The Nuclear Shielding Surface: The Shielding as a Function of Molecular Geometry and Intermolecular Separation

  • Cynthia J. Jameson
  • Angel C. de Dios
Part of the NATO ASI Series book series (ASIC, volume 386)


In making the connection between theoretical shielding values and experiments, it becomes necessary to consider medium effects and rovibrational averaging. The rovibrational averaging which takes the shielding for a molecule at its rigid equilibrium geometry into a thermal average shielding also provides the temperature dependence in the zero-pressure limit and the changes upon isotopic substitution which are experimentally accessible. The averaging of 15N and 31P shielding in the NH3 and PH3 molecules uses ab initio shielding surfaces and intramolecular potential surfaces or their derivatives. General trends are observed in comparing the shielding surfaces in these two molecules with H2O and CH4. A proper account of medium effects requires the knowledge of the intermolecular shielding surfaces, which are explored here for model systems 39Ar in Ar...Ar, Ar...Ne, Ar...Na+, Ar...NaH, and for 21Ne in Ne...Ne and Ne...He, employing ab initio calculations (LORG and SOLO). The shapes of the shielding function σ(R) for two atoms are shown to be similar for intra-and intermolecular shielding.


Diatomic Molecule Isotope Shift Virial Coefficient Equilibrium Bond Length Intermolecular Separation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jameson, C. J., (1980)’Effects of intermolecular interactions and intramolecular dynamics on nuclear resonance’, Bull. Magn. Reson. 3, 3–28.Google Scholar
  2. 2.
    Jameson, C. J., Jameson, A. K., and Burrell, P. M. (1980)’19F nuclear shielding scale from gas phase studies’, J. Chem. Phys. 73, 6013–6020.CrossRefGoogle Scholar
  3. 3.
    Hindermann, D. K. and Cornwell, C. D. (1968)’Fluorine and proton NMR study of gaseous hydrogen fluoride’, J. Chem. Phys. 48, 2017–2024.CrossRefGoogle Scholar
  4. 4.
    Jameson, C. J., Jameson, A. K., Oppusunggu, D., Wille, S., Burrell, P. M., and Mason, J. (1981) ‘EN nuclear magnetic shielding scale from gas phase studies’, J. Chem. Phys. 74, 81–88.CrossRefGoogle Scholar
  5. 5.
    Jameson, A. K., and Jameson, C. J. (1987)’Gas phase 13C chemical shifts in the zero-pressure limit: refinements to the absolute shielding scale for 13C’, Chem. Phys. Lett. 134, 461–466.CrossRefGoogle Scholar
  6. 6.
    Wasylishen, R. E., Mooibroek, S., and Macdonald, J. B. (1984) ‘A more reliable 170 absolute chemical shielding scale’, J. Chem. Phys. 81, 1057–1059.CrossRefGoogle Scholar
  7. 7.
    Davies, P. B., Neumann, R. M., Wofsy, S. C., and Klemperer, W. (1971) ‘Radiofrequency spectrum of phosphine (PH 3)’, J. Chem. Phys. 55, 3564–3568.CrossRefGoogle Scholar
  8. 8.
    Jameson, C. J., de Dios, A., and Jameson, A. K. (1990) ‘Absolute shielding scale for 31P from gas-phase nmr studies’, Chem. Phys. Lett. 167, 575–582.CrossRefGoogle Scholar
  9. 9.
    Wasylishen, R. E., Connor, C., and Friedrich, J. O. (1984) ‘An approximate absolute 33S nuclear magnetic shielding scale’, Can. J. Chem. 62, 981–985.CrossRefGoogle Scholar
  10. 10.
    Jameson, C. J. and Jameson, A. K. (1988), ‘Absolute shielding scale for 29Si’, Chem. Phys. Lett. 149, 300–305.CrossRefGoogle Scholar
  11. 11.
    Buckingham, A. D. and Pople, J. A. (1956) ‘Electromagnetic properties of compressed gases’, Faraday Soc. Discuss. 22, 17–21.CrossRefGoogle Scholar
  12. 12.
    Raynes, W. T., Buckingham, A. D., and Bernstein, H. J. (1962) ‘Medium effects in proton magnetic resonance. I. Gases’, J. Chem. Phys. 36, 3481–3488.CrossRefGoogle Scholar
  13. 13.
