Transmission probability, nonadiabatic

A and A = 0.1 eV. The adiabatic ground potential energy surface is shown in Fig. 11. The present results (solid line) are in good agreement with the quantum mechanical ones (solid circles). The minimum energy crossing point (MECP) is conventionally used as the transition state and the transition probability is represented by the value at this point. This is called the MECP approximation and does not work well, as seen in Fig. 10. This means that the coordinate dependence of the nonadiabatic transmission probability on the seam surface is important and should be taken into account as is done explicitly in Eq. (18). 

Figure 4 Effects of nonadiabatic coupling on transmission probability. Solid line nonadiabatic tunneling, dash line single adiabatic potential tunneling. T 2 is the probability and k is the wave number. (From Ref. 37.)...

Figure 13 Nonadiabatic tunneling (transmission) probability P12 = S,2 2 as a function of energy...

FIGURE 5.2 Transmission probability vs. energy. The oscillatory curve (solid line) corresponds to the nonadiabatic tunneling with the nonadiabatic coupling with the excited state taken into account. The monotonous curve (dotted line) is the ordinary transmission probability with the coupling neglected. 

The physically meaningful overall transmission probability, namely, the nonadiabatic tunneling probability, is given by... 

FIGURE 5.5 Overall transmission probability versus energy in the nonadiabatic tunneling type potential system [see Equation (5.52)]. Dots exact solid line Zhu-Nakamura formula (adiabatic) dashed hne Zhu-Nakamura formula (diabahc). (a) a =0.1 (diabatic). (b) a — 1.0. (c) = 10.0. Ei(Ef,) represents the top (bottom) of the lower (upper) adiabatic potential. 

In fact, such probability is < 1, if there are changes in the electronic state of the system. For instance, if systems of atoms move from one potential energy surface to another, which means that the reaction is nonadiabatic in the quantum mechanical sense. So far qualitative treatment of transmission coefficients is available only for simple cases with very little practical application to reactions on surfaces. Formally the expression for the rate constant should be completed with a transmission coefficient %, the value is often around KF6. 

The reference points Xl<2 to define the elastic scattering phases (Eqs. (123)) are Xt = r and X2 = di (see Fig. 10). The factors gx and g2 are introduced empirically in order to cover the whole range of coupling strength. These are unity and zero, respectively, in the original formulation. The overall transmission (nonadiabatic tunneling) probability P12 is explicitly expressed as (see Eq. (74))... 

In many cases the sudden changes in the electronic state, i.e., the nonadiabatic transitions from a lower to a higher potential energy surface, have to be taken into account /3/- The reflection in the curvilinear part of the reaction path may also considerably influence the reaction probability. Therefore, the introduction of a transmission coefficient ( < 1) in the rate equation ( A) is necessa-... 

If Pad in Eq. (116) is unity, the reaction is adiabatic, which corresponds to a transmission coefficient, k = 1, in the absolute reaction rate expression. If Pad is less than unity, the probability of a nonadiabatic process, Pnonad [cf. Eq. (117)], is not zero, and then the transmission coefficient, k, becomes less than unity. 

If an electron transfer does not accompany an attainment of the transition state in each case (nonadiabatic process), an additional factor appears in formula (3.24). This is the transmission coefficient 3 < 1, which takes into account the electron transfer probability. 

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