Electronically adiabatic process

Of course, the degree of non-adiabatic character in the electron-exchange process is an intrinsic property, independent of the wavefunction representation used to describe it. For example, in terms of t f+ and t f, an electronically adiabatic process is one which can be analyzed in terms of a single adiabatic... 

Within the quasiclassical approach the nuclei are considered to be subject to a classical motion in the field of force, the potential of which is given by the energy pertinent to one of the eigenstates of the electronic subsystem. In the case of electronically adiabatic processes, the field of force for the nuclear motion is determined by a single potential energy surface (pertinent to a single electronic state). 

Where the intermolecular potentiais are of the kind shown in Figure 6, the expression for the transition probability, again includes a vibrational matrix element of a similar form to that in equation (48). In the electronically adiabatic processes that were considered earlier, transition probabilities are extremely small, because enagy transfer requires a tunnelling process to carry the system between the parallel curves representing neighbouring vibronic states within the same electronic manifold. Now, however, curves cross and is replaced by a... 

Elementary processes can be classified as electronically adiabatic and nonadiabatic processes. The sense of the idea "electronically adiabatic process" is clear these are the processes that occur without a change in the electronic state of the system. This is precisely the class of processes for which we can remain in the framework of the adiabatic approximation. However, there are nonadiabatic processes for which the electronic state of the system changes. In the general case it is difficult to predict what processes are electronically adiabatic and what are nonadiabatic. It is clear from qualitative concepts that the higher the difference between the characteristic times of the electron and nuclear motions of the system, the better the description of the system by the adiabatic approximation. 

A comer-stone of a large portion of quantum molecular dynamics is the use of a single electronic surface. Since electrons are much lighter than nuclei, they typically adjust their wavefiinction to follow the nuclei [26]. Specifically, if a collision is started in which the electrons are in their ground state, they typically remain in the ground state. An exception is non-adiabatic processes, which are discussed later in this section. 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

Chemical processes, such as bond stretching or reactions, can be divided into adiabatic and diabatic processes. Adiabatic processes are those in which the system does not change state throughout the process. Diabatic, or nonadiabatic, processes are those in which a change in the electronic state is part of the process. Diabatic processes usually follow the lowest energy path, changing state as necessary. 

Caro s acid is finding increasing appHcation ia hydrometaHurgy, pulp bleaching, effluent treatment, and electronics. There are several appHcations of Caro s acid ia hydrometaHurgy. It is usually made on-site by either the isothermal or the adiabatic process. The latter method is preferred because its capital cost is less and the system is safer due to the fact that the product is used as soon as it is made. 

The electron capture processes are driven by non-adiabatic couplings between molecular states. All the non-zero radial and rotational eoupling matrix elements have therefore been evaluated from ab initio wavefunctions. 

The effects of deviations from the Born-Oppenheimer approximation (BOA) due to the interaction of the electron in the sub-barrier region with the local vibrations of the donor or the acceptor were considered for electron transfer processes in Ref. 68. It was shown that these effects are of importance for long-distance electron transfer since in this case the time when the electron is in the sub-barrier region may be long as compared to the period of the local vibration.68 A similar approach has been used in Ref. 65 to treat non-adiabatic effects in the sub-barrier region in atom transfer processes. However, nonadiabatic effects in the classically attainable region may also be of importance in atom transfer processes. In the harmonic approximation, when these effects are taken into account exactly, they manifest themselves in the noncoincidence of the... 

If the EDA and CT pre-equilibria are fast relative to such a (follow-up) process, the overall second-order rate constant is k2 = eda c e In this kinetic situation, the ion-radical pair might not be experimentally observed in a thermally activated adiabatic process. However, photochemical (laser) activation via the deliberate irradiation of the charge-transfer absorption (hvct) will lead to the spontaneous generation of the ion-radical pair (equations 4, 5) that is experimentally observable if the time-resolution of the laser pulse exceeds that of the follow-up processes (kf and /tBet)- Indeed, charge-transfer activation provides the basis for the experimental demonstration of the viability of the electron-transfer paradigm in Scheme l.21... 

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