    See for example, Jameson, C. J., Jameson, A. K., and Oppusunggu, D. (1986) ‘Temperature dependence of 77Se, 125Te, and 19F shielding and M-induced isotope shifts in MF6 molecules’, J. Chem. Phys. 85, 5480–5483.CrossRefGoogle Scholar
  14. 14.
    Jameson, A. K., Jameson, C. J., and Gutowsky, H. S. (1970) ‘Density dependence of 129Xe chemical shifts in mixtures of xenon and other gases’, J. Chem. Phys. 53, 2310–2321.CrossRefGoogle Scholar
  15. 15.
    Jameson, C. J., Jameson, A. K., and Cohen, S. M. (1975) ‘Temperature and density dependence of 129Xe chemical shift in rare gas mixtures’, J. Chem. Phys. 62, 4224–4226.CrossRefGoogle Scholar
  16. 16.
    Jameson, C. J., Jameson, A. K., and Cohen, S. M. (1976) ‘Second virial coefficient of 129Xe chemical shielding in mixtures of Xe with spherical top molecules, CH4, CF4, and SiF4’, J. Chem. Phys. 65, 3401–3406.CrossRefGoogle Scholar
  17. 17.
    Jameson, C. J. (1991) ‘Rovibrational averaging of molecular electronic properties’, in Z. B. Maksic (ed.), Theoretical Models of Chemical Bonding, Part 3. Molecular Spectroscopy, Electronic Structure, and Intramolecular Interactions, Springer-Verlag, Berlin, pp. 457–519.Google Scholar
  18. 18.
    Jameson, C. J. and Osten, H.-J. (1986) ‘Theoretical aspects of the isotope effect on nuclear shielding’, in G. A. Webb (ed.), Annual Reports on NMR Spectroscopy, Academic Press, London, Vol. 17, pp. 1–78.Google Scholar
  19. 19.
    Jameson, C. J., de Dios, A. C., and Jameson, A. K. (1991), ‘Nuclear magnetic shielding of nitrogen in ammonia’, J. Chem. Phys. 95, 1069–1079.CrossRefGoogle Scholar
  20. 20.
    Riley, G., Raynes, W. T., and Fowler, P. W. (1979) ‘The variation of molecular properties with vibration-rotation’, Mol. Phys. 38, 877–892.CrossRefGoogle Scholar
  21. 21.
    Fowler, P. W., Riley, G., and Raynes, W. T. (1981), ‘Dipole moment, magnetizability, and nuclear shielding surfaces for the water molecule’, Mol. Phys. 42, 1463–1481.CrossRefGoogle Scholar
  22. 22.
    Chesnut, D. B. (1986) ‘NMR chemical shift bond length derivatives of the first-and second-row hydrides’, Chem. Phys. 110, 415–420.CrossRefGoogle Scholar
  23. 23.
    Chesnut, D. B. and Wright, D. W. (1991) ‘Chemical shift bond derivatives for molecules containing first-row atoms’, J. Computational Chem. 12, 546–559.CrossRefGoogle Scholar
  24. 24.
    Chestnut, D. B. and Foley, C. K. (1986) ‘Chemical shifts and bond modification effects for some small first-row-atom molecules’, J. Chem. Phys. 84, 852–861.CrossRefGoogle Scholar
  25. 25.
    Ditchfield, R. (1981) ‘Theoretical studies of the temperature dependence of magnetic shielding tensors: H2, HF, and LiH’, Chem. Phys. 63, 185–202.CrossRefGoogle Scholar
  26. 26.
    Fleischer, U., Schindler, M., and Kutzelnigg (1987) ‘Magnetic properties in terms of localized quantitities. VI. Small hydrides, fluorides, and homonuclear molecules of phosphorus and silicon’, J. Chem. Phys. 86, 6337–6347.CrossRefGoogle Scholar
  27. 27.
    Hegstrom, R. A. (1979) ‘g factors and related magnetic properties of molecules. Formulation of theory and calculations for H2+, HD+, and D2+’, Phys. Rev. A 19, 17–30.CrossRefGoogle Scholar
  28. 28.
