Electronically nonadiabatic processes

W. H. Miller In treating electronically nonadiabatic processes one often introduces (usually on physical grounds) a diabatic model, which has a nondiagonal electronic potential matrix, and then neglects any remaining derivative coupling. The total (vibronic) wave function is... 

Thus, as long as the interference phenomena are suppressed, the quasiclassical method yields a reasonable qualitative view of the dynamics of elementary processes. We will adopt this view in the forthcoming discussions in the next section it will be shown that the quasiclassical trajectory method can be generalized to treat a large class of electronically nonadiabatic processes. 

One should not be left with the impression that electronically nonadiabatic processes are limited to predissociation. Figure 1(a) shows a crossing between two excited repulsive curves in the photolysis of methyl iodide. If the surface hopping process is efficient enough, it can even influence a dissociating molecule that passes the curve crossing within a few femtoseconds, as is the case for methyl iodide photodissociation. 

What wave packet methods enable one to do is to simultaneously examine the role of both interstate and of intrastate dynamics. This is important because of the increasing attention that is given to electronically nonadiabatic processes in photodissociation (87,88) and other experiments where the motion of the atoms is also of prime interest. 

The electronic nonadiabatic process, k, is frequently used to prepare vibrationally excited ground electronic state molecules and is discussed in more detail in the next chapter. 

In the Born-Oppenheimer approximation nuclei move on the single potential energy surface created by the faster moving electrons. This approximation works so well that is at the heart of the way we think about nuclear motion. Processes in which the Born-Oppenheimer approximation breaks down are known as electronically nonadiabatic processes. Despite the reverence duly accorded the Born-Oppenheimer approximation, electronically nonadiabatic processes are ubiquitous. Indeed the study of nonadiabatic processes goes back almost far as the Born-Oppenheimer approximation itself. It is useful to group nonadiabatic processes into... 

Let us loosely define processes requiring two or more potential energy surfaces as electronically nonadiabatic processes. More specific well-known examples of electronically nonadiabatic processes include the cis-trans photoisomerization induced upon absorption of a photon by the rhodopsin molecule... 

This method can be applied to electronically nonadiabatic processes if in some region of nuclear configuration space the siufaces are strongly brought together. The method of "jumps" between potential energy surftices is usually used for the description of these processe. 

Another topic in the classical treatment of reactive collisions which has advanced considerably in recent years concerns the treatment of electronically nonadiabatic processes. Early work on this topic followed either the semiclassical complex trajectory method of George and Miller,or the more approximate surface hopping model of Tully and Preston.Recent work in this field by McCurdy, Meyer, and Miller " has attempted to develop a purely classical description of the electronic degrees of freedom, thereby replacing the many-surface aspect of the dynamics with extra classical degrees of freedom (one for each surface beyond the first) which represent the collective electronic motions to which the nuclear motions can couple to cause transitions. This means that a multiple-surface problem can now be treated by standard" trajectory methods, which is a considerable computational simplification. Applications to the f ( Pi/2) 2... 

Yarkony D R 1995 Electronic structure aspects of nonadiabatic processes in polyatomic systems Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 642-721... 

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. 

We now turn to an example of nonadiabatic chemistry where the nonadiabatic process starts on the ground state, and is followed by an excursion upward onto the excited state electron transfer (see references 2-5). 

Han S, Yarkony DR (2003) Nonadiabatic processes involving three electronic states. I. Branch cuts and linked pairs of conical intersections. J Chem Phys 119 5058... 

Using this model they have tried to look at important chemical processes at metal surfaces to deduce the role of electronic nonadiabaticity. In particular, they have tried to evaluate the importance of electron-hole-pair excitation in scattering, sticking and surface mobility of CO on a Cu(100) surface.36,37 Those studies indicated that the magnitude of energy transferred by coupling to the electron bath was significantly less than that coupled to phonons. Thus the role of electron-hole-pair excitation in... 

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 this way the mass polarization term may be removed from the Hamiltonian. However, the resulting electronic wave functions which are obtained are then dependent upon the nuclear masses as well as the nuclear charges and such wave functions are an inconvenient basis from which to investigate nonadiabatic processes. 

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