physical nature of the chemical bond, Rev. Mod. Phys. 34, 326–376 (1962).Google Scholar
  188. 187.
    W. England and M. S. Gordon, Localized charge distributions. I. General theory, energy partitioning, and the internal rotation barrier in ethane, J. Am. Chem. Soc. 93, 4649–4657 (1971).Google Scholar
  189. 188.
    W. England and M. S. Gordon, Localized charge distributions. II. An interpretation of the barriers to internal rotation in H2O2, J. Am. Chem. Soc. 94, 4818–4823 (1972).Google Scholar
  190. 189.
    W. England and M. S. Gordon, Localized charge distributions. The internal rotation barrier in borazane, Chem. Phys. Lett. 15, 59–64 (1972).Google Scholar
  191. 190.
    M. S. Gordon and W. England, Localized charge distributions. V. Internal rotation barriers in methylamine, methyl alcohol, propene, and acetaldehyde, J. Am. Chem. Soc. 95, 1753–1760 (1973).Google Scholar
  192. 191.
    M. S. Gordon, Localized charge distributions. VI. Internal rotation in formaldoxime and formic acid, J. Mol. Struct. 23, 399–410 (1974).Google Scholar
  193. 192.
    S. F. Boys, Construction of molecular orbitals to be approximately invariant for changes from one molecule to another, Rev. Mod. Phys. 32, 296–299 (1960).Google Scholar
  194. 193.
    W. England and M. S. Gordon, On energy localization of approximate molecular orbitals, J. Am. Chem. Soc. 91, 6846–6866 (1969).Google Scholar
  195. 194.
    R. F. W. Bader, Molecular fragments of chemical bonds? Acc. Chem. Res. 8, 34–40 (1975).Google Scholar
  196. 195.
    C. Leibovicci, Electronic structure and the origin of energy differences between rotational isomers, J. Mol. Struct. 10, 333–342 (1971).Google Scholar
  197. 196.
    M. Pelissier, A. Serafini, J. Devanneaux, J. F. Labarre, and J. F. Tocanne, Theoretical conformational analysis of cyclopropylcarboxaldehyde, cyclopropyl methyl ketone, and cis and trans 2-methyl cyclopropyl methyl ketones, Tetrahedron 27, 3271–3284 (1971).Google Scholar
  198. 197.
    M. Pelissier, C. Leibovicci, and J. F. Labarre, Theoretical conformation analysis of the acid fluoride of cyclopropanecarboxylic acid, Tetrahedron Lett. 1971, 3759–3762 (1971).Google Scholar
  199. 198.
    C. Leibovicci, Electronic structure and the origin of energy differences between rotational isomers. II. Formaldoxime, J. Mol. Struct. 15, 249–255 (1973).Google Scholar
  200. 199.
    B. Robinet, C. Leibovicci, and J. F. Labarre, On the electronic origins of barriers to methyl rotation, CNDO/2 calculations on (CH3)2XHn (X = C, Si, N, P, O, S) molecules, Chem. Phys. Lett. 15, 90–95 (1972).Google Scholar
  201. 200.
    G. Robinet, F. Crasnier, J. F. Labarre, and C. Leibovicci, Theoretical conformational analysis of dimethylsulfone, Theor. Chim. Acta 25, 259–267 (1972).Google Scholar
  202. 201.
    G. Robinet, C. Leibovicci, and J. F. Labarre, Theoretical conformational analysis of dimethylsulfoxide, Theor. Chim. Acta 26, 257–265 (1972).Google Scholar
  203. 202.
    C. Leibovicci, Electronic structure and origin of energy differences between rotational isomers. III. Methyltrifluorosilane, J. Mol. Struct 18, 303–307 (1973).Google Scholar
  204. 203.
    F. Crasnier, J. F. Labarre, and C. Leibovicci, Theoretical conformational analysis of Lewis adducts. II. CNDO/2 calculations versus microwave data for methylphosphine borane (CH3)H2PBH3, J. Mol. Struct. 14, 405–412 (1972).Google Scholar
  205. 204.
    J. F. Labarre and C. Leibovicci, Electronic structure of Lewis acid-base complexes. I. Electronic structure and molecular conformation of the molecules F3P·BH3 and F2HP·BH3, Int. J. Quantum Chem. 6, 625–637 (1972).Google Scholar
  206. 205.
