Skip to main content
SpringerLink
Log in

Barriers to Rotation and Inversion

  • Chapter
Applications of Electronic Structure Theory

Part of the book series: Modern Theoretical Chemistry ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. A. Pople, Molecular orbital studies of conformation, Tetrahedron 30, 1605–1615 (1974).

    CAS  Google Scholar 

  2. A. Golebiewski and A. Parczewski, Theoretical conformational analysis of organic molecules, Chem. Rev. 74, 519–530 (1974).

    CAS  Google Scholar 

  3. D. T. Clark, Theoretical organic chemistry and ESCA, Annu. Rep. Prog. Chem., 69(B), 40–83 (1973).

    Google Scholar 

  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. 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. 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).

    CAS  Google Scholar 

  7. K. S. Pitzer, Thermodynamic functions for molecules having restricted internal rotations, J. Chem. Phys. 5, 469–472 (1937);

    CAS  Google Scholar 

  8. K. S. Pitzer, Thermodynamic functions for molecules having restricted internal rotations, J. Chem. Phys. 5, 473–479 (1937).

    CAS  Google Scholar 

  9. 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. S. Epstein, The Variational Method in Quantum Chemistry, Academic Press, New York (1974).

    Google Scholar 

  11. J. Goodisman and W. Klemperer, On error in Hartree-Fock calculations, J. Chem. Phys. 38, 721–725 (1963).

    CAS  Google Scholar 

  12. K. F. Freed, Geometry and barriers to internal rotation in Hartree-Fock theory, Chem. Phys. Lett. 2, 255–256 (1968).

    CAS  Google Scholar 

  13. 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).

    CAS  Google Scholar 

  14. R. E. Stanton, Hellmann-Feynman theorem and correlation energies, J. Chem. Phys. 36, 1298–1300. (1962).

    CAS  Google Scholar 

  15. B. Levy and M. C. Moireau, Correlation effect in the rotation barrier of ethane, J. Chem. Phys. 54, 3316–3321 (1971).

    CAS  Google Scholar 

  16. 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).

    CAS  Google Scholar 

  17. 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. R. Ahlrichs and F. Keil, Structure and bonding in dinitrogen tetroxide (N2O4), J. Am. Chem. Soc. 96, 7615–7620 (1974).

    CAS  Google Scholar 

  19. 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. U. Pincelli, B. Cadioli, and B. Levy, On the internal rotation in 1,3-butadiene, Chem. Phys. Lett. 13, 249–252 (1972).

    CAS  Google Scholar 

  21. 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).

    CAS  Google Scholar 

  22. 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).

    CAS  Google Scholar 

  23. 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).

    CAS  Google Scholar 

  24. R. M. Stevens, CI calculations for the inversion barrier of ammonia, J. Chem. Phys. 61, 2086–2090 (1974).

    CAS  Google Scholar 

  25. N. C. Dutta and M. Karplus, Correlation contribution to the ammonia inversion barrier, Chem. Phys. Lett. 31(3), 455–461 (1975).

    CAS  Google Scholar 

  26. 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).

    CAS  Google Scholar 

  27. 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. A. Rauk, L. C. Allen, and E. Clementi, Electronic structure and inversion barrier of ammonia, J. Chem. Phys. 52, 4133–4144 (1970).

    CAS  Google Scholar 

  29. 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. 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).

    CAS  Google Scholar 

  31. B. Kirtman, Interactions between ordinary vibrations and hindered internal rotation. I. Rotational energies, J. Chem. Phys. 37, 2516–2539 (1962).

    CAS  Google Scholar 

  32. 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).

    CAS  Google Scholar 

  33. D. Papousek, High resolution infrared spectra of ethane-like molecules and the barrier to internal rotation, J. Mol. Spectrosc. 28, 161–190 (1968).

    CAS  Google Scholar 

  34. 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).

    CAS  Google Scholar 

  35. 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).

    CAS  Google Scholar 

  36. 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. 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).

    CAS  Google Scholar 

  38. B. Kirtman, W. E. Palke, and C. S. Ewig, private communication, 1975.

    Google Scholar 

  39. D. R. Herschbach, Calculation of energy levels for internal torsion and over-all rotation. III, J. Chem. Phys. 31, 91–108 (1959).

    CAS  Google Scholar 

  40. A. Veillard, Relaxation during internal rotation in ethane and hydrogen peroxide, Theor. Chim. Acta 18, 21–33 (1970).

