Nonadiabatic effects

Thus, we have shown that nonadiabatic effects can be important in problems such as electron transfer where excited and ground states may be close together. We believe that future investigations in this area will be fruitful. 

INTERACTIONS OF VIBRATION ALLY-EXCITED MOLECULES AT SURFACES A PROBE FOR ELECTRONICALLY NONADIABATIC EFFECTS IN HETEROGENEOUS CHEMISTRY... 

Fig. 3(b). The stunning agreement between experiment and theory suggests that electronically nonadiabatic effects strongly influence this reaction. 

Nonadiabaticity Effects in Processes Involving Transfer of Atoms and Atomic Groups... 

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... 

In the process considered above, the corrections due to nonadiabaticity effects lead to an increase of Fa and to a decrease of cr. However, the first effect is greater than the second, and the joint... 

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

In Table II we also compare our total variational energies with the energies obtained by Wolniewicz. In his calculations Wolniewicz employed an approach wherein the zeroth order the adiabatic approximation for the wave function was used (i.e., the wave function is a product of the ground-state electronic wave function and a vibrational wave function) and he calculated the nonadiabatic effects as corrections [107, 108]. In general the agreement between our results... 

The effective hamiltonian in formula 29 incorporates approximations that we here consider. Apart from a term V"(R) that originates in nonadiabatic effects [67] beyond those taken into account through the rotational and vibrational g factors, other contributions arise that become amalgamated into that term. Replacement of nuclear masses by atomic masses within factors in terms for kinetic energy for motion both along and perpendicular to the internuclear axis yields a term of this form for the atomic reduced mass. 

In this section, we will present examples of the concerted ET reduction of the 0—0 bond in a number of simple alkyl peroxides (RO-OR) and endo-peroxides. These systems provide the first clear examples of the parabolic activation/driving force relationships. The necessary background is provided in the section below. The data provided by the peroxide systems also allow us to introduce important new insights into concerted dissociative processes, particularly the importance of steric and nonadiabatic effects. Finally, data for perbenzoates, another peroxide system related to the early studies, provide evidence for the transition between the concerted and stepwise dissociative mechanisms. 

In a condensed system, the local field on a magnetic spin can be considered as a stochastic process. If a constant magnetic field H0 is present in the z-direction, the local field H( ) can be decomposed into the parallel and the perpendicular components. If the constant field is strong enough, this decomposition is meaningful the parallel component Hz(t) causes adiabatic shifts of the resonance frequency, whereas the perpendicular component H t) produces nonadiabatic effects.6 If only the adiabatic part is considered, the problem is just that treated in Section II, and if the local field Hz(t) is assumed to be a Gaussian process, then the Gaussian model of Section III can be adopted. 

When the constant field is weak and the fluctuating field is comparable to or even larger than the constant field, the above decomposition becomes meaningless. There is no way of distinguishing between the adiabatic and nonadiabatic effects. In order to obtain an understanding of this rather complex situation, we have examined a stochastic model,14 extending the theory in Section II. The stochastic equation of motion of a spin in a random local field is written as... 

V. Engel You showed the plot of the Nal molecule, which is a system with a curve crossing. The treatment of classical mechanics in such a system is not well defined. What can be done to treat the nonadiabatic effects if you calculate periodic orbits that are then used for interpretation ... 

L. S. Cederbaum Prof. Jungen, you mentioned that MCQDT takes into account nonadiabatic effects. I would like to point out that this approach only considers those nonadiabatic effects that arise due to the motion of the Rydberg electron. The nonadiabatic effects in the ion core are not considered. These effects can often be substantial. 

Ch. Jungen You are quite right. The Renner-Teller effect in the water ion is an example of this kind. The strong vibronic coupling in the core leads to nonadiabatic effects in the Rydberg states of the neutral species, which are of course not accounted for by the coordinate dependence of the quantum defect and have to be taken into account separately. 

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