    H. J. Koehler and F. Birnstock, Conformational analysis by energy partitioning in the CNDO, INDO and NDDO formalisms, Z. Chem. 12, 196–198 (1972).Google Scholar
  207. 206.
    H. J. Koehler, Conformational analysis by energy partitioning in the CNDO, INDO, and NDDO formalisms. The rotational barrier of hydrazine and the interaction of adjacent lone pair orbitals, Z. Chem. 13, 157–159 (1973).Google Scholar
  208. 207.
    G. F. Musso and V. Magnasco, Nonadditivity of interbond interactions and the rotation barrier in ethane. A preliminary investigation, Chem. Phys. Lett. 23, 79–82 (1973).Google Scholar
  209. 208.
    L. Radom, W. J. Hehre, and J. A. Pople, Fourier-component analysis of internal rotation potential functions in saturated molecules, J. Am. Chem. Soc. 94, 2371–2381 (1972).Google Scholar
  210. 209.
    L. Radom and P. J. Stiles, An additivity scheme for conformational energies in substituted ethanes, J. Chem. Soc. D 1974, 190–192 (1974).Google Scholar
  211. 210.
    W. A. Latham, L. Radom, W. J. Hehre, and J. A. Pople, Molecular orbital theory of the electronic structure of organic compounds. XVIII. Conformations and stabilities of trisubstituted methanes, J. Am. Chem. Soc. 95, 699–703 (1973).Google Scholar
  212. 211.
    T. Dunning and N. W. Winter, private communication, 1975.Google Scholar
  213. 212.
    L. C. Allen, Energy component analysis of rotational barriers, Chem. Phys. Lett. 2, 597–601 (1968).Google Scholar
  214. 213.
    I. R. Epstein and W. N. Lipscomb, Comments on the barrier to internal rotation in ethane, J. Am. Chem. Soc. 92, 6094–6095 (1970).Google Scholar
  215. 214.
    D. T. Clark and D. M. J. Lilley, A non-empirical LCAO-MO-SCF investigation of cross sections through the potential energy surface for the [C2H4Cl]+ systems; comparison with the [C2H+ 5] and [C2H4F]+ systems, Tetrahedron 29, 845–856 (1973).Google Scholar
  216. 215.
    T. K. Ha, Theoretical study of the internal rotation and inversion in hydroxymethyl radical, Chem. Phys. Lett. 30, 379–382 (1975).Google Scholar
  217. 216.
    M. E. Schwartz, E. F. Hayes, and S. Rothenberg, Theoretical study of the barriers to internal rotation in formic acid, J. Chem. Phys. 52, 2011–2014 (1970).Google Scholar
  218. 217.
    M. E. Schwartz, E. F. Hayes, and S. Rothenberg, Theoretical study of the barriers to internal rotation in nitrous acid, Theor. Chim. Acta 19, 98–101 (1970).Google Scholar
  219. 218.
    P.-O. Löwdin, Scaling problem, virial theorem, and connected relations in quantum mechanics, J. Mol. Spectrosc. 3, 46–66 (1959).Google Scholar
  220. 219.
    J. E. Eilers and A. Liberies, A quantum mechanical approach to conformational analysis, J. Am. Chem. Soc. 97, 4183–4188 (1975).Google Scholar
  221. 220.
    S. Wolfe, The gauche effect, some stereochemical consequences of adjacent electron pairs and polar bonds, Acc. Chem. Res. 5, 102–111 (1972).Google Scholar
  222. 221.
    H. Hellmann, Einführing in Die Quantenchemie, Franz Denticke and Co., Leipzig (1937).Google Scholar
  223. 222.
    R. P. Feynman, Forces in molecules, Phys. Rev. 56, 340–343 (1939).Google Scholar
  224. 223.
    K. Ruedenberg, Hindered rotation, Hellman-Feynman theorem and localized molecular orbitals, J. Chem. Phys. 41, 588–589 (1964).Google Scholar
  225. 224.
    R. G. Parr, Theorem governing changes in molecular conformation, J. Chem. Phys. 40, 3726 (1964).Google Scholar
  226. 225.
    H. Kim and R. G. Parr, Integral Hellmann-Feynman theorem, J. Chem. Phys. 41, 2892–2897 (1964).Google Scholar
  227. 226.
    A. C. Hurley, The molecular orbital interpretation of bond length changes following excitation and ionization of diatomic molecules, in : Molecular Orbitals in Chemistry, Physics, and Biology (P.-O. Löwdin, ed.), pp. 161–190, Academic Press, New York (1964).Google Scholar
  228. 227.
