Computer Determination of Molecular Properties for Diatomics

  • L. Engelbrecht
  • Juergen Hinze


To understand and characterise matter, we determine as completely as possible the different properties of atoms and molecules to gain insight into their behavior; how they interact and react. The determination of molecular properties can be accomplished experimentally, by performing the appropriate measurement in the laboratory, or theoretically by using the laws of quantum mechanics to compute the desired property. In principle, the experiment will obviously yield the correct result, while the theoretical determination rests on our belief that quantum mechanics correctly describes atomic and molecular structure. In practice, both procedures are frought with difficulties, which are, however, quite different for the two methods. While many properties of a wide variety of molecules can be determined with ease by experiment, some are more readily and reliably obtained by computer. To be sure, the experimental approach is way ahead; experimentalists have determined molecular properties for more than a century, contributing greatly to our understanding of molecular structure and to the development of the laws of quantum mechanics. Nevertheless, there are cases, where the experimental approach breaks down or is severely hampered by difficulties, especially when the molecules in question are unstable or difficult to make. These present no limitations to the theoretical approach, since any molecule can be made and kept stable inside a computer. Here the problems and difficulties are of a different nature. The equations to be solved, and the quantities to be computed for a reliable theoretical determination of molecular properties are so complex that availability of high speed electronic computers was required before it became feasible to travel the theoretical avenue. Computers are young and the availability of machines with large enough capacity and high enough speed still more recent and limited. It is therefore not surprising that theoretical determination of molecular properties lags well behind experimental measurement.


Quantum Number Molecular Property Internuclear Distance Adiabatic Approximation Spectroscopic Constant 
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  1. 1).
    M. Born, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl., p.1 (1951), M. Born and K. Huang, “Dynamical Theory of Crystal Lattices” Oxford Univ. Press, N.Y. (1956).Google Scholar
  2. 3).
    J. Hinze, Adv. Chem. Phys. 26, 213 (1974).CrossRefGoogle Scholar
  3. 4) J.H. Wilkinson, “The Algebraic Eigenvalue Problem” Oxford Univ. Press, London 1965; J.H. Wilkinson and C. Reinsch, “Handbook for Automatic Computation” Vol. II “Linear Algebra” Springer, N.Y. (1971).Google Scholar
  4. 5).
    E.K. Nesbet, J. Chem. Phys. 43, 311 (1965)CrossRefGoogle Scholar
  5. C.F. Bender, R.P. Hosteny, A. Pipano and I. Shavitt, J. Comp. Phys. 11, 90 (1973)CrossRefGoogle Scholar
  6. E. Davidson, J. Comp. Phys. 17, 87 (1975).CrossRefGoogle Scholar
  7. 6).
    B. Roos, Chem. Phys. Lett. 15, 153 (1972)CrossRefGoogle Scholar
  8. R.F. Hausman Jr., S.D. Bloom and C.F. Bender, Chem. Phys. Lett. 32, 483 (1975).CrossRefGoogle Scholar
  9. 7).
    C.C.J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)CrossRefGoogle Scholar
  10. C.C.J. Roothaan, Rev. Mod. Phys. 32, 179 (1960).CrossRefGoogle Scholar
  11. 8).
    J. Hinze, J. Chem. Phys. 59, 6424 (1973)CrossRefGoogle Scholar
  12. G. Das and A.C. Wahl, J. Chem. Phys. 44, 87 (1966)CrossRefGoogle Scholar
  13. G. Das and A.C. Wahl, J. Chem. Phys. 56, 1769 (1972).CrossRefGoogle Scholar
  14. 9).
    I. Shavitt, Bull. Am. Phys. Soc. 19, 195 (1974); I. Shavitt, K. Hsu, R.C. Raffinetti, L.R. Kahn and P.J. Hay, “Energy Contribution and Selection of Configurations in Large Configuration Interaction Calculations” (to be published).Google Scholar
  15. 10).
    R.J. Bunker and S.D. Peyerimhoff, Theoret. Chim. Acta, 35, 33 (1974).CrossRefGoogle Scholar
  16. 11).
    E.R. Davidson, Rev. Mod. Phys. 44, 451 (1972).CrossRefGoogle Scholar
  17. 12).
    C.F. Bender and R.E. Davidson, J. Phys. Chem. 70, 2675 (1966).CrossRefGoogle Scholar
  18. 13).
    G.C. Lie, J. Hinze and B. Liu, J. Chem. Phys. 59, 1872 (1973).CrossRefGoogle Scholar
  19. 14).
    H.F. Schaefer, “The Electronic Structure of Atoms and Molecules” Addison Wesley, Reading, Mass. (1972).Google Scholar
  20. 15).
    W.G. Richardo, T.E.H. Walker and R.K. Hinkley, “A Bibliography of ab initio Molecular Wavefunctions” Clarendon Press, Oxford (1971).Google Scholar
  21. 16).
    F.A. Jenkins, J. Opt. Soc. Am. 43, 425 (1953).Google Scholar
  22. 17).
    G. Herzberg “Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules”, Van Nostrand, N.Y. (1950).Google Scholar
  23. 18).
    M. Mizushima “The Theory of Rotating Diatomic Molecules” John Wiley + Sons, N.Y. (1975).Google Scholar
  24. 19).
    J.L. Dunham, Phys. Rev. 41, 721 (1932)CrossRefGoogle Scholar
  25. I. Sandeman, Proc. Roy. Soc. (Edinburgh) 54, 1, 130 (1938)Google Scholar
  26. I. Sandeman, Proc. Roy. Soc. (Edinburgh) 60, 210 (1940).Google Scholar
  27. 20).
    B.J. Howard and R.E. Moss, Mol. Phys. 20, 147 (1971).CrossRefGoogle Scholar
  28. 21).
    A. Carrington, D.H. Levy and T.A. Miller, Adv. Chem. Phys. 18, 149 (1970).CrossRefGoogle Scholar
  29. 22).
    J.H. Van Vleck, Phys. Rev. 33, 467 (1929).CrossRefGoogle Scholar
  30. 23).
    see B.G. Wicke and D.O. Harris, J. Chem. Phys. 64, 5236 (1976) and reference cited there.CrossRefGoogle Scholar
  31. 24).
    F. Tobin, “Development of a Numerical H-F for Molecules”, Ph.D. Thesis, Univ. of Chicago, 1976.Google Scholar
  32. 25).
    R.L. Matcha, G. Malli and M.B. Miller, J. Chem. Phys. 56, 5982 (1972)CrossRefGoogle Scholar
  33. R.L. Matcha and C.W. Kern, J. Chem. Phys. 55, 469 (1970)CrossRefGoogle Scholar
  34. 26).
    W.H. Moores and R. McWeeny, Proc. Roy. Soc. (London) A 332, 365 (1973).Google Scholar
  35. 27).
    T.E.H. Walker and W.G. Richards, Phys. Rev. 177, 100 (1969).CrossRefGoogle Scholar
  36. 28).
    W.G. Richards, J. Raftery and R.K. Hinkley, Theoret. Chem. 1, 1 (1974).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • L. Engelbrecht
    • 1
  • Juergen Hinze
    • 1
  1. 1.Fakultät für ChemieUniversität BielefeldBielefeldGermany

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