Vibronic interactions in the stereochemistry of metal complexes

  • Roman Boča
  • Martin Breza
  • Peter Pelikán
Conference paper
Part of the Structure and Bonding book series (STRUCTURE, volume 71)


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.


Irreducible Representation Symmetry Point Group Vibronic Coupling Vibronic Interaction Electron Degeneracy 
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.

Symbols and Abbreviations


symmetry of vibration


symmetry of electron state; vibronic constant


adiabatic potential surface


Angular Overlap Model


symmetry of vibration


symmetry of electron state; vibronic constant


matrix of coupling coefficients


Clebsh-Gordan coefficient


Complete Neglect of Differential Overlap


symmetry of vibration


symmetry of electron state; energy, eigenvalue of Schrödinger equation


nuclear (vibration) function

Fi, Fij, Fijk...

pure nuclear term of force constants


symmetry point group


nonadiabatic coupling operator




matrix element of Hamiltonian

Ki, Kij, Kijkl...

force constants


Linear Combination of Atomic Orbitals


mass of nucleus


Molecular Orbital


group order


nuclear coordinate


electron coordinate; radial (polar) coordinate; distance

\(\hat R\)



trace of matrix V


symmetry of vibration


symmetry of electron state

\(\hat T\)

Kinetic energy operator


interaction potential

\(\hat V\)

potential energy operator

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

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


reduced matrix element

Xi, Xij, Xijk...

electron-nuclear term of force constants; vibronic constant

Yj, m

spherical harmonics with m and j quantum numbers


vibronic constant


component of irreducible representation Γ


representation of symmetry


Kronecker delta


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


angular coordinate; component of E representation


radial coordinate, Jahn-Teller radius


angular coordinate


electronic wave function

nabla operator


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Roman Boča
    • 1
  • Martin Breza
    • 1
  • Peter Pelikán
    • 1
  1. 1.Departments of Inorganic and Physical ChemistrySlovak Technical UniversityBratislavaCzechoslovakia

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