Transition non-adiabatic

Baer M 1985 The theory of electronic non-adiabatic transitions in chemical reactions Theory of Chemical Reaction Dynamics vol II, ed M Baer (Boca Raton, FL CRC Press) p 281... 

The reason that non-adiabatic transitions must be included for protons is that fluctuations in the potential for the quantum degrees of freedom due to the environment (e.g. solvent) contain frequencies comparable to the transition frequencies between protonic quantum states. In such cases pure quantum states do not persist. 

Berendsen, H.J.C., Mavri, J. Approach to non-adiabatic transitions by density matrix evolution and molecular dynamics simulation. Int. J. Quant. Chem. 57 (1996) 975-984. 

We have therefore shown that adiabatic surfaces can be said to cross off the real coordinate axes, and indeed if the classical equations of motion are solved in complex coordinate space then it is possible to simulate non-adiabatic processes. This can be considered as the basis of the Stuckelberg semi-classical approach to non-adiabatic transitions in atom-atom collisions (64) and it has been recently extended to more degrees of freedom (65). Moreover the actual form of potential surfaces in the complex plane has been obtained by direct calculation (66). 

SEMICLASSICAL SURFACE HOPPING METHODS FOR NON ADIABATIC TRANSITIONS IN CONDENSED PHASES... 

So far, we have considered the dynamics of chemical reactions within the adiabatic approximation. The motion of the atomic nuclei is, however, not always confined to a single electronic state as assumed in Eq. (1.5). This situation can, e.g., occur when two potential energy surfaces come close together for some nuclear geometry. The dynamics of such processes are referred to as non-adiabatic. This is a purely non-classical phenomenon [15]. Examples of reactions that involve non-adiabatic transitions are charge-transfer reactions, i.e., reactions in which charge is transferred between reactants. 

The expression (9) for the non-adiabatic transition probability is correct, naturally, if the phonon spectrum is quasi-continuous one. Moreover, use of Fermi s gold rule or the first order of the perturbation theory on Fif is correct, if the following inequality is realized. 

Now, the non-adiabatic electron transitions is examined only when electron matrix element Fif is small (see the criterion (10) and (10a)). It is the criterion of applicability of the perturbation theory on F f, but it is not the criterion of applicability of the concept of non-adiabatic transition between two crossing diabatic terms. As it is known (see, for example, ref. [5]) the true image of terms is changed on taking into account the interaction V. Denote two terms without inter-term interaction as E[(R) and E (R), where R is the generalized nuclear coordinate. If the crystal phonons (or the outer-sphere variables in a polar medium) only participate in the transition, then E[(R) and E (R) are the parabolic terms independent of the value of shift of... 

The consideration of the reactions of the electron tunneling transfer was until now based on Born-Oppenheimer s adiabatic approach (see Section 2 of Chapter 2) that was used for the description of the wave functions of the initial and final states. The electron tunneling interaction V results in the non-adiabatic transition between these states, if the matrix element Vtf... 

Consider the non-adiabatic transition a — b shown schematically in Figure 5.2, where a and b may denote the electronic states of D A and D A, respectively. To describe the dynamic processes of the system, one starts with the stochastic Liouville equation... 

On the right-hand side of Eq. (3.65), the first, second and third terms describe the dynamic behavior of paca due to the vibronic coherence dynamics, non-adiabatic transitions and vibrational relaxation, respectively. Several cases can be considered. First, if the vibrational relaxation is much faster than electronic processes, then... 

In the previous sections, the expressions for non-adiabatic transitions have been obtained to the first-order approximations. To treat photo-induced energy transfer and photo-induced electronic transfer, to take into account the bridge effect between donor and accepter molecules, the higher order approximations need to be considered. In this case, instead of Eq. (40), the following equation is used ... 

Fig. 5 Adiabatic and non-adiabatic ET processes. In the adiabatic process (Fig. 5a), Vel > 200 cm and the large majority of reaction trajectories (depicted as solid arrows) which reach the avoided crossing region remain on the lower energy surface and lead to ET and to the formation of product (i.e., the electronic transmission coefficient is unity). In contrast, non-adiabatic ET is associated with Vel values <200 cm-1, in which case the majority of reaction trajectories which reach the avoided crossing region undergo non-adiabatic transitions (surface hops) to the upper surface. These trajectories rebound off the right-hand wall of the upper surface, enter the avoided crossing region where they are likely to undergo a non-adiabatic quantum transition to the lower surface. However, the conservation of momentum dictates that these trajectories will re-enter the reactant well, rather than the product well. Non-adiabatic ET is therefore associated with an electronic transmission coefficient which is less than unity.

E. E. Nikitin, Theory of Non-Adiabatic Transitions. Recent Development on the Landau-Zener Model, in Chemische Elementazprozesse edited by H. Hartmann, Springer-Verlag, Berlin, 1968. 

The qualitative features are explained nicely by the theory of non-adiabatic transitions due to Berry (3). Unfortunately the spectra cannot be resolved and identified to yield quantitative data relevant to the ionic-covalent interaction. For alkali halides these interactions are more amenable to atomic beam scattering experiments (4). In contrast the optical spectra of... 

Jortner and Ulstrup have demonstrated that for isothermic atom transfers and for sufficiently high temperatimes, the non-adiabatic transition rate takes the form 49)... 

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