Coupling of electronic states

Nakamura and Truhlar [26] have developed direct calculation techniques to obtain quasi-diabatic states. Yet, a main issue remains there is no clear quantum-mechanical interpretation as to the meaning of an electronic wave ftinction that depends parametrically on the positive charge positions [4]. The multi-electronic-state molecular dynamics approach by Martinez et al. [27] highlights the problems raised by the use of the BO scheme. The crossing points and the uncontrolled coupling of electronic states... 

Finally, semi-classical approaches to non-adiabatic dynamics have also been fomuilated and siiccessfLilly applied [167. 181]. In an especially transparent version of these approaches [167], one employs a mathematical trick which converts the non-adiabatic surfaces to a set of coupled oscillators the number of oscillators is the same as the number of electronic states. This mediod is also quite accurate, except drat the number of required trajectories grows with time, as in any semi-classical approach. 

In this series of results, we encounter a somewhat unexpected result, namely, when the circle surrounds two conical intersections the value of the line integral is zero. This does not contradict any statements made regarding the general theory (which asserts that in such a case the value of the line integral is either a multiple of 2tu or zero) but it is still somewhat unexpected, because it implies that the two conical intersections behave like vectors and that they arrange themselves in such a way as to reduce the effect of the non-adiabatic coupling terms. This result has important consequences regarding the cases where a pair of electronic states are coupled by more than one conical intersection. 

The electronic wave function has now been removed from the first two terms while the curly bracket contains tenns which couple different electronic states. The first two of these are the first- and second-order non-adiabatic coupling elements, respectively, vhile the last is the mass polarization. The non-adiabatic coupling elements are important for systems involving more than one electronic surface, such as photochemical reactions. 

An alternative to the traditional approach is to generate the electronic states as needed during the dynamics. This has been done for atomic collisions, where detailed calculations and comparisons with experimental results are possi-ble.(4-8) General treatments of the coupling of electronic and nuclear motions in molecular systems can be done in a variety of formulations. In particular, Ohrn, Deumens and collaborators have implemented a general variational treatment in... 

Let us consider the possible relations of LS and HS potential energy surfaces as shown schematically in Fig. 9. As long as the zero-order or diabatic surfaces are considered, the eleetrons remain localized on the particular spin state, no eleetron transfer being possible. In order that a conversion between the LS and HS state takes place, electronic coupling of the states is required. This coupling effectively removes the degeneracy at the interseetion of the zero-order surfaces... 

In the previous section, we discussed the calculation of the PESs needed in Eq. (2.16a) as well as the nonadiabatic coupling terms of Eqs. (2.16b) and (2.16c). We have noted that in the diabatic representation the off-diagonal elements of Eq. (2.16a) are responsible for the coupling between electronic states while Dp and Gp vanish. In the adiabatic representation the opposite is true The off-diagonal elements of Eq. (2.16a) vanish while Du and Gp do not. In this representation, our calculation of the nonadiabatic coupling is approximate because we assume that Gp is negligible and we make an approximation in the calculation of Dp. (See end of Section n.A for more details.)... 

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