Jahn-Teller effect calculation

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. 

Ballhausen, C. and H. Johansen Molecular-orbital calculation of static Jahn-Teller effect in CuFg. Mol. Phys. 10, 183 (1966). 

In paper [49] various models of the active site of metal-containing enzyme glutathion-transferase having structures with five and six coordinated ions Mn + and Fe + are explored. In both cases it is assumed, that the respective metal ion is in its HS state. It essentially facilitates calculation since such a ground state can be reasonably modelled by a single-configuration (HER) wave function. Structural studies of the Jahn-Teller effect in TMCs by the ab initio CC methods are performed in [50,51]. 

The preceding three reduced molybdenum clusters indicate that rhomboidal cluster units are common among this kind of oxide, and the Mo-Mo distances in the cluster units are dependent on CVE assignable to the Mo4 units. MO calculations on Mo4 molecular cluster compounds containing 10 CVE and 8 CVE have shown that the 8-electron clusters distort from a second-order Jahn-Teller effect (116). Such a distortion has been observed in the 8-electron W4(OEt)16 (117). 

All the off-diagonal matrix elements of the spin-orbit coupling in the >, Tl> [ basis are thus reduced by the factor y, and we use the experimentally observed quenching to calculate Ej j and the corresponding geometrical distortion (14). In the Cs2NaYClg host lattice the total spread of the four spin-orbit components of T2 is 32 cm whereas crystal field theory without considering a Jahn-Teller effect predicts a total spread of approximately 107 cm-. ... 

In the present paper we assume that the molecule has the icosahedral symmetry. If one wants to consider a distortion of C 0+ or Cb0. the energy levels and their eigenvectors obtained here can be used as a starting point for the description of the Jahn-Teller effect in these systems. Indeed, the electron-phonon (or vibronic) coupling occurs if [.Tei]2 contains Fvib [19]. (Here Fd is the symmetry of an electronic molecular term, while J b is the symmetry of a vibrational normal mode.) Calculations using the terms in scheme of Ref. [4] have been performed in Ref. [20]. 

It seems natural to suppose that the tetragonal distortion of the tri-anion results from the Jahn-Teller effect. In order to study the problem more thoroughly we undertook recently the DFT calculations of this cluster as well as of several other hexanuclear rhenium chalcohalide clusters. The technical details of these calculations can be found in the original publication [8]. Here we only want to note that the introduction of relativistic corrections for Re atoms is crucial for the correct reproduction of the geometry of clusters. In our calculations, this was done by the zero order regular approximation (ZORA) Hamiltonian [9] within ADF 2000.02 package [10]. 

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