Wavefunctions bifurcation

Saddle-node bifurcations taking place for the reasons just described have been observed for HOBr [41], HOCl [36,38,39], and HCP [34-36]. For HOBr and HOCl, the stable PO bom at the saddle-node bifurcations is called [D] for dissociation, because this PO stretches along the dissociation pathway and scars OBr- or OCl-stretch quantum mechanical wavefunctions (see Fig. lie of Ref. 38, Figs. 3b and 3g of Ref. 41, or Section III.B). In the case of HCP, the stable PO born at the bifurcation is better called [I], for isomerization, because this PO stretches along the isomerization pathway and scars bending quantum mechanical wavefunctions (see Figs. 6b and 6d of Ref. 35 or Figs. 7b and 7d of Ref. 36). 

For planar motion the wavefunction in bifurcation coordinates was expanded as... 

To understand the internal molecular motions, we have placed great store in classical mechanics to obtain a picture of the d5Uiamics of the molecule and to predict associated patterns that can be observed in quantum spectra. Of course, the classical picture is at best an imprecise image, because the molecular dynamics are intrinsically quantum mechanical. Nonetheless, the classical metaphor must surely possess a large kernel of truth. The classical structure brought out by the bifurcation analysis has accounted for real patterns seen in wavefunctions and also for patterns observed in spectra, such as the existence of local mode doublets, and the... 

The first approximation made in the Ehrenfest method is thus the factorisation of the total wavefunction into a product of electronic and nuclear parts. One deficiency of the ansatz (2) is the fact that the electronic wavefunction does not have the possibility to decohere the populated electronic states in P(r,t) share the same nuclear wave-packet x(R, t) by definition of the total wavefunction. Decoherence here is defined as the tendency of the time-evolved electronic wavefunction to behave as a statistical ensemble of electronic states rather than a coherent superposition of them [26]. The neglect of electronic decoherence could lead to non-physical asymptotic behaviors in case of bifurcating paths. It is not expected to be a problem here as we are interested in relatively short timescale dynamics. 

A striking experimental result is that the speed distribution of S (or the rotational distribution of CO) is bimodal (8,14,15). Since the bending wavefunction of a parent molecule and the rotational distribution of a diatomic fragment can be related by the rotational reflection principle (16), a Gaussian-shaped rotational distribution of CO may be anticipated for a single dissociation channel. The observed bimodal distribution implies that there is bifurcation in dissociation dynamics. The scattering distribution of S atoms observed by ion imaging indicates that the bimodal distribution occurs only for dissociation from the A ( A) state and not for the A ( 2 ) state. The question is why does it occur only from the A ( A) state ... 

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