Distortion modes

Figure 29, The effect of the phase-preserving component of the degenerate 2 distorting mode, It may be regarded as a major component of the reaction coordinate that leads to the A] structure (going left, one phase of the mode). Going right, the other phase of the same vibration, the B2 state is formed. (A type-V structure is also obtained along the same coordinate).

A general approach for predicting Jahn-Teller distortions of copper(II) hexa-amines has recently been published, and it has the potential to be applied to donor atoms other than nitrogen, metal centers other than copper(II), and various types of coordination polyhedra11641. The method is based on a harmonic first-order model11651 where the Jahn-Teller stabilization energy is the result of the Qg distortion mode (Fig. 11.1, Eqs. 11.3, 11.4). 

Due to the biochemical importance of porphyrine systems their metal complexes have been modeled extensively. Metalloporphyrines are assumed to be planar but there is a relatively high degree of flexibility, and six low energy distortion modes have been described (Figure 3).127 MM with a variety of force fields has been used to compute the structural and dynamic properties,65 66 128-131 and these studies also include information on the orientation of the axial donors.132 133 Reaction dynamics related to the interaction of substrates with the metal site have also been modeled,134-136 and MM has been used to correlate structural and spectroscopic properties (primarily Raman frequencies).137 138... 

The significance of the symmetry treatment is that it shows explicitly which of the Heilbronner modes are inherently distortive. Any totally symmetric Heilbronner mode corresponds to readjustment of /3 parameters and hence of bondlengths, but without loss of symmetry. Since the point of departure of the model is that the molecule is already in its cr-optimal geometry, such modes can be ignored, and only the non-totally symmetric distorting modes retained. 

Heilbronner mode symmetries have been tabulated for various series of n systems [13]. Some specific results are in unbranched polyenes, the unique Heilbronner mode is either totally symmetric (2/ )-polyene] or has the symmetry of a dipole moment along the chain [(2n + l)-polyene] in 2n -linear acenes the Heilbronner modes span nAg + nB u of D2h, and in [2n + l]-linear acenes have an extra BXu component the Heilbronner modes of the tetrahedron, cube and dodecahedron span E(Td), Eg + T2u(Oh), and //, + Hu(Ih), respectively, reducing the sets of modes to be considered from 2, 5 and 10 to just 1, 2, and 2 independent distortive modes which can be constructed easily by hand . 

A parameterization method of the Hamiltonian for two electronic states which couple via nuclear distortions (vibronic coupling), based on density functional theory (DFT) and Slaters transition state method, is presented and applied to the pseudo-Jahn-Teller coupling problem in molecules with an s2-lone pair. The diagonal and off-diagonal energies of the 2X2 Hamiltonian matrix have been calculated as a function of the symmetry breaking angular distortion modes and r (Td)] of molecules with the coordination number CN = 3... 

The first term, //reflects the linear coupling between the electronic state (displayed by lajg) and 1// )) and the E distortion mode [1-3]... 

Lipkowitz, K.B. and Schefzick, S. (2002) Ligand distortion modes leading to increased chirality content of Katsuki—Jacobsen catalysts. Chirality, 14, 677. 

FIGURE 6.22 Generation of a conical intersection (CI) by crossing of the twin states along the bending distortion mode, (a) in H3 and (b) in SN2 systems. Symmetry labels refer to the mirror plan, m. 

Generally, there is good agreement between the experimentally observed and calculated EPR spectra. Areas, where considerable errors resulted from a large variation of the g-values as a function of a specific distortion mode, were identified by model AOM calculations of the g-values as a function of the corresponding distortion mode. Two structural problems were addressed with the MM-AOM method applied to low spin iron(III) ... 

To emphasize the importance of structural studies at LT or HP, let us take the example of TTF-TCNQ. This prototype charge density wave (CDW) system undergoes at ambient pressure a succession of three structural and electronic phase transitions, from a high-temperature metallic phase down to a low-temperature insulator phase. There has been a considerable debate about the mechanism of these transitions, and many distortional modes have been proposed to account for the physical properties of this material (e.g., rigid molecule displacement as translations [73,74] or librations [75,76] or even internal deformations of the molecules [77,78]. Indeed, an experi-... 

The cooperative Jahn-Teller type interaction is obtained by the orbital-lattice coupled model [12,13]. Let us consider the Hamiltonian with the Jahn-Teller coupling g, the kinetic energy and the lattice potential for the Jahn-Teller phonon mode, the orbital-strain interaction, and the elastic-strain energy. The Jahn-Teller distortion mode Qi around a metal site i is represented by the Jahn-Teller phonon coordinates k- By introduce the canonical transformation for k, the orbital and lattice degrees of freedom are separated. The final form of the interaction between the inter-site orbitals given by... 

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