Avoided crossing diabatic/adiabatic dynamics

Finally, we discuss applications of the ZPE-corrected mapping formalism to nonadiabatic dynamics induced by avoided crossings of potential energy surfaces. Figure 27 shows the diabatic and adiabatic electronic population for Model IVb, describing ultrafast intramolecular electron transfer. As for the models discussed above, it is seen that the MFT result (y = 0) underestimates the relaxation of the electronic population while the full mapping result (y = 1) predicts a too-small population at longer times. In contrast to the models... 

We return finally in this section to the question of avoided crossings in potential energy surfaces. We have already noted in section 2 that diabatic potentials may be a more suitable basis for a dynamical calculation than adiabatic. By expanding on the relationship between the two we will be able to introduce the concept of analytic continuation of adiabatic surfaces into complex coordinate space which has proved useful for some dynamical problems. 

Hyperspherical coordinates provide another powerful tool for precise three-body calculations, on one hand, and for visual understanding of QBS dynamics in terms of hyperspherical potentials playing a role similar to molecular adiabatic potentials. Adiabatic hyperspherical potentials exhibit many avoided crossings, which often must be cast into diabatic potentials to extract essential physics. 

The sudden changes in the adiabatic wavefunctions near avoided crossings make it more convenient to use diabatic potential energy surfaces when simulating photodissociation dynamics. The adiabatic potentials, usually constructed from electronic structure calculation data, should therefore be transformed to diabatic potentials. The adiabatic-diabatic transformation yields diabatic states for which the derivative couplings above approximately vanish. The diabatic potential energy surfaces are obtained from the adiabatic ones by a unitary orthogonal transformation [22,23]... 

If the coupling is different from zero, the dynamics can either follow the avoided crossing (adiabatic evolution), cross it (diabatic evolution), or partially cross it, depending on the speed of the dynamics with respect to the shape of the avoided crossing. 

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