    CAS  Google Scholar 

  41. A. Veillard, Distortional effects on the ethane internal rotation barrier and rotation barriers in borazane and methylsilane, Chem. Phys. Lett. 3, 128–130 (1969).

    CAS  Google Scholar 

  42. 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).

    CAS  Google Scholar 

  43. 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).

    CAS  Google Scholar 

  44. 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).

    CAS  Google Scholar 

  45. W. E. Palke, Calculation of the internal rotation barrier and its derivatives in BH3NH3, J. Chem. Phys. 56, 5308–5311 (1972).

    CAS  Google Scholar 

  46. J. O. Jarvie and A. Rauk, A theoretical study of the conformational changes in hydrazine, Can. J. Chem. 52, 2785–2791 (1974).

    CAS  Google Scholar 

  47. A. Veillard, Distortional effects on the internal rotation in hydrogen peroxide, Chem. Phys. Lett. 4, 51–52 (1969).

    CAS  Google Scholar 

  48. R. B. Davidson and L. C. Allen, Rotational barriers in hydrogen peroxide, J. Chem. Phys. 55, 519–527(1971).

    CAS  Google Scholar 

  49. T. H. Dunning, Jr. and N. W. Winter, private communication.

    Google Scholar 

  50. 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).

    CAS  Google Scholar 

  51. 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).

    CAS  Google Scholar 

  52. L. Radom and J. A. Pople, Internal rotation in hydrocarbons using a minimal Slater-type basis, J. Am. Chem. Soc. 92, 4786–4795 (1970).

    CAS  Google Scholar 

  53. 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).

    CAS  Google Scholar 

  54. K. R. Sundberg and L. M. Cheung, Potential energy curve in the trans-cis isomerization of glyoxal, Chem. Phys. Lett. 29, 93–97 (1974).

    CAS  Google Scholar 

  55. 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).

    CAS  Google Scholar 

  56. P. A. Kollman and C. F. Bender, The structure of the H3O+ (hydronium) ion, Chem. Phys. Lett 21, 271–273 (1973).

    CAS  Google Scholar 

  57. 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).

    CAS  Google Scholar 

  58. 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).

    CAS  Google Scholar 

  59. 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).

    CAS  Google Scholar 

  60. 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).

    CAS  Google Scholar 

  61. U. Wahlgren, Calculations of potential barriers using the SCF-Xa method, Chem. Phys. Lett. 20, 246–249 (1973).

    CAS  Google Scholar 

  62. S. Weiss and G. Leroi, Direct observations of the infrared torsional spectrum of C2H6, CH3CD3, and C2D6, J. Chem. Phys. 48, 962–967 (1968).

    CAS  Google Scholar 

  63. P. A. Christiansen and W. E. Palke, Ethane internal rotation barrier, Chem. Phys. Lett. 31, 462–466 (1975).

    CAS  Google Scholar 

  64. W. E. Palke, Calculations of the barrier to internal rotation in ethyl fluoride: a comparison with ethane, Chem. Phys. Lett. 15, 244–247 (1972).

    CAS  Google Scholar 

  65. L. C. Allen and H. Basch, Theory of the rotational barriers in ethyl fluoride and ethane, J. Am. Chem. Soc. 93, 6373–6377 (1971).

    CAS  Google Scholar 

  66. 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).

    CAS  Google Scholar 

  67. R. M. Stevens, Geometry optimization in the computation of barriers to internal rotation, J. Chem. Phys. 52, 1397–1402 (1970).

    CAS  Google Scholar 

  68. 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).

    CAS  Google Scholar 

  69. R. M. Pitzer, Calculation of the barrier to internal rotation in ethane with improved exponential wavefunctions, J. Chem. Phys. 47, 965–967 (1967).

    CAS  Google Scholar 

  70. 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. 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).

    CAS  Google Scholar 

  72. 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. J. R. Hoyland, Ab initio bond-orbital calculations. I. Application to methane, ethane, propane, and propylene, J. Am. Chem. Soc. 90, 2227–2232 (1968).

    CAS  Google Scholar 

  74. 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).

    CAS  Google Scholar 

  75. 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).

    CAS  Google Scholar 

  76. J. L. Nelson and A. A. Frost, Local orbitals for bonding in ethane, Theor. Chim. Acta 29, 75–83 (1973).

    CAS  Google Scholar 

  77. 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).

    CAS  Google Scholar 

  78. 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).

