By Ben-nun M., Martinez T.J.

ISBN-10: 0471205044

ISBN-13: 9780471205043

ISBN-10: 0471264318

ISBN-13: 9780471264316

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**Example text**

This is at variance with previous studies at lower levels of theory [18], but in agreement with our AIMS results. The lowest points on the S1 PES are conical intersections, not true minima. Of these, we have found two nearly isoenergetic intersections: (a) the twisted/pyramidalized geometry that the AIMS simulations also highlighted and (b) another that corresponds to ethylidene. A third type of intersection involving hydrogen migration is similar to the 493 Figure 16. Left panel: The ground and first excited electronic states of ethylene, computed using the OA-GVB-CAS(2/2)Ã S wavefunction, as a function of the pyramidalization and twist angles.

Figure adapted from Ref. ) consequence of the uncertainty principle, the quantum mechanical ‘‘phase space’’ accessed by the wavefunction is not restricted to lie on a classical energy shell, but rather will have a finite energy width which can never be modeled with a single classical trajectory, time displaced or not. Therefore, the limit of a single seed should not be expected to be sufficient. The TDB approach can be applied alone or combined with the hybrid approach discussed in the previous section.

The potential energy surfaces shown in Fig. 7 differ from this canonical picture, and in particular it is not at all clear that the wavepacket on the lower adiabatic state will be funneled away from the intersection. For the conditions chosen in our calculations, we ab initio quantum molecular dynamics 479 Figure 8. Li þ H2: Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Li(2p) þ H2(n ¼ 0; j ¼ 0) initial state at an impact parameter of 2 bohr.

### AB INITIO Quantum molecular dynamics by Ben-nun M., Martinez T.J.

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