Jahn Teller problems

The Exe Jahn-Teller problem, described by Eq. (7) or (8), plus an additional nuclear term /io(Q), common to the two electronic states, is the prototype for all... 

The simplest way to write down the 2 x 2 Hamiltonian for two states such that its eigenvalues coincide at trigonally symmetric points in (x,y) or (q, ( )), plane is to consider the matrices of vibrational-electronic coupling of the e Jahn-Teller problem in a diabatic electronic state representation. These have been constructed by Haiperin, and listed in Appendix TV of [157], up to the third... 

The cyclopentadienyl radical and the cyclopentadienyl cation are two well-known Jahn-Teller problems The traditional Jahn-Teller heatment starts at the D k symmetry, and looks for the normal modes that reduce the symmetry by first-01 second-order vibronic coupling. A Longuet-Higgins treatment will search for anchors that may be used to form the proper loop. The coordinates relevant to this approach are reaction coordinates. 

Fig. 1. Conical intersection surface topologies (top), and Renner-Teller surface topologies (bottom). Top left is a generic circular cone, such as is obtained from a Jahn-Teller problem involving only the linear vibronic coupling. Top right is a sloped conical intersection obtained in a general vibronic coupling problem where all three linear vibronic coupling constants are different. Bottom left to right show type-1, -II, -III Renner-Teller surfaces. These are obtained when only second-order vibronic coupling is included.

The conventional procedure is to retain only the linear term in the expansion (8-3). It should be noted that while the indicated truncation may be justified in the Jahn-Teller problem, it is likely not to be as accurate in our case, where molecular wavefunctions at large nuclear displacements must be considered. In this context, it is interesting to draw the reader s attention to a classical calculation of the force constants for nuclear displacement in the excited electronic states of aromatic molecules.133 It... 

General considerations of the butterfly geometry (opening (C2v)) of the 62-electron tetra nuclear metal clusters are given in Ref. [10] by solving the (A + T2) X (e + t2) Jahn-Teller problem. 

Magnetic Properties of a d5 Complex A Jahn-Teller Problem... 

In previous work we have shown how this embedding of the icosahedron in can be used to resolve the product multiplicity in the icosahedral H (g + 2h) Jahn-Teller problem [10,20]. In the context of atomic spectroscopy, Judd and Lo have made use of the connection to explain some puzzling degeneracies in the... 

In some situations, especially in the BO approximation, the term vibronic coupling is identical to non-adiabatic coupling. In the Jahn-Teller theory, however, the concept of vibronic coupling is different from that of non-adiabatic coupling. To clarify the difference, we discuss the adiabatic approximation in the i (8> e dynamic Jahn-Teller problem [27] in the strong coupling limit [32]. In this subsection, we employ... 

Acknowledgements TS gratefully acknowledges Prof. Arnout Ceulemans and Prof. Liviu F. Chibotaru for valuable discussions on the dynamic Jahn-Teller problem and vibronic couplings in fullerene ions. Numerical calculation was partly performed in the Supercomputer Laboratory of Kyoto University and Research Center for Computational Science, Okazaki, Japan. This work was supported by Grant-in-Aid for Scientific Research (C) (20550163), Priority Areas Molecular theory for real system (20038028) from Japan Society for the Promotion of Science (JSPS), and the JSPS-FWO (Fonds voor Wetenschappelijk Onderzoek-Vlaanderen) Joint Research Project. 

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