Orbital Models and the Photochemistry of Transition-Metal Complexes

  • A. Ceulemans
Part of the NATO ASI Series book series (ASIC, volume 288)


This article examines the ligand field based orbital models, that are being used to explain photochemical properties of transition-metal complexes. Special attention is devoted to the formalism of dynamic ligand field theory, which constitutes a promising new tool in this respect. A case study is presented to illustrate the important role of the Jahn-Teller effect in inorganic photochemistry.


Potential Energy Surface Ligand Field Bond Index Vibronic Coupling Ligand Field Theory 
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]
    Griffith, J.S. “The Theory of Transition-Metal Ions”; Cambridge University Press, Cambridge, 1961.Google Scholar
  2. [2]
    As a general rule symmetry operations will be defined in an active sense, i.e. as leaving the Cartesian axes immobile while rotating or reflecting the orbital functions.Google Scholar
  3. [3]
    Ceulemans, A.; Bongaerts, N.; Vanquickenborne, L.G. Inorg. Chem. 1987, 26, 1566.CrossRefGoogle Scholar
  4. In table II of this reference the sign of the |a1 θε| determinant in the |2A2> component of 2T1g should be negative. 4 Dionne, G.F.; Palm, B.J. J. Magn. Resonance 1986, 68, 355.Google Scholar
  5. [5]
    Ballhausen, C.J. “Introduction to Ligand Field Theory”; McGraw-Hill, New York, 1962.Google Scholar
  6. [6]
    Ceulemans, A.; Beyens, D.; Vanquickenborne, L.G. J. Am. Chem. Soc. 1982, 104, 2988 (For a rigorous treatment, see [7]).CrossRefGoogle Scholar
  7. [7]
    Ceulemans, A. Meded. K. Acad. Wet., Lett. Schone Kunsten Belg. Kl. Wet. 1985, 46, 82.Google Scholar
  8. For a discussion of the physical background, see: Stedman, G.E. J. Phys. A 1987, 20, 2629.CrossRefGoogle Scholar
  9. [8]
    Ceulemans, A. Chem. Phys. 1982, 66, 169.CrossRefGoogle Scholar
  10. [9]
    Turnbull, H.W. “The Theory of Determinants, Matrices and Invariants”, Dover Publications, New York, 1960 (3rd edition).Google Scholar
  11. [10]
    Clearly a fixed standard order for the closed-shell parent determinant is required. If one changes the phase of this determinant, the phase factor in equation (10) will change as well, and so will the hole-electron exchange parities.Google Scholar
  12. [11]
    The time reversal operator Y turns spatial functions into their complex conjugates. Its effect on the electron spin is to turn |α> into β>, and β> into -|α>. Strictly speaking ℐ’ is defined up to an arbitrary phase factor. See also: Wigner, E. “Group Theory” (translated from the german by J.J. Griffin); Academic Press, New York, 1964 (4th printing).Google Scholar
  13. [12] Cited from 1], p. 247.Google Scholar
  14. [13]
    Flint, C.D. J. Mol. Spectrosc. 1971, 37, 414.CrossRefGoogle Scholar
  15. [14]
    Forster, L.S.; Rund, J.V.; Fucaloro, A.F. J. Phys. Chem. 1984, 88,5012.CrossRefGoogle Scholar
  16. [15]
    Forster, L.S.; Rund, J.V.; Fucaloro, A.F.; Lin, S.H. J. Phys. Chem. 1984, 88, 5017.CrossRefGoogle Scholar