    M. P. Melrose and R. G. Parr, Some integral Hellmann-Feynman calculations on hydrogen peroxide and ammonia, Theor. Chim. Acta 8, 150–156 (1967).Google Scholar
  229. 228.
    W. H. Fink and L. C. Allen, Numerical test of the integral Hellmann-Feynman theorem, J. Chem. Phys. 46, 3270–3271 (1967).Google Scholar
  230. 229.
    R. E. Wyatt and R. G. Parr, Theory of the origin of the internal rotation barrier in the ethane molecule. II, J. Chem. Phys. 44, 1529–1545 (1966).Google Scholar
  231. 230.
    J. Goodisman, Barrier to internal rotation in ethane using the Hellmann-Feynman theorem, J. Chem. Phys. 45, 4689–4696 (1966).Google Scholar
  232. 231.
    J. Goodisman, Postscript to barrier to internal rotation in ethane by Hellmann-Feynman theorem, J. Chem. Phys. 47, 334–335 (1967).Google Scholar
  233. 232.
    S. M. Rothstein and S. M. Blinder, The internal Hellmann-Feynman theorem applied to hydrogen peroxide, Theor. Chim. Acta 8, 427–430 (1967).Google Scholar
  234. 233.
    L. Zülicke and H. J. Spangenberg, On calculating the internal rotation potential in hydrogen peroxide, Theor. Chim. Acta 8, 139–147 (1966).Google Scholar
  235. 234.
    P. Pulay, Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. II. Force constants of water, Mol. Phys. 18, 473–480 (1970).Google Scholar
  236. 235.
    S. T. Epstein, A. C. Hurley, R. E. Wyatt, and R. G. Parr, Integrated and integral Hellmann-Feynman formulas, J. Chem. Phys. 47, 1275–1286 (1967).Google Scholar
  237. 236.
    J. I. Musher, On Parr’s theorem, J. Chem. Phys. 43, 2145–2146 (1965).Google Scholar
  238. 237.
    R. E. Wyatt and R. G. Parr, Theory of the internal-rotation barrier in the ethane molecule. I, J. Chem. Phys. 43S, 217–227 (1965).Google Scholar
  239. 238.
    R. Mulliken, Electronic population analysis on LCAO-MO molecular wavefunctions. I, J. Chem. Phys. 23, 1833–1840 (1955).Google Scholar
  240. 239.
    R. Mulliken, Electronic population analysis on LCAO-MO molecular wavefunctions. II. Overlap populations, bond orders, and covalent bond energies, J. Chem. Phys. 23, 1841–1846 (1955).Google Scholar
  241. 240.
    J. J. Kaufman, Mulliken population analysis in CNDO and INDO LCAO-MO-SCF methods, Int. J. Quantum Chem., Symp. 4, 205–208 (1971).Google Scholar
  242. 241.
    J. P. Lowe, A simple molecular orbital explanation for the barrier to internal rotation in ethane and other molecules, J. Am. Chem. Soc. 92, 3799–3800 (1970).Google Scholar
  243. 242.
    J. P. Lowe, The barrier to internal rotation in ethane, Science 179, 527–532 (1973).Google Scholar
  244. 243.
    J. P. Lowe, The Woodward-Hoffmann approach, the extended Hückel method, and the barrier to rigid internal rotation in ethane, J. Am. Chem. Soc. 96, 3759–3764 (1974).Google Scholar
  245. 244.
    N. D. Epiotis, Attractive nonbonded interactions in organic molecules, J. Am. Chem. Soc. 95, 3087–3096 (1973).Google Scholar
  246. 245.
    N. D. Epiotis, D. Bjorkquist, L. Bjorkquist, and S. Sarkanen, Attractive nonbonded interactions in 1-substituted propenes. Consequences for geometric and conformational isomerism, J. Am. Chem. Soc. 95, 7558–7562 (1973).Google Scholar
  247. 246.
    N. D. Epiotis, S. Sarkanen, D. Bjorkquist, L. Bjorkquist, and R. Yates, Open shell interactions, nonbonded attraction, and aromaticity. Implications for regiochemistry, J. Am. Chem. Soc. 96, 4075–4084 (1974).Google Scholar
  248. 247.
    L. Salem, Intermolecular orbital theory of the interaction between conjugated systems. I. General theory, J. Am. Chem. Soc. 90, 543–552 (1968).Google Scholar
  249. 248.