    CAS  Google Scholar 

  79. 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).

    CAS  Google Scholar 

  80. 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).

    CAS  Google Scholar 

  81. 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).

    CAS  Google Scholar 

  82. W. E. Palke and R. M. Pitzer, On the internal rotation potential in H2O2, J. Chem. Phys. 46, 3948–3950 (1967).

    CAS  Google Scholar 

  83. 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).

    CAS  Google Scholar 

  84. U. Kaldor and I. Shavitt, LCAO-SCF computations for hydrogen peroxide, J. Chem. Phys. 44, 1823–1829 (1966).

    CAS  Google Scholar 

  85. 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).

    CAS  Google Scholar 

  86. 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).

    CAS  Google Scholar 

  87. G. Winnewisser, M. Winnewisser, and W. Gordy, Bull. Am. Phys. Soc. 2, 312 (1966).

    Google Scholar 

  88. A. Veillard and J. Demuynck, Barrier to internal rotation in hydrogen persulfide, Chem. Phys. Lett. 4, 476–478 (1970).

    CAS  Google Scholar 

  89. E. V. Ivash and D. M. Dennison, The methyl alcohol molecule and its microwave spectrum, J. Chem. Phys. 21, 1804–1816 (1953).

    CAS  Google Scholar 

  90. 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).

    CAS  Google Scholar 

  91. C. W. Kern, R. M. Pitzer, and O. J. Sovers, Bond-function analysis of rotational barriers: methanol, J. Chem. Phys. 60, 3583–3587 (1974).

    CAS  Google Scholar 

  92. 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).

    CAS  Google Scholar 

  93. D. R. Lide, Jr., Structure of the methylamine molecule. I. Microwave spectrum of CD3ND2, J. Chem. Phys. 27, 343–352 (1941).

    Google Scholar 

  94. 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. J. R. Hoyland, Internal rotation in propane. Reanalysis of the microwave spectrum and quantum-mechanical calculations, J. Chem. Phys. 49, 1908–1912 (1968).

    CAS  Google Scholar 

  96. 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. J. R. Hoyland, Barriers to internal rotation in propane, Chem. Phys. Lett. 1, 247–248 (1967).

    CAS  Google Scholar 

  98. 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).

    CAS  Google Scholar 

  99. T. Kasuya and T. Kojima, Internal motions of hydrazine, J. Phys. Soc. Japan 18, 364–368 (1963).

    CAS  Google Scholar 

  100. 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).

    CAS  Google Scholar 

  101. 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).

    CAS  Google Scholar 

  102. 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).

    CAS  Google Scholar 

  103. E. L. Wagner, Ab initio versus CNDO barrier calculations. I. N2H4 and N2F4, Theor. Chim. Acta 23, 115–126 (1971).

    CAS  Google Scholar 

  104. R. G. Snyder and I. C. Hisatsune, Infrared spectrum of dinitrogen tetroxide, J. Mol. Spectrosc. 1, 139–150(1957).

    CAS  Google Scholar 

  105. 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).

    CAS  Google Scholar 

  106. 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. D. R. Lide, Jr., and D. Christiansen, Microwave structure of propylene, J. Chem. Phys. 35, 1374–1378 (1962).

    Google Scholar 

  108. 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).

    CAS  Google Scholar 

  109. 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. 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).

    CAS  Google Scholar 

  111. 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).

    CAS  Google Scholar 

  112. R. B. Davidson and L. C. Allen, Attractive nature of the rotational barrier in acetaldehyde, J. Chem. Phys. 54, 2828–2830 (1971).

    CAS  Google Scholar 

  113. N. L. Allinger and Sister M. J. Hickey, Acetone, ab initio calculations, Tetrahedron 28, 2157–2161 (1972).

    CAS  Google Scholar 

  114. 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. 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. G. N. Currie and D. A. Ramsay, The 4875 Å band system of cis glyoxal, Can. J. Phys. 49, 317–322 (1971).

    CAS  Google Scholar 

  117. 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).

    CAS  Google Scholar 

  118. T. K. Ha, Ab initio calculation of cis-trans isomerization in glyoxal, J. Mol. Struct. 12, 171–178 (1972).

    CAS  Google Scholar 

  119. B. Sunners, L. H. Piette, and W. G. Schneider, Proton magnetic resonance measurements of formamide, Can. J. Chem. 38, 681–688 (1960).