  17. [16]
    Fucaloro, A.F.; Forster, L.S.; Glover, S.G.; Kirk, A.D. Inorg. Chem. 1985, 24, 4242.CrossRefGoogle Scholar
  18. [17]
    Ryu, C.K.; Endicott, J.F. Inorg. Chem. 1988, 27,2203.CrossRefGoogle Scholar
  19. [18]
    Basolo, F.; Pearson, R.G. “Mechanisms of Inorganic Reactions”; Wiley, New York, 1967 (2nd edition).Google Scholar
  20. [19]
    Vanquickenborne, L.G.; Ceulemans, A. J. Am. Chem. Soc. 1977, 99,2208.CrossRefGoogle Scholar
  21. [20]
    Vanquickenborne, L.G.; Ceulemans, A. Coord. Chem. Revs 1983, 48, 157.CrossRefGoogle Scholar
  22. [21]
    McClure, D.S. “VIth International Conference on Coordination Chemistry” (Ed. S. Kirschner); MacMillan, New York, 1961, p. 498.Google Scholar
  23. [22]
    Kettle, S.F.A. J. Chem. Soc. A 1966, 420.Google Scholar
  24. [23]
    Burdett, J.K. J. Chem. Soc. Faraday Trans. 2 1974, 70, 1599.CrossRefGoogle Scholar
  25. [24]
    Schäffer, C.E.; Jorgensen, C.K. Mol. Phys. 1965, 9, 401.CrossRefGoogle Scholar
  26. [25]
    Schäffer, C.E. “XIIth International Conference on Coordination Chemistry, Sydney 1969”, IUPAC, Butterworths, London, 1970, p. 316.Google Scholar
  27. [26]
    Zink, J.I. J. Am. Chem. Soc. 1972, 94, 8039.CrossRefGoogle Scholar
  28. [27]
    Adamson, A.W. J. Phys. Chem. 1967, 71, 798.CrossRefGoogle Scholar
  29. [28]
    Kirk, A.D.; Frederick, L.A. Inorg. Chem. 1981, 20, 60.CrossRefGoogle Scholar
  30. [29]
    Endicott, J.F.; Ramasami, T.; Tamilarasan, R.; Lessard, R.B.; Ryu, C.K. Coord. Chem. Revs. 1987, 77, 1.CrossRefGoogle Scholar
  31. [30]
    Riccieri, P.; Zinato, E.; Damiani, A. Inorg. Chem. 1987, 26, 2667.CrossRefGoogle Scholar
  32. [31]
    Monsted, L.; Monsted, O. Acta Chem. Scand. 1984, A88, 679.CrossRefGoogle Scholar
  33. [32]
    Herbert, B.; Reinhard, D.; Saliby, M.J.; Sheridan, P.S. Inorg. Chem. 1987, 26, 4024.CrossRefGoogle Scholar
  34. [ 33]
    Wilson, R. B., Solomon, E. I. Inorg. Chem. 1978, 17, 1729.CrossRefGoogle Scholar
  35. [34]
    Güdel, H.U.; Snellgrove, T.R. Inorg. Chem. 1978, 17, 1617.CrossRefGoogle Scholar
  36. [35]
    Bacci, M. Chem. Phys. Lett. 1978, 58, 537.CrossRefGoogle Scholar
  37. [36]
    Bacci, M. Chem. Phys. 1979, 40, 237. In table 1 of this reference the matrix element for the b2 mode in a square pyramidal MX5 compound is erroneous. The correct matrix element is given in our Table 7.Google Scholar
  38. [37]
    Warren, K.D. Structure and Bonding 1984, 57, 120. In table 2 of this reference the matrix elements <z2|> ∂‰/Qyz|yz> and <x2-y2|∂ν/∂Qyz|yz> should read \[\frac{1}{2}\sqrt 3 \] σ and \[ - \frac{3}{2}\]σ respectively.Google Scholar
  39. [38]
    Ceulemans, A.; Beyens, D.; Vanquickenborne, L.G. J. Am. Chem. Soc. 1984, 106, 5824. Equation (10) of this reference contains some misprints: second row, the term 1/4 \[Q_\zeta ^2\] should read 1/4 \[Q_\xi ^2\]; fourth (fifth) row, a minus sign in front of 1/2 QϑQ,ε(1/2 QϑQη)should be added; sixth row, the term XtQQη should read XtQεQη.Google Scholar
  40. [39]
