MMVB method

Ehrenfest dynamics with the MMVB method has also been applied to the study of intermolecular energy transfer in anthryl-naphthylalkanes [85]. These molecules have a naphthalene joined to a anthracene by a short alkyl —(CH)n— chain. After exciting the naphthalene moiety, if n = 1 emission is seen from both parts of the system, if n = 3 emission is exclusively from the anthracene. The mechanism of this energy exchange is still not clear. This system is at the limits of the MMVB method, and the number of configurations required means that only a small number of trajectories can be run. The method is also unable to model the zwitterionic states that may be involved. Even so, the calculations provide some mechanistic information, which supports a stepwise exchange of energy, rather than the conventional direct process. 

In principle, one can carry out the analysis of conical intersections for any problem of n electrons and n orbitals in the manner discussed in the previous section. However, it does get increasingly rather complicated. Nevertheless, the 6 orbital with 6 electrons problem merits discussion because the VB structures of benzene in ground and excited states is such a fundamental part of basic chemistry. Accordingly, in other work, our strategy was to determine the complete space of Sq/Si conical intersections for benzene" and to analyze the computed conical intersection stmctures obtained at the ab initio level using the MMVB method. One could then deduce the VB analysis a posteriori by comparison with various theoretical hypotheses about the nature of the intersecting states. 

Now let us turn to a much more difficult problem the 8 orbitals with 8 electrons photochemical addition of ethylene to benzene (Figure 3.23). At first sight this system would seem intractable for the VB approach. And, in fact, it is not easy to get analytical results such as those obtainable for the 6 orbitals with 6 electrons problem. Accordingly, our strategy, similar to the 6 orbitals with 6 electrons case, is to analyze the computed conical-intersection structures obtained at the ab initio level using the MMVB method and thus deduce the VB analysis. The end result rationalizes a complicated reaction mechanism (more than 10 MECI were located) quite simply as we will now discuss. The details can be found in our recent... 

In the preceding sections we show that, by postulating simple VB structures on a photochemical reaction path, one can deduce not only that a conical intersection may be involved but also the nature of the branching space of the conical intersection. For problems such as 3 orbitals with 3 electrons or 4 orbitals with 4 electrons it is simple to manipulate the VB matrix elements to make these deductions. By the time one gets to 6 orbitals with 6 electrons there are very many possibihties. So one has to leam " by extracting the VB structures from the ab initio data. For the 6 orbitals with 6 electron case, we use the MMVB method to do this. Once the more important structures are identified this way, we can perform the manipulations analytically to confirm the result by comparison with numerical data. Finally, for 8 orbitals with 8 electrons we were able to show that one may also extract the VB data from the MMVB method and come to understand the nature of the conical intersection. However, it is rather tedious to do the calculations analytically and this work has never been carried out. 

Bearpark MJ et al (2006) Excited states of conjugated hydrocarbons using the molecular mechanics-valence bond (MMVB) method Conical intersections and dynamics. Theor Chem Acc 116 670-682... 

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