Minimal energy conical intersection

To better visualize the situation, we present in Fig. 2 representative cuts through the PES of the benzene cation (Fig. 2a) as well as the monofluoro derivative (Fig. 2b). A linear combination of the normal coordinates of the JT active modes vg — vg is chosen for the benzene cation and one of the totally symmetric modes for the monofluoro benzene cation. Both are defined to minimize the energy of the conical intersection between the A and C states of the monofluoro derivative, and between the X and B states of the parent cation (within the subspace of JT active coordinates). For the parent cation one identifies a low-energy inter-state curve crossing which is mediated by the multimode JT effect in the two degenerate electronic states. The latter is reflected by the symmetric crossing between the two lowest potential energy curves in Fig. 2a which acmally represents a cut... 

Fig. 12.4. Energy profiles along the Si photoisomerization coordinate of a PSBll minimal model at CASPT2//CASSCF and TD-DFT//CASSCF levels of theory. Notice that both the reaction paths and the conical intersection family are qualitatively described at the TDDFT levels (redrawn with permission from Ref. [28] 2004 American Chemical Society).

The squared energy difference is used because it varies more smoothly in the vicinity of a conical intersection. The norm of ci has no significance, the step size should only depend on the energy difference AE, therefore the gradient to be used to minimize AE is defined as... 

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