    CAS  Google Scholar 

  120. H. Kamei, Nuclear magnetic double-resonance study of the hindered internal rotation in formamide, Bull. Chem. Soc. Japan 41, 2269–2273 (1968).

    CAS  Google Scholar 

  121. 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. L. A. Carreira, Determination of the torsional potential function of 1,3-butadiene, J. Chem. Phys. 62, 3851–3854 (1975).

    Google Scholar 

  123. 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. R. J. Buenker, Theoretical study of the rotational barriers of allene, ethylene, and related systems, J. Chem. Phys. 48, 1368–1379 (1968).

    CAS  Google Scholar 

  125. 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. L. J. Schaad, The internal rotation barrier in allene, Tetrahedron 26, 4115–4118 (1970).

    CAS  Google Scholar 

  127. L. J. Schaad, L. A. Burnelle, and K. P. Dressier, The excited states of allene, Theor. Chim. Acta 15, 91–99 (1969).

    CAS  Google Scholar 

  128. 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).

    CAS  Google Scholar 

  129. R. M. Stevens, Accurate SCF calculation for ammonia and its inversion motion, J. Chem. Phys. 55, 1725–1729 (1971).

    CAS  Google Scholar 

  130. 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).

    CAS  Google Scholar 

  131. 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. R. E. Kari and I. G. Csizmadia, Potential-energy surfaces of CH+ 3 and CH3– 11, J. Chem. Phys. 50, 1443–1448 (1969).

    CAS  Google Scholar 

  133. R. E. Kari and I. G. Csizmadia, Near molecular Hartree-Fock wavefunction for CH3– 11, J. Chem. Phys. 46, 4585–4590.

    CAS  Google Scholar 

  134. R. Grahn, A theoretical study of the H3O+ ion, Arkiv. Fys. 19, 1417 (1961).

    Google Scholar 

  135. 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).

    CAS  Google Scholar 

  136. 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).

    CAS  Google Scholar 

  137. 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. 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).

    CAS  Google Scholar 

  139. 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).

    CAS  Google Scholar 

  140. 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).

    CAS  Google Scholar 

  141. 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. 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).

    CAS  Google Scholar 

  143. 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).

    CAS  Google Scholar 

  144. R. Moccia, One-center basis set SCF MO’s. II. NH3, NH+ 4, PH3, and PH+ 4, J. Chem. Phys. 40, 2176–2192 (1964).

    CAS  Google Scholar 

  145. 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).

    CAS  Google Scholar 

  146. A. Rauk, L. C. Allen, and K. Mislow, Pyramidal inversion, Angew. Chem. 82, 453–468 (1970).

    Google Scholar 

  147. T. Kojima, E. L. Breig, and C. C. Lin, Microwave spectrum and internal barrier of methylphosphine, J. Chem. Phys. 35, 2139–2144 (1961).

    CAS  Google Scholar 

  148. 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).

    CAS  Google Scholar 

  149. 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).

    CAS  Google Scholar 

  150. J. R. Sabin, On the barrier to internal rotation in phosphineborane, Chem. Phys. Lett. 20, 212–214 (1973).

    CAS  Google Scholar 

  151. D. R. Herschbach, Calculation of energy levels for internal torsion and over-all rotation. III, J. Chem. Phys. 31, 91–108 (1959).

    CAS  Google Scholar 

  152. 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).

    CAS  Google Scholar 

  153. 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).

    CAS  Google Scholar 

  154. 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).

    CAS  Google Scholar 

  155. 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).

    CAS  Google Scholar 

  156. 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).

    CAS  Google Scholar 

  157. 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).

    CAS  Google Scholar 

  158. 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. A. Pullman and G. N. J. Port, An ab initio SCF molecular orbital study of acetylcholine, Theor. Chim. Acta 32, 77–79 (1973).

    CAS  Google Scholar 

  160. 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).

    CAS  Google Scholar 

  161. 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).

    CAS  Google Scholar 

  162. 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).

    CAS  Google Scholar 

  163. 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).

    CAS  Google Scholar 

  164. 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).

    CAS  Google Scholar 

  165. 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).

    CAS  Google Scholar 

  166. 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).

    CAS  Google Scholar 

  167. 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. J. Koller, S. Kaiser, and A. Azman, Ab initio calculation on 2-amino-ethylacetate ion, Z. Naturforsch. 28A, 1745 (1973).

