Diabatic coupling

The problem of branching of the wavepacket at crossing points is very old and has been treated separately by Landau and by Zener [H, 173. 174], The model problem they considered has the following diabatic coupling matrix ... 

An equivalent foiiti of Eq. (31) can be obtained by inserting Eq. (30) into Eq. (15). Comparison of the result with Eq. (31) furnishes the following relations between the adiabatic and diabatic coupling matrices... 

The direction of X2 is parallel to the direction g of the diabatic coupling matrix mentioned above... 

Here and V( are the terms of initial and final states, the diabatic coupling. We have explicitly added the counterterm YCjQ /lcoj in order to cancel the adiabatic renormalization caused by vibrations. We shall consider the particular case of two harmonic diabatic terms,... 

It is to be emphasized that, despite the formal similarity, the physical problems are different. Moreover, in general, diabatic coupling is not small, unlike the tunneling matrix element, and this circumstance does not allow one to apply the noninteracting blip approximation. So even having been formulated in the standard spin-boson form, the problem still remains rather sophisticated. In particular, it is difficult to explore the intermediate region between nonadiabatic and adiabatic transition. 

Zhu and Nakamura treated the two-state time-independent linear potential model (two linear diabatic potentials coupled by a constant diabatic coupling)... 

The formulas derived in the time-independent framework can be easily transferred into the corresponding time-dependent solutions. The formulas in the time-independent linear potential model, for example, provide the formulas in the time-dependent quadratic potential model in which the two time-dependent diabatic quadratic potentials are coupled by a constant diabatic coupling [1, 13, 147]. The classically forbidden transitions in the time-independent framework correspond to the diabatically avoided crossing case in the time-dependent framework. One more thing to note is that the nonadiabatic tunneling (NT) type of transition does not show up and only the LZ type appears in the time-dependent problems, since time is unidirectional. 

To Specify the off-diagonal elements 14 / of the diabatic potential matrix, we consider two cases of the diabatic coupling Vkk/ which are of particular interest in molecular physics ... 

Mulliken-Hush formula for the diabatic electronic coupling. We suggest that the latter approach might be rather useful to thoroughly investigate multistate effects on the electronic diabatic coupling recently pursued by Cave and co-workers [66]. 

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