    Lazzeretti, P., Zanasi R., Sadlej, A. J., and Raynes, W. T. (1987) ‘Magnetizability and carbon-13 shielding surfaces for the methane molecule’, Mol. Phys. 62, 605–616.CrossRefGoogle Scholar
  29. 29.
    Raynes, W. T., Fowler, P. W., Lazzeretti, P., Zanasi, R., and Grayson, M. (1988) ‘The effects of rotation and vibration on the carbon-13 shielding, magnetizabilities and geometrical parameters of some methane isotopomers’, Mol. Phys. 64, 143–162.CrossRefGoogle Scholar
  30. 30.
    Jameson, C. J., de Dios, A. C., and Jameson, A. K. (1991) ‘The 31P shielding in phosphine’, J. Chem. Phys. 95, 9042–9053.CrossRefGoogle Scholar
  31. 31.
    RPAC version 8.5, Thomas D. Bouman, Southern Illinois University at Edwardsville, and Aage E. Hansen, H. C. Oersted Institute, Copenhagen, Denmark.Google Scholar
  32. 32.
    Hansen, A. E. and Bouman, T. D. (1985) ‘Localized orbital/local origin method for calculation and analysis of NMR shieldings. Applications to 13C shielding tensors’, J. Chem. Phys. 82, 5035–5047.CrossRefGoogle Scholar
  33. 33.
    GAUSSIAN88, M. J. Frisch, M. Head-Gordon, H. B. Schlegel, K. Raghavachari, J. S. Binkley, C. Gonzalez, D. J. Fox, R. A. Whiteside, R. Seeger, C. F. Melius, J. Baker, R. Martin, L. R. Kahn, J. J. P. Stewart, E. M. Ruder, S. Topial, and J. A. Pople, Gaussian, Inc., Pittsburgh, PA. 1988.Google Scholar
  34. 34.
    Spirko, V., Stone, J. M. R., and Papousek, D. (1976) ‘Vibration-inversion-rotation spectra of ammonia: centrifugal distortion, coriolis interactions, and force field in14NH3 15NH3 14ND3, and 14NT3’, J. Mol. Spectrosc. 60, 159–178.CrossRefGoogle Scholar
  35. 35.
    Jameson, C. J. and Osten, H. J. (1985) ‘Systematic trends in the variation of 19F nuclear magnetic shielding with bond extension in halomethanes’, Mol. Phys. 55, 383–395.CrossRefGoogle Scholar
  36. 36.
    Stevens, R. M., Pitzer, R. M., and Lipscomb, W. N. (1963) ‘Perturbed Hartree-Fock calculations I. Magnetic susceptibility and shielding in the LiH molecule’, J. Chem. Phys. 38, 550–560.CrossRefGoogle Scholar
  37. 37.
    Jameson, C. J. (1991) ‘Gas phase NMR spectroscopy’, Chem. Rev. 91, 1375–1395.CrossRefGoogle Scholar
  38. 38.
    Rummens, F. H. A. (1975) ‘Van der Waals forces and shielding effects’, in P. Diehl, E. Ruck, and R. Kosfeld (eds.) NMR Basic Principles and Progress, Springer, Berlin, Vol. 10, pp. 1–118.Google Scholar
  39. 39.
    Malli, G. and Froese C. (1967) ‘Nuclear magnetic shielding constants calculated from numerical Hartree-Fock wave functions’, Intl. J. Quantum Chem. 1S, 95–98.Google Scholar
  40. 40.
    Bouman, T. D. and Hansen, A. E. (1990) ‘NMR shielding calculations beyond coupled Hartree-Fock: Second order correlation effects in localized-orbital/localorigin calculations of molecules containing phosphorus’, Chem. Phys. Lett. 175, 292–299.CrossRefGoogle Scholar
  41. 41.
    Amos, R. D. (1980) ‘SCF and CI calculations of the one-electron properties, polarizabilities and polarizability derivatives of the nitrogen molecule’, Mol. Phys. 39, 1–14.CrossRefGoogle Scholar
  42. 42.
    Amos, R. D. (1979) ‘SCF and CI calculations of the one-electron properties of carbon monoxide as a function of internuclear distance’, Chem. Phys. Lett. 68, 536–539.CrossRefGoogle Scholar
  43. 43.