    Google Scholar 

  169. J. Almlöf, Ab initio calculations on the equilibrium geometry and rotation barriers in biphenyl, Chem. Phys. 6, 135–139 (1974).

    Google Scholar 

  170. 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).

    CAS  Google Scholar 

  171. 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. 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. D. Cremer and J. A. Pople, A general definition of ring puckering coordinates, J. Am. Chem. Soc. 97, 1354–1358 (1975).

    CAS  Google Scholar 

  174. D. Cremer and J. A. Pople, Pseudorotation in saturated five-membered ring compounds, J. Am. Chem. Soc. 97, 1358–1367 (1975).

    CAS  Google Scholar 

  175. 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).

    CAS  Google Scholar 

  176. P. A. Christiansen and W. E. Palke, Ethane internal rotation barrier, Chem. Phys. Lett. 31, 462–466 (1975).

    CAS  Google Scholar 

  177. V. Magnasco and A. Perico, Uniform localization of atomic and molecular orbitals. I, J. Chem. Phys. 47, 971–981 (1967).

    CAS  Google Scholar 

  178. V. Magnasco and A. Perico, Uniform localization of atomic and molecular orbitals. II, J. Chem. Phys. 48, 800–808 (1968).

    CAS  Google Scholar 

  179. M. Levy, T. S. Nee, and R. G. Parr, Method for direct determination of localized orbitals, J. Chem. Phys. 63, 316–318 (1975).

    CAS  Google Scholar 

  180. R. M. Pitzer, Localized molecular orbitals for ethane, J. Chem. Phys. 41, 2216–2217 (1964).

    CAS  Google Scholar 

  181. C. Edmiston and K. Ruedenberg, Localized atomic and molecular orbitals, Rev. Mod. Phys. 35, 457–465 (1963).

    CAS  Google Scholar 

  182. R. M. Pitzer and W. N. Lipscomb, Calculation of the barrier to internal rotation in ethane, J. Chem. Phys. 39, 1995–2004 (1963).

    CAS  Google Scholar 

  183. 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).

    CAS  Google Scholar 

  184. V. Magnasco and G. F. Musso, Localized orbitals and short-range molecular interactions. I. Theory, J. Chem. Phys. 60, 3744–3748 (1974).

    CAS  Google Scholar 

  185. V. Magnasco and G. F. Musso, On factors contributing to rotational barriers, Chem. Phys. Lett. 9, 433–436 (1971).

    CAS  Google Scholar 

  186. V. Magnasco and G. F. Musso, Simple model of short-range interactions. III. Ethane, propane, and butane, J. Chem. Phys. 54, 2925–2935 (1971).

    CAS  Google Scholar 

  187. K. Ruedenberg, The physical nature of the chemical bond, Rev. Mod. Phys. 34, 326–376 (1962).

    CAS  Google Scholar 

  188. 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).

    CAS  Google Scholar 

  189. 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).

    CAS  Google Scholar 

  190. 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. 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).

    CAS  Google Scholar 

  192. M. S. Gordon, Localized charge distributions. VI. Internal rotation in formaldoxime and formic acid, J. Mol. Struct. 23, 399–410 (1974).

    CAS  Google Scholar 

  193. 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).

    CAS  Google Scholar 

  194. W. England and M. S. Gordon, On energy localization of approximate molecular orbitals, J. Am. Chem. Soc. 91, 6846–6866 (1969).

    Google Scholar 

  195. R. F. W. Bader, Molecular fragments of chemical bonds? Acc. Chem. Res. 8, 34–40 (1975).

    CAS  Google Scholar 

  196. C. Leibovicci, Electronic structure and the origin of energy differences between rotational isomers, J. Mol. Struct. 10, 333–342 (1971).

    Google Scholar 

  197. 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. 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. 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. 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).

    CAS  Google Scholar 

  201. G. Robinet, F. Crasnier, J. F. Labarre, and C. Leibovicci, Theoretical conformational analysis of dimethylsulfone, Theor. Chim. Acta 25, 259–267 (1972).

    CAS  Google Scholar 

  202. G. Robinet, C. Leibovicci, and J. F. Labarre, Theoretical conformational analysis of dimethylsulfoxide, Theor. Chim. Acta 26, 257–265 (1972).

    CAS  Google Scholar 

  203. C. Leibovicci, Electronic structure and origin of energy differences between rotational isomers. III. Methyltrifluorosilane, J. Mol. Struct 18, 303–307 (1973).

    Google Scholar 

  204. 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).

