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Stereochemistry and Bonding pp 57–97Cite as

Vibronic interactions in the stereochemistry of metal complexes

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Part of the book series: Structure and Bonding ((STRUCTURE,volume 71))

Abstract

A survey of the theoretical foundations of vibronic interactions in molecular systems, with special attention to metal complexes, is given. A detailed analysis of the conditions leading to the adiabatic potential surface in various degrees of generality represents the central idea of the article. Use of the partitioning method enables consideration of the Jahn-Teller effect, the Renner-Teller effect and the pseudo Jahn-Teller effect on an equal footing. Analytic forms of the adiabatic potential surfaces are rederived for the most important cases by including the totally symmetric vibrational mode up to the second order of vibronic expansion. A complete third-order formula for the adiabatic potential surface of Eg − (a1g + eg) vibronic coupling is presented. The consequences for structural features of molecular systems are discussed and exemplified by various metal complexes. Recent progress in molecular-orbital calculations of vibronic constants is reviewed.

This paper deals with pure (pseudo) Jahn-Teller effect only. On the other hand, some qualitatively new types of interaction may arise due to interaction of (pseudo) Jahn-Teller centers with the lattice. We do not consider the competitive spin-orbit-lattice coupling that may arise below a magnetic-ordering temperature at Jahn-Teller ions with a threefold orbital degeneracy. Inclusion of interactions like this is, however, outside the scope of the present work.

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Abbreviations

a:

symmetry of vibration

A:

symmetry of electron state; vibronic constant

APS:

adiabatic potential surface

AOM:

Angular Overlap Model

b:

symmetry of vibration

B:

symmetry of electron state; vibronic constant

Ci :

matrix of coupling coefficients

CG:

Clebsh-Gordan coefficient

CNDO:

Complete Neglect of Differential Overlap

e:

symmetry of vibration

E:

symmetry of electron state; energy, eigenvalue of Schrödinger equation

fk :

nuclear (vibration) function

Fi, Fij, Fijk...:

pure nuclear term of force constants

G:

symmetry point group

Ĝ1k :

nonadiabatic coupling operator

Ĥ:

Hamiltonian

Hkl :

matrix element of Hamiltonian

Ki, Kij, Kijkl...:

force constants

LCAO:

Linear Combination of Atomic Orbitals

MA :

mass of nucleus

MO:

Molecular Orbital

Σ:

group order

Q:

nuclear coordinate

r:

electron coordinate; radial (polar) coordinate; distance

\(\hat R\) :

resolvent

Sp(V):

trace of matrix V

t:

symmetry of vibration

T:

symmetry of electron state

\(\hat T\) :

Kinetic energy operator

U:

interaction potential

\(\hat V\) :

potential energy operator

\(\dot V,\ddot V,\dddot V\) :

derivatives of \(\hat V\) (first, second, third...)

X:

reduced matrix element

Xi, Xij, Xijk...:

electron-nuclear term of force constants; vibronic constant

Yj, m :

spherical harmonics with m and j quantum numbers

Z:

vibronic constant

γ:

component of irreducible representation Γ

Γ:

representation of symmetry

δij :

Kronecker delta

ε:

eigenvalue of matrix; vibronic correction term; component of E representation

ι:

angular coordinate; component of E representation

ϱ:

radial coordinate, Jahn-Teller radius

ϕ:

angular coordinate

φ:

electronic wave function

∇:

nabla operator

References

  1. Murrell, J. N.: Struct. Bonding 32, 93 (1977)

    CAS  Google Scholar 

  2. Ammeter, J. H.: Nouv. J. Chim. 4, 631 (1980)

    CAS  Google Scholar 

  3. Ammeter, J. H., Bürgi, H. B. Gamp, E., Meyer-Sandrin, V., Jensen W. P.: Inorg. Chem. 18, 733 (1979)

    Article  CAS  Google Scholar 

  4. Gažo, J.: Pure Appl. Chem. 38, 279 (1974)

    Google Scholar 

  5. Hathaway, B. J.: Coord. Chem. Rev. 35, 211 (1981); ibid. 41, 423 (1982); ibid. 52, 87 (1983); Struct. Bonding 57, 55 (1984)

    Article  CAS  Google Scholar 

  6. Gažo, J., Bersuker, I. B., Garaj, J., Kabeŝová, M., Kohout, J., Langfelderová, H., Melnik, M., Serátor, M., Valach, F.: Coord. Chem. Rev. 19, 253 (1976)