    Stone, A.J. Mol. Phys. 1980, 41, 1339. In equation (3.4) of this reference the matrix element in the third column should read: — cos θeϑ — sin θer.Google Scholar
  41. [40]
    Griffith, J.S. “The Irreducible Tensor Method for Molecular Symmetry Groups”; Prentice-Hall, Englewood Cliffs, NJ, 1962.Google Scholar
  42. [41]
    Englman, R. “The Jahn-Teller Effect in Molecules and Crystals”; Wiley, New York, 1972.Google Scholar
  43. [42]
    Schmidtke, H.-H.; Degen, J. Structure and Bonding, in press.Google Scholar
  44. [43]
    Agresti, A.; Ammeter, J.H.; Bacci, M. J. Chem. Phys. 1984, 81, 1861. Erratum: ibid. 1985, 82, 5299.Google Scholar
  45. [44]
    Parrot, R.; Naud, C.; Gendron, F.; Porte, C.; Boulanger, D. J. Chem. Phys. 1987, 87, 1463.CrossRefGoogle Scholar
  46. [45]
    Stavrev, K.K.; Kynev, K.D.; Nikolov G. St. J. Chem. Phys., 1988, 88, 7027.CrossRefGoogle Scholar
  47. [46]
    Reinen, D.; Atanasov, M.; Nikolov, G.S.; Steffens, F. Inorg. Chem. 1988, 27, 1678.CrossRefGoogle Scholar
  48. [47]
    Bacci, M. J. Phys. Chem. Solids 1980, 41,1267.CrossRefGoogle Scholar
  49. [48]
    Kirk, A.D. Mol. Photochem. 1973, 5, 127.Google Scholar
  50. [49]
    Kirk, A.D. Coord. Chem. Revs. 1981, 39,225.CrossRefGoogle Scholar
  51. [50]
    Zinato, E.; Riccieri, P., Prelati, M. Inorg. Chem. 1981, 20, 1432.CrossRefGoogle Scholar
  52. [51]
    Riccieri, P.; Zinato, E. Inorg. Chem. 1983, 22, 2305.CrossRefGoogle Scholar
  53. [52]
    Vanquickenborne, L.G.; Ceulemans, A. J. Am. Chem. Soc. 1978, 100, 475.CrossRefGoogle Scholar
  54. [53]
    Bacci, M.; Chem. Phys. 1986, 104, 191. Equation (22) of this reference uses the erroneous value for the b2 coupling element of ref. [36]. For the correct value, see our table 7.Google Scholar
  55. [54]
    Bersuker, I.B. “The Jahn-Teller Effect and Vibronic Interactions in Modern Chemistry”, Plenum, New York, 1984.Google Scholar
  56. [55]
    Endicott, J.F. Comments Inorg. Chem. 1985, 3,349.CrossRefGoogle Scholar
  57. [56]
    Dyachkov, P.N.; Levin, A.A. “Vibronic Theory of the relative isomeric Stability of Inorganic Molecules and Complexes”, in: Itogi Nauki Tekh.: Str. Mol. Khim. Svyaz, Moscow, 1987, vol. 11.Google Scholar
  58. [57]
    Riley, M.J.; Hitchman, M.A.; Reinen, D.; Steffen, G. Inorg. Chem. 1988, 27, 1924.CrossRefGoogle Scholar
  59. [58]
    Ham, F.S. Phys. Rev. 1968, 166, 307.CrossRefGoogle Scholar
  60. [59]
    Even if no symmetry is present, the crossing point may persist and is said to be topologically sustained. See: Longuet-Higgins, H.C. Proc. Roy. Soc. Lond. 1975, A344, 147.Google Scholar
  61. [60]
    Carpenter, B.K. J. Am. Chem. Soc. 1985, 107, 5730.CrossRefGoogle Scholar
  62. [61]
    Poliakoff, M.; Ceulemans, A. J. Am. Chem. Soc. 1984, 106, 50.CrossRefGoogle Scholar
  63. [62]
    Reinen, D.; Friebel, C. Inorg. Chem. 1984, 23, 791.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • A. Ceulemans
    • 1
  1. 1.Department of ChemistryUniversity of LeuvenLeuvenBelgium

Personalised recommendations