    CAS  Google Scholar 

  205. 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).

    CAS  Google Scholar 

  206. H. J. Koehler and F. Birnstock, Conformational analysis by energy partitioning in the CNDO, INDO and NDDO formalisms, Z. Chem. 12, 196–198 (1972).

    CAS  Google Scholar 

  207. 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).

    CAS  Google Scholar 

  208. 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).

    CAS  Google Scholar 

  209. 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).

    CAS  Google Scholar 

  210. 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. 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. T. Dunning and N. W. Winter, private communication, 1975.

    Google Scholar 

  213. L. C. Allen, Energy component analysis of rotational barriers, Chem. Phys. Lett. 2, 597–601 (1968).

    CAS  Google Scholar 

  214. I. R. Epstein and W. N. Lipscomb, Comments on the barrier to internal rotation in ethane, J. Am. Chem. Soc. 92, 6094–6095 (1970).

    CAS  Google Scholar 

  215. 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).

    CAS  Google Scholar 

  216. T. K. Ha, Theoretical study of the internal rotation and inversion in hydroxymethyl radical, Chem. Phys. Lett. 30, 379–382 (1975).

    CAS  Google Scholar 

  217. 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).

    CAS  Google Scholar 

  218. 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).

    CAS  Google Scholar 

  219. P.-O. Löwdin, Scaling problem, virial theorem, and connected relations in quantum mechanics, J. Mol. Spectrosc. 3, 46–66 (1959).

    Google Scholar 

  220. J. E. Eilers and A. Liberies, A quantum mechanical approach to conformational analysis, J. Am. Chem. Soc. 97, 4183–4188 (1975).

    CAS  Google Scholar 

  221. S. Wolfe, The gauche effect, some stereochemical consequences of adjacent electron pairs and polar bonds, Acc. Chem. Res. 5, 102–111 (1972).

    CAS  Google Scholar 

  222. H. Hellmann, Einführing in Die Quantenchemie, Franz Denticke and Co., Leipzig (1937).

    Google Scholar 

  223. R. P. Feynman, Forces in molecules, Phys. Rev. 56, 340–343 (1939).

    CAS  Google Scholar 

  224. K. Ruedenberg, Hindered rotation, Hellman-Feynman theorem and localized molecular orbitals, J. Chem. Phys. 41, 588–589 (1964).

    CAS  Google Scholar 

  225. R. G. Parr, Theorem governing changes in molecular conformation, J. Chem. Phys. 40, 3726 (1964).

    CAS  Google Scholar 

  226. H. Kim and R. G. Parr, Integral Hellmann-Feynman theorem, J. Chem. Phys. 41, 2892–2897 (1964).

    CAS  Google Scholar 

  227. 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. M. P. Melrose and R. G. Parr, Some integral Hellmann-Feynman calculations on hydrogen peroxide and ammonia, Theor. Chim. Acta 8, 150–156 (1967).

    CAS  Google Scholar 

  229. W. H. Fink and L. C. Allen, Numerical test of the integral Hellmann-Feynman theorem, J. Chem. Phys. 46, 3270–3271 (1967).

    CAS  Google Scholar 

  230. 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).

    CAS  Google Scholar 

  231. J. Goodisman, Barrier to internal rotation in ethane using the Hellmann-Feynman theorem, J. Chem. Phys. 45, 4689–4696 (1966).

    CAS  Google Scholar 

  232. J. Goodisman, Postscript to barrier to internal rotation in ethane by Hellmann-Feynman theorem, J. Chem. Phys. 47, 334–335 (1967).

    CAS  Google Scholar 

  233. S. M. Rothstein and S. M. Blinder, The internal Hellmann-Feynman theorem applied to hydrogen peroxide, Theor. Chim. Acta 8, 427–430 (1967).

    CAS  Google Scholar 

  234. 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. 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).

    CAS  Google Scholar 

  236. 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).

    CAS  Google Scholar 

  237. J. I. Musher, On Parr’s theorem, J. Chem. Phys. 43, 2145–2146 (1965).

    CAS  Google Scholar 

  238. 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. R. Mulliken, Electronic population analysis on LCAO-MO molecular wavefunctions. I, J. Chem. Phys. 23, 1833–1840 (1955).

    CAS  Google Scholar 

  240. 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).

    CAS  Google Scholar 

  241. 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. 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).

