Coupling element

As shown in Eq. (92), the gauge field aJ is simply related to the non-adiabatic coupling elements For an infinite set of electtonic adiabatic states [A = 00 in Eq. (90)], Ftc = 0. This important results seems to have been first established... 

These coupling elements are 3(lVnu — l)-dimensional vectors. If the Cartesian components of Rx in 3(A u — 1) space-fixed nuclear congifuration space are... 

The electronic wave function has now been removed from the first two terms while the curly bracket contains tenns which couple different electronic states. The first two of these are the first- and second-order non-adiabatic coupling elements, respectively, vhile the last is the mass polarization. The non-adiabatic coupling elements are important for systems involving more than one electronic surface, such as photochemical reactions. 

In the adiabatic approximation the form of the total wave function is restricted to one electronic surface, i.e. all coupling elements in eq. (3.12) are neglected (only the terms with i = i survive). Except for spatially degenerate wave functions, the diagonal first-order non-adiabatic coupling element is zero. 

Czader A, Bittner ER (2008) Calculations of the exciton coupling elements between DNA bases using the transition density cube method. J Chem Phys 128 035101... 

Polyurethanes are used in a wide variety of applications, seals, metal forming dies, liners, coupling elements, rollers, wheels and conveyor belts being examples. The thermoplastic polyurethanes are used as cable jacketing materials, conduits, fabric coatings, in ski boots and other rigid boot soles, automotive body components, gear wheels and other business machine parts. 

A semi-classical treatment171-175 of the model depicted in Fig. 15, based on the Morse curve theory of thermal dissociative electron transfer described earlier, allows the prediction of the quantum yield as a function of the electronic matrix coupling element, H.54 The various states to be considered in the region where the zero-order potential energy curves cross each other are shown in the insert of Fig. 15. The treatment of the whole kinetics leads to the expression of the complete quenching fragmentation quantum yield, oc, given in equation (61)... 

A higher level of understanding would require a knowledge of molecular dynamics and presently represents a rather distant goal. In addition to reliable knowledge of the shapes of potential energy hypersurfaces, it would also require information such as vibronic coupling elements, densities of vibrational states, detailed mechanism of the action of the heat bath, etc. 

In general, the coupling elements make communication of the outside world with the waveguide possible and are used to monitor the above-mentioned effective refractive indices. 

Fig. 15.4 Two common light coupling elements used for waveguides (a) a prism and (b) a grating...

Fiereby, Vq refers to the maximal electronic coupling element and p is the decay coefficient factor (damping factor), which depends primarily on the nature of the bridging molecule. From the linear plot of In ETmax versus R the p value is obtained as 0.60 A [47]. This p value is located within the boundaries of nonadiabatic ET reactions for saturated hydrocarbon bridges (0.8-1.0 A ) and unsaturated phenylene bridges (0.4 A ) [1-4,54,55]. 

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