    K. Müller, Slow inversion at pyramidal nitrogen: configuration and conformation of N,N-dialkoxy-alkylamine in terms of a semi-empirical MO model, Helv. Chim. Acta 53, 1112–1127 (1970).Google Scholar
  250. 249.
    W. J. Hehre and L. Salem, Conformation of vinylic methyl groups, J. Chem. Soc. D 1973, 754 (1973).Google Scholar
  251. 250.
    R. Hoffmann, C. C. Levin, and R. A. Moss, On steric attraction, J. Am. Chem. Soc. 95, 629–631 (1973).Google Scholar
  252. 251.
    C. C. Levin, R. Hoffmann, W. J. Hehre, and J. Hudec, Orbital interaction in amino ketones, J. Chem. Soc., Perkin Trans. 2 1973, 210 (1973).Google Scholar
  253. 252.
    H. Fuijimoto and R. Hoffmann, Perturbation of molecules by static fields, orbital overlap, and charge transfer, J. Phys. Chem. 78, 1874–1880 (1974).Google Scholar
  254. 253.
    D. Cremer, J. S. Binkley, J. A. Pople, and W. J. Hehre, Molecular orbital theory of the electronic structure of organic compounds. XXI. Rotational potentials for geminal methyl groups, J. Am. Chem. Soc. 96, 6900–6903 (1974).Google Scholar
  255. 254.
    M. Schwartz, Theoretical study of the barrier to internal rotation in hydrogen persulfide, HSSH, J. Chem. Phys. 51, 4182–4186 (1969).Google Scholar
  256. 255.
    W. L. Jorgensen and L. C. Allen, Charge distribution characteristics of attractive dominant barriers, Chem. Phys. Lett. 7, 483–485 (1970).Google Scholar
  257. 256.
    W. L. Jorgensen and L. C. Allen, Charge density analysis of rotational barriers, J. Am. Chem. Soc. 93, 567–574 (1971).Google Scholar
  258. 257.
    P. W. Payne and L. C. Allen, Charge density difference analysis. Comparison of internal rotation in ethane and methylamine, J. Am. Chem. Soc., to be published (1977).Google Scholar
  259. 258.
    P. W. Payne and L. C. Allen, Charge density difference analysis. Internal rotation in ethylamine, J. Am. Chem. Soc., to be published (1977).Google Scholar
  260. 259.
    R. Hoffmann, An extended Hückel theory. Hydrocarbons, J. Chem. Phys. 39, 1397–1412 (1963).Google Scholar
  261. 260.
    S. W. Benson and M. Luria, Electrostatics and the chemical bond. I. Saturated hydrocarbons, J. Am. Chem. Soc. 97, 704–709 (1975).Google Scholar
  262. 261.
    S. W. Benson and M. Luria, Electrostatics and the chemical bond. II. Unsaturated hydrocarbons, J. Am. Chem. Soc. 97, 3337–3342 (1975).Google Scholar
  263. 262.
    M. Luria and S. W. Benson, Electrostatics and the chemical bond. III. Free radicals, J. Am. Chem. Soc. 97, 3342–3346 (1975).Google Scholar
  264. 263.
    H. A. Scheraga, Calculations of conformations of polypeptides, Adv. Phys. Org. Chem. 6, 103–185 (1968).Google Scholar
  265. 264.
    L. L. Shipman, A. W. Burgess, and H. A. Scheraga, A new approach to empirical inter-molecular and conformational potential energy functions. I. Description of model and derivation of parameters, Proc. Natl. Acad. Sci. USA 72, 543–547 (1975).Google Scholar
  266. 265.
    R. A. Scott and H. A. Scheraga, Conformational analysis of macromolecules. III. Helical structures of polyglycine and poly-L-alanine, J. Chem. Phys. 45, 2091–2101 (1966).Google Scholar
  267. 266.
    A. Rahman, F. H. Stillinger, and H. L. Lemberg, Study of a central force model for liquid water by molecular dynamics, J. Chem. Phys. 63, 5223–5230 (1975).Google Scholar
  268. 267.
    F. H. Stillinger, Construction and use of central force fields for the theory of polyatomic fluids, to be published.Google Scholar
  269. 268.
    W. J. Hehre and P. C. Hiberty, Theoretical approaches to rearrangements in carbocations. I. The haloethyl system, J. Am. Chem. Soc. 96, 2665–2678 (1974).Google Scholar
  270. 269.