    Article  Google Scholar 

  7. Hathaway, B. J., Duggan, M., Murphy, A., Mullane, J., Power D. C., Walsh, A., Walsh, B.: ibid. 36, 267 (1981)

    Article  CAS  Google Scholar 

  8. Gažo, J., Boča, R., Jóna, E., Kabešovâ, M., Macášková, L., Šima, J., Pelikán, P., Valach, F.: ibid. 43, 87 (1982)

    Article  Google Scholar 

  9. Gažo, J., Boča, R., Jóna, E., Kabešovâ, M., Macášková, Ľ., Šima, J.: Pure Appl. Chem. 55, 65 (1983)

    Google Scholar 

  10. Reinen, D.: Comments Inorg. Chem. 2, 227 (1983)

    CAS  Google Scholar 

  11. Englman, R.: The Jahn-Teller Effect in Molecules and Crystals. Wiley-Interscience, New York 1972

    Google Scholar 

  12. Bersuker, I. B.: Coord. Chem. Rev. 14, 357 (1975)

    Article  CAS  Google Scholar 

  13. Bersuker, I. B., Polinger V. Z.: Adv. Quantum Chem. 15, 85 (1982)

    CAS  Google Scholar 

  14. Bacci, M.: Nouv. J. Chim. 4, 577 (1980)

    CAS  Google Scholar 

  15. Bacci, M.: Struct. Bonding 55, 67 (1983)

    CAS  Google Scholar 

  16. Reinen, D., Friebel, C.: ibid. 37, 1 (1979)

    CAS  Google Scholar 

  17. Pearson, R. G.: Symmetry Rules for Chemical Reactions. Wiley-Interscience, New York 1976

    Google Scholar 

  18. Özkan, I., Goodman, L.: Chem. Rev. 79, 275 (1979)

    Article  Google Scholar 

  19. Lowe, J. P.: Quantum Chemistry. Academic Press, New York 1978

    Google Scholar 

  20. Jahn, H. A., Teller, E.: Proc. Roy. Soc. A161, 220 (1937); Jahn, H. A.: Proc. Roy. Soc. A 164, 117 (1938)

    CAS  Google Scholar 

  21. Salthouse, J. A., Ware, M. J.: Point Group Character Tables and Related Data. University Press, Cambridge 1972

    Google Scholar 

  22. Ruch, E., Schönhofer, A.: Theoret. Chim. Acta 3, 291 (1965)

    Article  CAS  Google Scholar 

  23. Blount E. L.: J. Math. Phys. 12, 1890 (1971)

    Article  CAS  Google Scholar 

  24. Pelikán, P., Breza, M., Boča, R.: Polyhedron 4, 1543 (1985)

    Article  Google Scholar 

  25. Breza, M., Pelikân, P., Boča, R.: ibid. 5, 1607 (1986)

    Article  CAS  Google Scholar 

  26. Pelikân, P., Breza, M., Boča, R.: ibid. 5, 753 (1986)

    Article  Google Scholar 

  27. Coffman, R. E.: J. Chem. Phys. 44, 2305 (1966)

    Article  CAS  Google Scholar 

  28. Öpik, U., Pryce, M. H. L.: Proc. Roy. Soc. A 238, 425 (1957)

    Google Scholar 

  29. O'Brien, M.: ibid. A 281, 323 (1964)

    Google Scholar 

  30. Goodenough, J.: J. Phys. Chem. Solids 25, 151 (1964)

    Article  CAS  Google Scholar 

  31. Boĉa, R., Pelikân, P., Breza, M., Gažo, J.,: Polyhedron 2, 921 (1983)

    Article  Google Scholar 

  32. Judd, B. R.: Can. J. Phys. 52, 999 (1974)

    CAS  Google Scholar 

  33. Jotham, R. W., Kettle, S. F. A.: Inorg. Chim. Acta 5, 183 (1971)

    Article  CAS  Google Scholar 

  34. Dagis, R. S., Levinson, I. B.: in: Frish, S. E. (ed.) Optika i spektroskopiya 3. Molekulyarnaya spektroskopiya. Nauka, Moscow 1967