    CAS  Google Scholar 

  243. J. P. Lowe, The barrier to internal rotation in ethane, Science 179, 527–532 (1973).

    CAS  Google Scholar 

  244. 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).

    CAS  Google Scholar 

  245. N. D. Epiotis, Attractive nonbonded interactions in organic molecules, J. Am. Chem. Soc. 95, 3087–3096 (1973).

    CAS  Google Scholar 

  246. 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).

    CAS  Google Scholar 

  247. 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).

    CAS  Google Scholar 

  248. L. Salem, Intermolecular orbital theory of the interaction between conjugated systems. I. General theory, J. Am. Chem. Soc. 90, 543–552 (1968).

    CAS  Google Scholar 

  249. 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. W. J. Hehre and L. Salem, Conformation of vinylic methyl groups, J. Chem. Soc. D 1973, 754 (1973).

    Google Scholar 

  251. R. Hoffmann, C. C. Levin, and R. A. Moss, On steric attraction, J. Am. Chem. Soc. 95, 629–631 (1973).

    CAS  Google Scholar 

  252. 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. 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. 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).

    CAS  Google Scholar 

  255. M. Schwartz, Theoretical study of the barrier to internal rotation in hydrogen persulfide, HSSH, J. Chem. Phys. 51, 4182–4186 (1969).

    CAS  Google Scholar 

  256. W. L. Jorgensen and L. C. Allen, Charge distribution characteristics of attractive dominant barriers, Chem. Phys. Lett. 7, 483–485 (1970).

    CAS  Google Scholar 

  257. W. L. Jorgensen and L. C. Allen, Charge density analysis of rotational barriers, J. Am. Chem. Soc. 93, 567–574 (1971).

    Google Scholar 

  258. 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. 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. R. Hoffmann, An extended Hückel theory. Hydrocarbons, J. Chem. Phys. 39, 1397–1412 (1963).

    CAS  Google Scholar 

  261. S. W. Benson and M. Luria, Electrostatics and the chemical bond. I. Saturated hydrocarbons, J. Am. Chem. Soc. 97, 704–709 (1975).

    CAS  Google Scholar 

  262. S. W. Benson and M. Luria, Electrostatics and the chemical bond. II. Unsaturated hydrocarbons, J. Am. Chem. Soc. 97, 3337–3342 (1975).

    CAS  Google Scholar 

  263. M. Luria and S. W. Benson, Electrostatics and the chemical bond. III. Free radicals, J. Am. Chem. Soc. 97, 3342–3346 (1975).

    CAS  Google Scholar 

  264. H. A. Scheraga, Calculations of conformations of polypeptides, Adv. Phys. Org. Chem. 6, 103–185 (1968).

    CAS  Google Scholar 

  265. 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).

    CAS  Google Scholar 

  266. 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).

    CAS  Google Scholar 

  267. 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).

    CAS  Google Scholar 

  268. F. H. Stillinger, Construction and use of central force fields for the theory of polyatomic fluids, to be published.

    Google Scholar 

  269. 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).

    CAS  Google Scholar 

  270. W. L. Jorgensen and L. Salem, The Organic Chemist’s Book of Orbitals, Academic Press, New York (1973).

    Google Scholar 

  271. J. M. Howell, Ab initio calculations of the rotational barrier in PH4NH2, Chem. Phys. Lett. 25, 51–54 (1974).

    CAS  Google Scholar 

  272. E. Lassettre and L. Dean, An electrostatic theory of the potential barriers hindering rotation around single bonds, J. Chem. Phys. 17, 317–352 (1949).

    CAS  Google Scholar 

  273. 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).

    CAS  Google Scholar 

  274. 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).

    CAS  Google Scholar 

  275. 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. 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. 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. 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. 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. 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. M. Levy, Unconstrained exchange localization and distant orbital tails, J. Chem. Phys. 65, 2473–2475 (1976).

    CAS  Google Scholar 

  5. 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. 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 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Princeton University, Princeton, New Jersey, USA

    Philip W. Payne & Leland C. Allen

Authors
  1. Philip W. Payne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leland C. Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Berkeley, USA

    Henry F. Schaefer III

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Plenum Press, New York

About this chapter

Cite this chapter

Payne, P.W., Allen, L.C. (1977). Barriers to Rotation and Inversion. In: Schaefer, H.F. (eds) Applications of Electronic Structure Theory. Modern Theoretical Chemistry, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8541-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-8541-7_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-8543-1

  • Online ISBN: 978-1-4684-8541-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation