Vibronic couplings Jahn-Teller coupling

Here Pa(a = 6, e) is the momentum conjugate to Qa. In the absence of spin-orbit interaction, the e vibration does not mix the orbital components of the 4T2 g and we have vibrational potential energy surfaces consisting of three separate ( disjoint ) paraboloids in the two-dimensional (2D) space of the Qe and Qe coordinates of the e vibration. The Jahn-Teller coupling leads only to a uniform shift (—ZsPJX = — V2/2fia>2 = —Sha>) of all vibronic levels. 

Here we consider the case that the two excited electronic states <1> and belong to dipole-allowed representations, namely, one to A2 and the other to E, (Zgierski and Pawlikowski, 1979b). In the absence of pseudo-Jahn-Teller coupling between them, the corresponding vibronic wave-functions are of the form... 

Within the approximation of crystal-field theory, the Jahn-Teller coupling constants may be evaluated in a simple way. For example, in the case of E-e vibronic coupling in octahedral MX complexes ... 

The quadratic Jahn-Teller coupling constants can be easily obtained by introducing second derivatives into (76) and (80). The results of d systems for a number of symmetries were published by Bacci and Warren. The vibronic coupling constants can... 

Non-adiabatic coupling is also termed vibronic coupling as the resulting breakdown of the adiabatic picture is due to coupling between the nuclear and electi onic motion. A well-known special case of vibronic coupling is the Jahn-Teller effect [14,164-168], in which a symmetrical molecule in a doubly degenerate electronic state will spontaneously distort so as to break the symmetry and remove the degeneracy. 

The majority of photochemistry of course deals with nondegenerate states, and here vibronic coupling effects aie also found. A classic example of non-Jahn-Teller vibronic coupling is found in the photoelection spectrum of butatiiene, formed by ejection of electrons from the electronic eigenfunctions [approximately the molecular orbitals). Bands due to the ground and first... 

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. 

In the limit of strong vibronic coupling, F4S = 0, c = 5 /3, s=, c2 - s2 =, and the dynamic Jahn-Teller effect thus renders nugatory the orbital contributions to the angular momentum, and reduces the splitting, A, by a factor of two. Note in addition that the c and s quantities used in the vibronic treatment do not correspond to those of the adiabatic case, although the expressions are formally similar, so that the static distortion, A, cannot accurately be calculated from the c and s values deduced from the and 4 data. 

II electronic states, 638-640 vibronic coupling, 628-631 triatomic molecules, 594-598 Hamiltonian equations, 612-615 pragmatic models, 620-621 Kramers doublets, geometric phase theory linear Jahn-Teller effect, 20-22 spin-orbit coupling, 20-22 Kramers-Kronig reciprocity, wave function analycity, 201 -205 Kramers theorem ... 

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