    W. L. Jorgensen and L. Salem, The Organic Chemist’s Book of Orbitals, Academic Press, New York (1973).Google Scholar
  271. 270.
    J. M. Howell, Ab initio calculations of the rotational barrier in PH4NH2, Chem. Phys. Lett. 25, 51–54 (1974).Google Scholar
  272. 271.
    E. Lassettre and L. Dean, An electrostatic theory of the potential barriers hindering rotation around single bonds, J. Chem. Phys. 17, 317–352 (1949).Google Scholar
  273. 272.
    S. Lifson and A. Warshel, Consistent force field for calculations of conformations, vibrational spectra, and enthalpies of cyclohexane and n-alkane molecules, J. Chem. Phys. 49, 5116–5129 (1968).Google Scholar
  274. 273.
    A. Warshel and S. Lifson, Crystal structures, sublimation energies, molecular and lattice vibrations, molecular conformations, and enthalpies of alkanes, J. Chem. Phys. 53, 582–594 (1970).Google Scholar
  275. 274.
    M. L. Huggins, Interaction between nonbonded atoms, in :Structural Chemistry and Molecular Biology (A. Rich and N. Davidson, eds.), pp. 761–768, W. H. Freeman, San Francisco (1968).Google Scholar
  276. 275.
    R. Rein, T. J. Swissler, V. Renugopalakrishnan, and G. R. Pack, Some refinements in the electrostatic theory of rotational potential functions, in: The Jerusalem Symposium on Quantum Chemistry and Biochemistry, Vol. 5 (E. D. Bergmann and B. Pullman, eds.), Academic Press, New York (1973).Google Scholar
  277. 276.
    A. D. Tait and G. G. Hall, Point charge models for LiH, CH4, and H2O, Theor. Chim. Acta 31,311–324(1973).Google Scholar

Note Added in Proof

  1. 1.
    The contrasting roles of orbital orthogonality and electron exchange are further clarified in a recent paper by Levy.(277) Levy has found that application of Edmiston-Ruedenberg exchange localization without orbital orthogonality constraints generates localized orbitals that are nearly orthogonal. This result helps rationalize the apparent dependence of some barrier models on electron exchange energy. Exchange energy minimization has little intrinsic importance for rotational barrier mechanisms; but exchange energy minimization tends to orthogonalize orbitals, and orthogonality is important for the barrier mechanism.Google Scholar
  2. 2.
    Brunck and Weinhold(278) attribute rotational barriers in ethane, methylamine, and methanol to vicinal mixing between bonds and antibonds. Their key step is expansion of the INDO Hamiltonian matrix in a basis set of local bonding and antibonding orbitals. Since the rotational barriers disappear if the pseudomolecular orbitals are constructed as a linear combination of local bonding orbitals, they claim that vicinal mixing between bonds and antibonds is at the heart of barriers. This model has a strong intuitive appeal. In order to establish its credibility, further work is needed on the following problems: First, the definitions of local bonding and antibonding orbitals are arbitrary. It is not clear that the model would hold up under small adjustments in the bond orbitals. Second, the balance between INDO matrix elements is often quite different from that in an ab initio theory. Third, a barrier model should not be sensitive to geometry optimization if total energy is insensitive. Because INDO barrier heights are poor when geometries are optimized, any barrier model derived from INDO wave functions is tentatively best.Google Scholar
  3. 3.
    Another interesting paper that is formulated within the framework of a one-electron orbital theory and addresses a long-standing problem is that of Salem, Hoffmann, and Otto on barriers in substituted ethanes.(279) Google Scholar
  4. 277.
    M. Levy, Unconstrained exchange localization and distant orbital tails, J. Chem. Phys. 65, 2473–2475 (1976).Google Scholar
  5. 278.
    T. K. Brunck and F. Weinhold, Quantum-mechanical origin of barriers to internal rotation about single bonds, J. Am. Chem. Soc. (1977), in press.Google Scholar
  6. 279.
    L. Salem, R. Hoffmann, and P. Otto, The energy of substituted ethanes: Asymmetry orbitals, Proc. Nat. Acad. Sci. (U.S.A.), 70, 531–532 (1970).Google Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Philip W. Payne
    • 1
  • Leland C. Allen
    • 1
  1. 1.Department of ChemistryPrinceton UniversityPrincetonUSA

Personalised recommendations