Conical intersections problem

The outline of the remainder of this contribution is as follows. In Section 3.7.2, we discuss radical anion dissociation in solution, in which a conical intersection has an important impact on the ground state reaction barrier, rate constant and reaction path, all of which are also influenced by nonequilibrium solvation. The excited electronic state conical intersection problem for the cis-trans isomerization of a model protonated Schiff base in solution is discussed in Section 3.7.3, focusing on the approach to, and passage through, the conical intersection, and the influence of nonequilibrium solvation thereupon. Some concluding remarks are offered in Section 3.7.4. We make no attempt to give a complete discussion for these topics, but rather focus solely on several highlights. Similarly, the references herein are certainly incomplete. We refer the interested reader to refs [1-9] for much more extensive discussions and references. 

Rather than summarize the discussions of the two conical intersection problems of radical anion dissociation and protonated Schiff base photoisomerization in a nonequilibrium... 

A review article by the top experts in conical intersection problems. 

Other studies have also been made on the dynamics around a conical intersection in a model 2D system, both for dissociahve [225] and bound-state [226] problems. Comparison between surface hopping and exact calculations show reasonable agreement when the coupling between the surfaces is weak, but larger errors are found in the shong coupling limit. 

Conical intersections are involved in other types of chemistry in addition to photochemistry. Photochemical reactions are nonadiabatic because they involve at least two potential energy surfaces, and decay from the excited state to the ground state takes place as shown, for example, in Figure 9.2a. However, there are also other types of nonadiabatic chemistry, which start on the ground state, followed by an ex-cnrsion npward onto the excited state (Fig. 9.2b). Electron transfer problems belong to this class of nonadiabatic chemistry, and we have documented conical intersection... 

Let us summarize briefly at this stage. We have seen that the point of degeneracy forms an extended hyperline which we have illnstrated in detail for a four electrons in four Is orbitals model. The geometries that lie on the hyperline are predictable for the 4 orbital 4 electron case using the VB bond energy (Eq. 9.1) and the London formula (Eq. 9.2). This concept can be nsed to provide nseful qualitative information in other problems. Thns we were able to rationalize the conical intersection geometry for a [2+2] photochemical cycloaddition and the di-Jt-methane rearrangement. 

We now proceed to look at three examples from recent work in some depth. In the first example, we wish to illustrate that a knowledge of the VB structure or of the states involved in photophysics and photochemistry rationalize the potential surface topology in an intuitively appealing way. We then proceed to look at an example where the extended hyperline concept has interesting mechanistic implications. Finally, we shall look at an example of how conical intersections can control electron transfer problems. 

Our work on photochemistry was started in collaboration with Massimo Olivucci, and the study of electron transfer problems was initiated with Lluis Blancafort. However, our study of conical intersections has involved many other collaborators, postdocs, and students. Only some of their work has been cited explicitly here. However, articles such as this, which collect many ideas and thoughts, are possible only through the dedicated hard work of our co-workers over many years who helped to develop them. 

Most of the AIMD simulations described in the literature have assumed that Newtonian dynamics was sufficient for the nuclei. While this is often justified, there are important cases where the quantum mechanical nature of the nuclei is crucial for even a qualitative understanding. For example, tunneling is intrinsically quantum mechanical and can be important in chemistry involving proton transfer. A second area where nuclei must be described quantum mechanically is when the BOA breaks down, as is always the case when multiple coupled electronic states participate in chemistry. In particular, photochemical processes are often dominated by conical intersections [14,15], where two electronic states are exactly degenerate and the BOA fails. In this chapter, we discuss our recent development of the ab initio multiple spawning (AIMS) method which solves the elecronic and nuclear Schrodinger equations simultaneously this makes AIMD approaches applicable for problems where quantum mechanical effects of both electrons and nuclei are important. We present an overview of what has been achieved, and make a special effort to point out areas where further improvements can be made. Theoretical aspects of the AIMS method are... 

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