Minimum-energy conical intersections

Fig. 7. The excited-state reaction path of the penta-2,4-dienimminium cation intercepts the conical intersection point CI700 located ca. 5 kcal mol above the minimum-energy conical intersection CIq2o. FC— Cl7oo MEP ( i open diamonds and So full diamonds), Cl7oo Cl92o MEP (5i open circles and So full circles). The values of the relevant structural parameters are given in A and degrees.

The position and energy of the minimum energy conical intersection (MECI) are given by... 

The intersections of the A2 state with the two E components immediately below are also in astonishingly close proximity to the equilibrium structure. The intersection regions in Table VIE are raised in energy relative to the minimum by less than 0.02 kcal/mol, and the minimum and intersection structures are nearly indistinguishable. This concurrence of the minimum and conical intersection regions can again have great impact on the observed vibrational structure. 

The potential surfaces of the ground and excited states in the vicinity of the conical intersection were calculated point by point, along the trajectory leading from the antiaromatic transition state to the benzene and H2 products. In this calculation, the HH distance was varied, and all other coordinates were optimized to obtain the minimum energy of the system in the excited electronic state ( Ai). The energy of the ground state was calculated at the geometry optimized for the excited state. In the calculation of the conical intersection... 

To obtain the Hamiltonian at zeroth-order of approximation, it is necessary not only to exclude the kinetic energy of the nuclei, but also to assume that the nuclear internal coordinates are frozen at R = Ro, where Ro is a certain reference nucleai configuration, for example, the absolute minimum or the conical intersection. Thus, as an initial basis, the states t / (r,s) = t / (r,s Ro) are the eigenfunctions of the Hamiltonian s, R ). Accordingly, instead of Eq. (3), one has... 

At minimum of the conical intersection on the upper sheet of potential energy surface. Rotation about the axis perpendicular to the plane of the molecule. 

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