    Google Scholar 

  35. Pelikân, P., Breza, M.: Chem. Papers 39, 255 (1985)

    Google Scholar 

  36. Pelikân, P., Breza, M.: J. Mol. Struct. (Theochem.) 124, 231 (1985)

    Article  Google Scholar 

  37. Liehr, A. D.: J. Phys. Chem. 67, 389 (1963)

    CAS  Google Scholar 

  38. Boča, R.: Chem. Papers 35, 769 (1981)

    Google Scholar 

  39. Boča, R.: ibid. 35, 779 (1981)

    Google Scholar 

  40. Boča, R.: ibid. 37, 297 (1983)

    Google Scholar 

  41. Cullen, D. L., Lingafelter, E. C.: Inorg. Chem. 10, 1265 (1971); Noda, Y., Mori, M., Yamada, Y.: Solid State Commun. 19, 1071 (1976); Joesten, M. D., Takagi, S., Lenhert, P. G.: Inorg. Chem. 16, 2681 (1977)

    Google Scholar 

  42. Hellwege, K. H. (ed.): Crystal Structures of Inorganic Compounds. Key-Elements: d9−, d10−, d1... d3−, f-Elements (Landolt-Börnstein. New Series. Vol. III/7 f). Springer, Berlin-Heidelberg-New York 1976

    Google Scholar 

  43. Hellwege, K. H. (ed.): Crystal Structures of Inorganic Compounds. Key-Elements: d4... d8-elements (Landolt-Börnstein. New Series. Vol. III/7 f). Springer, Berlin-Heidelberg-New York 1977

    Google Scholar 

  44. van Vleck, J. H.: J. Chem. Phys. 7, 1972 (1939)

    Google Scholar 

  45. Bersuker, I. B.: Elektronnoe stroenie i svoistva koordinatsionnykh soedinenii. Khimiya, Leningrad 1976

    Google Scholar 

  46. Bersuker, I. B.: Zh. Eksp. Teor. Fiz. 43, 1315 (1962)

    CAS  Google Scholar 

  47. Bacci, M.: Chem. Phys. 40, 237 (1979)

    Article  CAS  Google Scholar 

  48. Bacci, M.: Biophys. Chemistry 11, 39 (1980).

    Article  CAS  Google Scholar 

  49. Warren, K. D.: Struct. Bonding 57, 119 (1984)

    Article  CAS  Google Scholar 

  50. Nikiforov, A. E., Shashkin, S. Yu., Krotkii, A. I.: Phys. Stat. Sol. (b) 97, 475 (1980)

    CAS  Google Scholar 

  51. Nikiforov, A. E., Shashkin, S. Yu., Krotkii, A. I.: ibid. 98, 289 (1980)

    CAS  Google Scholar 

  52. Lee, T. J., Fox, D. J., Shaeffer III, H. F., Pitzer, R. M.: J. Chem. Phys. 81, 356 (1984)

    Article  CAS  Google Scholar 

  53. Dixon, R. N.: Mol. Phys. 20, 113 (1971)

    Article  CAS  Google Scholar 

  54. Pelikân, P., Breza, M., Liška, M.: Inorg. Chim. Acta 45, L 1 (1980)

    Google Scholar 

  55. Griffith, J. S.: The Theory of Transition-Metal Ions. University Press, Cambridge 1964

    Google Scholar 

  56. Griffith, J. S.: The Irreducible Tensor Method for Molecular Symmetry Groups. Prentice-Hall, Englewood Cliffs NJ 1962

    Google Scholar 

  57. Jucys, A. P., Bandzaitis, A. A.: Theory of Angular Momentum in Quantum Mechanics (in russian). Mokslas, Vilnius 1977

    Google Scholar 

  58. Hellwege, K. H. (ed.): Numerical Tables for Angular Correlation Computations... (Landolt-Börnstein. New Series. Vol. I/3). Springer, Berlin-Heidelberg-New York 1968

    Google Scholar 

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Authors and Affiliations

  1. Departments of Inorganic and Physical Chemistry, Slovak Technical University, CS-812 37, Bratislava, Czechoslovakia

    Roman Boča, Martin Breza & Peter Pelikán

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  1. Roman Boča
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  2. Martin Breza
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  3. Peter Pelikán
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© 1989 Springer-Verlag

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Boča, R., Breza, M., Pelikán, P. (1989). Vibronic interactions in the stereochemistry of metal complexes. In: Stereochemistry and Bonding. Structure and Bonding, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50775-2_2

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  • DOI: https://doi.org/10.1007/3-540-50775-2_2

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  • Print ISBN: 978-3-540-50775-8

  • Online ISBN: 978-3-540-46083-1

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