Minimum Energy Conical Intersection Optimization

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 

The minimization of E2 in the intersection space is done by mean of a projector 

Overall the MECI optimization uses the composite gradient 

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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... 

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