Conical intersection reaction paths

Figure 2.19 Schematic of a photochemical reaction path involving a conical intersection. The path starts on the excited-state potential energy surface and decays to the ground-state potential energy surface through a conical intersection, leading to the formation of different photoproducts 1, 2, and 3.

Accordingly, the reaction path then proceeds via the Ag excited state on the excited state PES until the conical intersection region is reached, passing through an excited state minimum. At the conical intersection, the molecule drops down to the ground... 

Figure 14. Classical trajectories for the H + H2(v = l,j = 0) reaction representing a 1-TS (a-d) and a 2-TS reaction path (e-h). Both trajectories lead to H2(v = 2,/ = 5,k = 0) products and the same scattering angle, 0 = 50°. (a-c) 1-TS trajectory in Cartesian coordinates. The positions of the atoms (Ha, solid circles Hb, open circles He, dotted circles) are plotted at constant time intervals of 4.1 fs on top of snapshots of the potential energy surface in a space-fixed frame centered at the reactant HbHc molecule. The location of the conical intersection is indicated by crosses (x). (d) 1-TS trajectory in hyperspherical coordinates (cf. Fig. 1) showing the different H - - H2 arrangements (open diamonds) at the same time intervals as panels (a-c) the potential energy contours are for a fixed hyperradius of p = 4.0 a.u. (e-h) As above for the 2-TS trajectory. Note that the 1-TS trajectory is deflected to the nearside (deflection angle 0 = +50°), whereas the 2-TS trajectory proceeds via an insertion mechanism and is deflected to the farside (0 = —50°).

Part of the explanation that follows concerns the reasons why a conical intersection may be found in a particular system. This part could be skipped over in a first reading, as it is more mathematical. Nevertheless, it is closely connected with an explanation of the shape of a conical intersection, which in turn determines the crossing s accessibility on the excited state, and the subsequent reaction paths on the ground... 

Figure 9.3. Cartoon of a classic double cone conical intersection, showing the excited state reaction path and two ground state reaction paths. See color insert.

The important points on a conical intersection hyperline are those where the reaction path meets with the seam (see Fig. 9.10)... 

Our hypothesis for discussion in this section has been that the conical intersection can be characterized like any other reactive intermediate. On examining Figure 9.3 or 9.10, it is clear that a conical intersection divides the excited-state branch of the reaction path from the ground-state branch in a photochemical transformation. (We shall... 

Figure 11-9. CASSCF potential-energy profiles of the ground-state So (circles), the lnjr state (triangles), the Lb state (squares), and the La state (filled squares) of the 9H-adenine along the linear interpolation reaction path from the equilibrium geometry of the nit state to the CI32 (a) and CI16 (b) conical intersections. The diabatic correlation of the states is shown in (a). (From Ref. [138])...

This is the case for the quadricyclane - to norbornadiene" reaction. Although the C2K reaction path provides an attractive interpretational tool for understanding the progress of this reaction, its highest point represents a conical intersection at which the two relevant states have the same energy at the same geometry. This point cannot be a transition state, so that lowering the symmetry in any direction leads to a stabilization. The result is an asynchronous reaction path in which one of the two cyclopropane bonds is broken first to form the biradical-like transition state la. The second bond can then break to form the norbornadiene radical cation 2. 

Figure 4 Opening of a fast radiationless decay channel via conical intersection for (a) a barrier controlled reaction, (b) a barrierless path, and (c) an uphill path without transition state (sloped conical intersection). M" is an excited state intermediate and FC is a Franck-Condon point.

When such structural or static information is not sufficient (i.e., the excited state may not decay at the minimum of the conical intersection line, or the momentum developed on the excited state branch of the reaction coordinate may be sufficient to drive the ground state reactive trajectory along paths that are far from the ground state valleys), a dynamics treatment of the excited state/ ground state motion is required.53 54 These techniques also are illustrated in the next subsection. 

We have shown that an accessible conical intersection forms a bottleneck that separates the excited state branch of a nonadiabatic photochemical reaction path from the ground state branch, thus connecting the excited state reactant to two or more products on the ground state surface via a branching of the... 

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