Avoided crossings, potential energy surfaces

Figure 3.1 Avoided crossing of potential energy surfaces for LiF...

Fig. 28. Schematic of potential energy surfaces of the vinoxy radical system. All energies are in eV, include zero-point energy, and are relative to CH2CHO (X2A//). Calculated energies are compared with experimentally-determined values in parentheses. Transition states 1—5 are labelled, along with the rate constant definitions from RRKM calculations. The solid potential curves to the left of vinoxy retain Cs symmetry. The avoided crossing (dotted lines) which forms TS5 arises when Cs symmetry is broken by out-of-plane motion. (From Osborn et al.67)...

Finally, we consider the performance of the MFT method for nonadiabatic dynamics induced by avoided crossings of the respective potential energy surfaces. We start with the discussion of the one-mode model. Model IVa, describing ultrafast intramolecular electron transfer. The comparison of the MFT method (dashed line) with the quantum-mechanical results (full line) shown in Fig. 5 demonstrates that the MFT method gives a rather good description of the short-time dynamics (up to 50 fs) for this model. For longer times, however, the dynamics is reproduced only qualitatively. Also shown is the time evolution of the diabatic electronic coherence which, too, is... 

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. 

Figure 11. Dressed state potential energy surfaces for D2 plus one, two, or three 532-nm photons. The avoided crossing gaps increase with increasing laser intensity.

Potential energy surfaces of van der Waals molecules have — in comparison to the PESs of excited states of chemically bound molecules like H2O, H2S, or CH3ONO — a relatively simple general appearance. There are no barriers due to avoided crossings and no saddle points etc. Moreover, the coupling between R, on one hand, and r and 7, on the other hand, is usually weak so that a representation of the form... 

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