Photochemical funnel

Figure 5.1. Various adiabatic photochemical reaction mechanisms (see text for details), (a) Simple case of dual fluorescence (b) illumination changes sample (i.e., photochemistry) (c) strong fluorescence quenching (photochemical funnel) (d) competitively coupled product species (e) consecutively coupled product species.

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. 

The surface touchings correspond to photochemical funnels [20] which can lead to ultrafast Si-Sq transitions [80] as typically encountered for the energy storage step of retinal pigments in the visual process or in bacterial photosynthesis. The transition along the 5 axis in Figs. 7 and 8 can be made smoothly by an external perturbation, e.g. solvent relaxation. 

Experimentally, in all cases studied, intramolecular fluorescence quenching can be observed due to the adiabatic photoreaction towards the photochemical funnel (twisted double bond, close-lying So/Sj, ultrafast nonradiative... 

The data in Table 1 refer to the nonradiative decay rate k , in DCS and DCM and are indicative of the reaction to the photochemical funnel through double-bond twisting. They reveal that k, is highly polarity dependent, slowest in strongly and fastest in weakly polar solvents (negative solvatokinetic effect). In view of the above, we recognize this as signifying that the funnel state P is of less polar nature than the precursor state E. ... 

Fig. 13a-c. Push-pull cyclobutadienes as biradicaloid species [20]. a The two degenerate frontier orbitals localize upon introduction of donor and acceptor substituents as shown and energetically split by the energy gap b. b Ground and S, states can therefore be assigned hole-pair (hp - one doubly occupied, one unoccupied frontier orbital) and dot-dot character (dd - two singly occupied frontier orbitals) similarly as in the case of twisted ethylene (Fig. 7). The energetic order is determined by the interplay of electron repulsion and the orbital energy gap h which depends on the substituents, c In-plane relaxational deformations in Si can lead to an approach of S and S, and thus to fluorescence red shifts or even to photochemical funnels...

A photochemical funnel corresponds to a molecular structure that lives for only few femtoseconds (10 s). For this reason computer simulations based on modern quantum chemical methods appear to be the only practical source of direct information. 

These initial results suggested that conical intersections could indeed act as photochemical funnels. 

An instructive, albeit trivial, example is the hydrogen exchange reaction, Ha — Hb + He Ha -b Hb — He where the thermal transition state has a collinear geometry, Ha — Hb — He. In the linear structure, the ground state is the resonating combination of R and P, and it constitutes the transition state for the thermal reaction, while the twin-excited state P is the corresponding antiresonant combination that forms the photochemical funnel ... 

Fig. 2. The relationship between (a) the Van der Lugt-Oosterhoff model and (b) a model (see Sec. 2.1) based on MEP computations for the photochemical electrocycliza-tion of buta-1,3-diene. The Van der Lugt-Oosterhoff model is based on an assumed (interpolated) reaction coordinate and suggests that the photochemical funnel corresponds to an avoided crossing at M (see dashed frame). MEP computations yield a different, but unbiased coordinate, corresponding to the steepest-descent path from the excited-state reactant. The reaction coordinate characterizing such a path leads to a conical intersection between the excited (5i) and ground (So) states. The framed region in part (b) indicates the position of the Van der Lugt-Oosterhoff avoided crossing in the conical intersection region.

Weingart, O., Migani, A., Olivucci, M., Robb, M. A., Buss, V., 8c Hunt, P. (2004). Probing the photochemical funnel of a retinal chromophore model via zero-point energy sampling semiclassical dynamics. The Journal of Physical Chemistry A, 108(21), 4685-4693. 

Excited state reactivity is controlled by three factors (a) the presence and magnitude of barriers in the excited state branch of the reaction coordinate, (b) the dynamics of IC or ISC as the system returns to the ground state, and (c) the nature of ground state reaction pathways that are populated following IC or ISC. The central concept of the photochemical funnel introduced by Zimmerman" and Michl has now been documented by substantial computational work (see, for example. 

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