Conical intersection funnel

We hope the reader has been convinced that it is technically feasible to describe a photochemical reaction coordinate, from energy absorption to photoproduct formation, by means of methods that are available in standard quantum chemistry packages such as Gaussian (e.g., OPT = Conical). The conceptual problems that need to be understood in order to apply quantum chemistry to photochemistry problems relate mainly to the characterization of the conical intersection funnel. We hope that the theoretical discussion of these problems and the examples given in the last section can provide the information necessary for the reader to attempt such computations. 

An experimental and computational investigation into the photorearrangement of N-cyclopropylimines to yield pyrrolines (Scheme 122) has shown that the, regiochem-istry and stereochemistry can be understood in terms of a mechanism involving barrierless evolution in three different (S2, Si, and So) singlet states and sequential decay through two different (S2/S1 and S1/S0) conical intersection funnels.183... 

Chapter 4 introduces the fundamental concepts needed for a discussion of photophysical and photochemical phenomena. Here, the section on bi-radicals and biradicaloids has been particularly expanded relative to the German original. The last three chapters deal with the physical and chemical transformations of excited states. The photophysical processes of radiative and radiationless deactivation, as well as energy and electron transfer, are treated in Chapter 5. A qualitative model for the description of photochemical reactions in condensed media is described in Chapter 6, and then used in Chapter 7 to examine numerous examples of phototransformations of organic molecules. All of these chapters incorporate the recent advances in the understanding of the role of conical intersections ( funnels ) in singlet photochemical reactions. 

Conical intersections, introduced over 60 years ago as possible efficient funnels connecting different elecbonically excited states [1], are now generally believed to be involved in many photochemical reactions. Direct laboratory observation of these subsurfaces on the potential surfaces of polyatomic molecules is difficult, since they are not stationary points . The system is expected to pass through them veiy rapidly, as the transition from one electronic state to another at the conical intersection is very rapid. Their presence is sunnised from the following data [2-5] ... 

Commonly, it is asserted that upward transitions from the lower adiabat to the upper one should be less likely than downward transitions because of the funneling property of the intersection [144,145]. This is clearly seen in the usual model conical intersection—as seen, for example, in Fig. 1 of Ref. 146, where there is (a) a well, or funnel, in the upper adiabat which guides the wavepacket to the intersection and (b) a peak on the lower adiabat which tends to guide the wavepacket away from the intersection. The potential energy surfaces shown in Fig. 7 differ from this canonical picture, and in particular it is not at all clear that the wavepacket on the lower adiabatic state will be funneled away from the intersection. For the conditions chosen in our calculations, we... 

Figure 8. Li + H2 Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Lit2/j) + H2(v — 0, j — 0) initial state at an impact parameter of 2 bohr. Individual nonadiabatic events for each basis function are completed in less than a femtosecond (solid line) and due to the sloped nature of the conical intersection (see Fig. 7), there is considerable up-funneling (i.e., back-transfer) of population from the ground to the excited electronic state. (Figure adapted from Ref. 140.)...

We have already mentioned in the Introduction (Section 3.7.1) the importance of conical intersections (CIs) in connection with excited electronic state dynamics of a photoexcited chromophore. Briefly, CIs act as photochemical funnels in the passage from the first excited S, state to the ground electronic state S0, allowing often ultrafast transition dynamics for this process. (They can also be involved in transitions between excited electronic states, not discussed here.) While most theoretical studies have focused on CIs for a chromophore in the gas phase (for a representative selection, see refs [16, 83-89], here our focus is on the influence of a condensed phase environment [4-9], In particular, as discussed below, there are important nonequilibrium solvation effects due to the lack of solvent polarization equilibration to the evolving charge distribution of the chromophore. 

Valence bond ideas also contributed to the revival of theories for photochemical reactivity. Early VB calculations by Oosterhoff et al (98,99). revealed a potentially general mechanism for the course of photochemical reactions. Michl (100,101) articulated this VB-based mechanism and highlighted the importance of funnels as the potential energy features that mediate the excited-state species back into the ground state. Subsequently, Robb and co-workers (102 105) showed that these funnels are conical intersections that can be predicted by simple VB arguments, and computed at a high level of sophistication. Similar applications of VB theory to deduce the structure of conical intersections in photoreactions were done by Shaik and Reddy (106) and recently by Elaas and Zilberg (107). 

Twin-States The ground and excited states that arise from avoided crossing in the VBSCD (see below). Usually, the twin-states correspond to a transition state of a thermal reaction and an excited-state intermediate. This excited-state intermediate can be converted to a funnel (a conical intersection) for the products of a photochemical reaction. See Chapter 6. 

Funnels IVue and Weakly Avoided Conical Intersections... 

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