    RPAC Version 9.0 T. D. Bouman, Southern Illinois University, Edwardsville, and A. E. Hansen, H. C. Oersted Institute, Copenhagen, Denmark.Google Scholar
  44. 44.
    Boys, S. F. and Bernardi, F. (1970) ‘The calculation of small molecular interactions by the differences of separate total energies’, Mol. Phys. 19, 553–566.CrossRefGoogle Scholar
  45. 45.
    Jameson, C. J. and de Dios, A. C. (1992) ’Ab initio calculations of the intermolecular chemical shift in nuclear magnetic resonance in the gas phase and for adsorbed species’, J. Chem. Phys. 97, 417–434.CrossRefGoogle Scholar
  46. 46.
    Jameson, C. J. and de Dios, A. C. (1992) ‘The NMR shielding as a function of internuclear separation’, to be published.Google Scholar
  47. 47.
    Buckingham, A. D. (1978) ‘Basic theory of intermolecular forces: applications to small molecules’, in B. Pullman (ed.), Intermolecular Interactions: From Diatomics to Biopolymers, John Wiley, New York pp. 1–67.Google Scholar
  48. 48.
    Buckingham, A. D. (1960) ‘Chemical shifts in the nuclear magnetic resonance spectra of molecules containing polar groups’, Can. J. Chem. 38, 300–307.CrossRefGoogle Scholar
  49. 49.
    Marshall, T. W. and Pople, J. A. (1958) ‘Nuclear magnetic shielding of a hydrogen atom in an electric field’ Mol. Phys. 1, 199–202.CrossRefGoogle Scholar
  50. 50.
    Raynes, W. T. and Ratcliffe, R. (1979) ‘Nuclear site symmetry and nuclear magnetic shielding in a uniform electric field’, Mol. Phys. 37, 571–578.CrossRefGoogle Scholar
  51. 51.
    Augspurger, J. D., Dykstra, C. E., and Oldfield, E. (1990) ‘Correlation of carbon-13 and oxygen-17 chemical shifts and the vibrational frequency of electrically perturbed carbon monoxide: A possible model for distal ligand effects in carbonmonoxyheme proteins’, J. Am. Chem. Soc. 113, 2447–2451.CrossRefGoogle Scholar
  52. 52.
    Augspurger, J. D. and Dykstra, C. E. (1991) ‘Electromagnetic properties of molecules from a uniform procedure for differentiation of molecular wave functions to high order’, J. Phys. Chem. 95, 9230–9238.CrossRefGoogle Scholar
  53. 53.
    Buckingham, A. D. (1967) ‘Permanent and induced molecular moments and long-range intermolecular forces’, in J. O. Hirschfelder (ed.), Adv. Chem. Phys. Vol. 12, pp. 107–142.CrossRefGoogle Scholar
  54. 54.
    Buckingham, A. D. and Clarke, K. L. (1978) ‘Long-range effects of molecular interactions on the polarizability of atoms’, Chem. Phys. Lett. 57, 321–325.CrossRefGoogle Scholar
  55. 55.
    London, F. (1930) ’über einige Eigenschaften und Anwendungen der Molekularkräfte’, Z. physik. Chem. (Leipzig) B, 11, 222–251.Google Scholar
  56. 56.
    London, F. (1937) Trans. Faraday Soc. 33, 8-CrossRefGoogle Scholar
  57. 57.
    Jameson, C. J. and Mason, J. (1987) ‘The chemical shift’, in J. Mason (ed.) Multi-nuclear NMR, Plenum, New York, pp. 51–88.CrossRefGoogle Scholar
  58. 58.
    Maitland, G. C., Rigby, M., Smith, E. B., and Wakeham, W. A. (1981) Intermolecular Forces their Origin and Determination, Clarendon Press, Oxford.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Cynthia J. Jameson
    • 1
  • Angel C. de Dios
    • 2
  1. 1.Department of Chemistry M/C-111University of Illinois at ChicagoChicagoUSA
  2. 2.Department of ChemistryUniversity of Illinois at UrbanaUrbanaUSA

Personalised recommendations