Transition vector

Fig. 18. Hypothetical orientation of the flavin photoreceptor within the plasma-lemma in cells of Funaria leaves202, based on known angles of flavin transition vectors in the blue105)...

The change in permanent and induced dipole moments might induce an electrical signal for transfer in a given direction indicated by the change in the transition vector. 

There are significant differences in the polarization directions of absorption and emission spectra for two types of transition. In the case of cyclic compounds, like pyridine, the transition vectors lie in the plane of the molecule for - n transition hut perpendicular to it for / - w transition. 

Fukui s reaction path, corresponding to a vibrationless and rotationless trajectory, passes gradually into the normal decomposition mode of the reactants (or products) or into the transition vector of the activated complex. Strictly speaking, Fukui s concept requires the knowledge of an accurately localized saddle point. However, it is also possible to exploit Fukui s procedure for approximately localized saddle points these points are usually obtained by an independent method. The respective resulting path is then an approximation to the real intrinsic reaction path. 

Roca and coworkers next examined the potential coupling between the reactants and the COMT enzyme. Employing the same computational methods as in the previous paper, they carried out a 600-ps MD trajectory with the system constrained to remain near the TS. Using the geometry at every 50 ps, they optimized true TS structures and determined their transition vectors. An average of these vectors showed a near complete dominance of motion that one associates with the Sn2 reaction and little motion in the rest of the QM or MM regions. 

The electronic transition moment can be easily calculated on the basis of further simplifications that will be introduced in Section 4.4. For symmetrical molecules, group theory provides a simple tool for predicting which, if any, of the three components (x, y or z) of the electronic transition vector Mc , m are different from zero (Section 4.4). The effect of vibrational overlap will be considered in Section 2.1.9. 

Steady-State Anisotropy Following continuous excitation with vertically polarized light, a distribution of fluorophores whose transition vectors for the absorption process are vertically aligned will be photoselected, creating an excited state population, which possesses a degree of anisotropy (r) or optical order, in an otherwise isotropic distribution of fluorophores. Measurement of the intensity of fluorescence, via an emission polarizer in planes parallel (z n) and perpendicular (zx) to the vertical plane allows estimation of r from... 

The comparison of the geometries of the located transition states and the analysis of the transition vectors allow one to obtain a deeper insight into the... 

In Figure 2.20b these transition structures locate the energy ridges that separate the IRD valleys located by Mi and Mg. Thus, although there is no analogue of the transition vector for a conical intersection, the simple case of an elliptic cone shows that the IRDs are still uniquely defined in terms of Ml and Mg. 

We will now recast this amplitude into a form that is more convenient for RRGM calculations. It may not be obvious, but this transition amplitude can be written in terms of the difference between two survival amplitudes. This result can be shown as follows. If we define two orthonormal transition vectors, w ) = [ i) + /)]/ /2, and v ) = [ i) - /)]/V/2, then the transition amplitude can be expresed as... 

Here a is the fine-structure constant ( 1/137), g(2w) the line shape function, and the two-photon transition probability tensor, which is the counterpart of the transition vector in one-photon spectroscopy. For electric dipole transitions, by far the most important ones, Sg may be written as... 

The operator governing 8 is thus not a transition vector, but rather a transition tensor, which may be represented by a 3x3 matrix. Matrix elements are of the form... 

Before this development took place the definition of the reaction pathway on the surface, with the concomitant characterization of the transition state had solicited considerable attention. Fukui [191] contributed the idea of the intrinsic reaction coordinate (IRC), but earlier Murrell [192] had discussed the possible symmetries of transition states. This would turn up again in Salem s [193] treatment of the so-called narcissistic reactions. Stanton and Mclver [194] and Pechukas [195] formulated general symmetry conditions for the transition vector. It was thought that symmetry could bring... 

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