Franck-Condon geometry

Figure 9. Schematic reprsentation of a classical trajectory moving on the Si and So energy surfaces of the H2—(CH) -NHt trans cis photoisomerization, starting near the planar Franck-Condon geometry. The geometric coordinates are (a) torsion of the C2—C3 and C3 C4 bonds and (b) asymmetric stretching coupled with pyramidalization. Both Si and So intersect at a conical intersection (Si/S0 Cl) located near the minimum of the Si surface (Min-C ) where the C2C3C4N5 torsion angle is 104°. [Reproduced with permission from [87], Copyright 2000 Amercian Chemical Society],...

A small or nonexisting barrier E0other hand, implies that the initial conditions (Franck-Condon geometry, and so on) can influence the reaction rate. A consequence of the resulting nonstationary probability distribution functions are time-dependent reaction rates (see Section IV). 

Fig. 10 For the 3-state model of Sec. 5.2., projections of the coupled diabatic XT, CT and IS potential surfaces (E configuration) onto the XT-CT branching plane are shown. The white and black circles indicate the conical intersection and Franck-Condon geometry, respectively. Reproduced from Ref. [52]. Copyright 2008 by the American Physical Society.

Figure 3.40 Adiabatic S0 and 5, surfaces for the isolated PSB chromophore. The Franck-Condon geometry (FC) and the Cl point are indicated.

Figure 3.41 Free energy surfaces S0 and 5, for a frozen solvent situation with the solvent equilibrated to the S0 charge distribution at the Franck-Condon geometry, indicating the lack of a Cl This should be contrasted with Figure 3.40 for the isolated chromophore.

Figure 3.42 The Cl seam in the (r, z) plane (0 = 90°) for the combined PSB chromophore plus solvent system, comprising the coupling mode Q, tuning mode r, and the solvent coordinate z in the role of an additional tuning mode. The minimum free energy Cl (MECI) is indicated. The (r, z) projection of the Franck-Condon geometry is shown for reference.

Photochemistry is controlled in two ways. First, there is the avoidance of excited-state energy barriers, which plays a major role. Second, the placement of conical intersections and avoided crossings determine reaction success vs. radiationless decay. A conical intersection positioned close to the Franck-Condon geometry and before to an appreciable barrier favors decay to the reactant ground state and a low or zero quantum yield. A conical intersection positioned after the first energy barrier on the excited state hypersurface facilitates reaction, epecially if the conical intersection appears close to a product geometry. 

Starting with y= 120° and 0 = 0°, the MNDOC-CI method yields a conical intersection, the structure of which is shown in Figure 6.8. The values 0=0° for the rotational angle and 7 = 143,7° for the bond angle are as expected the bond distances are between those of azirine and nitrile ylide, especially because the distance between nitrogen and the methylene carbon r N = 1.34 A has decreased and is equal to the double-bond value r N = 1.34 A in the nitrile ylide. To completely establish the mechanism, it remains to be shown that the conical intersection is accessible without a barrier from the Franck-Condon geometry and that the nitrile ylide can be reached from the conical intersection. This is easily... 

The energetics of the photoreaction of 2if-azirine as well as the thermal ground-state reaction as obtained from CASPT2 calculations are summarized in Figure 6.14. From this diagram it can be concluded that the photolysis of 2H-azirine to form nitrile ylide occurs from the nji -excited state by way of an S -Sq conical intersection. Because the reaction paths on the surface from the Franck-Condon geometry to the conical intersection as well as on the Sq surface from the conical intersection to the nitrile ylide are... 

Franck-Condon geometry ) as compared to the minimum of that surface is 32 kcal/mol. One of Ohmine s primary goals was to determine how the excess energy flowed into the solvent thereby resulting in the relaxation of the ethylene molecule to its minimum energy configuration on the triplet surface. 

In a previous section, we considered as a barrier the energy difference between the minimum of the Srt state and the crossing point (S7t/T )x, which is 0.36 eV, but the present approach accounts for the excess vibrational energy available in the system from the initially populated Stt state (at the Franck-Condon geometry) to the crossing point (0.03 eV), which seems to be more relevant in this context, where the interest focuses on rate constants. The results were 1.11 X 10 s and 0.90 ns for /c[sc and t[sc> respectively. 

Initial conditions for the wavepacket calculations correspond to the Franck-Condon geometry, and the effective-mode expansion is defined with respect to this reference geometry. Figure 15.3 shows the time-dependent diabatic S2 populations and autocorrelation functions C(f) = (V (0) vf(f)) generated from the successive spectral density approximants J (o), M = 1,...,3. All orders agree over the shortest time scale ( 5 fs), and the orders M = 2,3 are found to be very close over the complete observation interval. The M = 3 result is virtually indistinguishable from the result obtained for the reference spectral density and can be considered converged. 

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