Potential curves dissociative

The main result of these first detailed experimental studies of the AI mechanism is that, even at thermal velocity, the system R -H follows a potential curve F ( R) that diabatically crosses an infinite number of potential curves dissociating into R+H, H being hydrogen in a Rydberg state, and continues to be well defined in the ionization continuum. We might mention that results on AI are also interesting because AI is the reverse reaction to the important process of dissociative recombination of molecular ions. 

Figure 8.24 Potential energy curves of HC1 (solid curves) and HC1+ (dashed curves). It is clear that the potential curves for Rydberg states converging to HC1+ A2S+ are intersected by potential curves dissociating to H++ Cl-, H+Cl (3p44s 2P), H (n = 2)+ Cl, and H+Cl (3p44p 4P). The potential curve with non-labeled asymptote is the (A2E+)3d7r 1II state (from Lefebvre-Brion and Suzor-Weiner, 1994).

In addition, O3 has weak absorption bands called the Chappuis bands in the visible range and the Wulf bands in further longer wavelengths as shown in Fig. 4.2. These bands corresponds to the forbidden transitions to the lower electronically excited states that cross with repulsive potential curve dissociating into the ground states of an O atom and O2 molecule. 

Figure B3.4.12. A schematic ID vibrational pre-dissociation potential curve (wide flill line) with a superimposed plot of the two bound fimctions and the resonance fimction. Note that the resonance wavefiinction is associated with a complex wavevector and is slowly increasing at very large values of R. In practice this increase is avoided by iismg absorbing potentials, complex scaling, or stabilization.

This difference is shown in the next illustration which presents the qualitative form of a potential curve for a diatomic molecule for both a molecular mechanics method (like AMBER) or a semi-empirical method (like AMI). At large internuclear distances, the differences between the two methods are obvious. With AMI, the molecule properly dissociates into atoms, while the AMBERpoten-tial continues to rise. However, in explorations of the potential curve only around the minimum, results from the two methods might be rather similar. Indeed, it is quite possible that AMBER will give more accurate structural results than AMI. This is due to the closer link between experimental data and computed results of molecular mechanics calculations. 

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

Tig and T)", the dissociation energies relative to the minima in the potential curves, are obtained from Tig and T)g by... 

There would, however, be a certain probability, dependent on the nature of the eigenfunctions, that actual non-adiabatic dissociation would give ions rather than atoms, and this might be nearly unity, in case the two potential curves come very close to one another at some point. See I. v. Neumann and E. Wigner, Physik. Z., 30, 467 (1929). 

Figure 1.3. Real-time femtosecond spectroscopy of molecules can be described in terms of optical transitions excited by ultrafast laser pulses between potential energy curves which indicate how different energy states of a molecule vary with interatomic distances. The example shown here is for the dissociation of iodine bromide (IBr). An initial pump laser excites a vertical transition from the potential curve of the lowest (ground) electronic state Vg to an excited state Vj. The fragmentation of IBr to form I + Br is described by quantum theory in terms of a wavepacket which either oscillates between the extremes of or crosses over onto the steeply repulsive potential V[ leading to dissociation, as indicated by the two arrows. These motions are monitored in the time domain by simultaneous absorption of two probe-pulse photons which, in this case, ionise the dissociating molecule.

The recombination of He is a special case. We include it here because of the similarities with H3 and because it is the only known example where three-body recombination of a diatomic molecular ion dominates over the binary process. The literature on the helium afterglow is quite large and we will not be able to do justice to all aspects of this problem. Mulliken71 had predicted that fast dissociative recombination of Hej should not occur due to a lack of a suitable curve crossing between the ionic potential curve and repulsive curves of He. Afterglow experiments in pure helium, at sufficient pressure to enable formation of Hej ions, have confirmed this expectation. It does not appear that the true binary recombination... 

Fig. 2. The singlet-triplet reversion of SiH2, referenced to CH2, leads to the avoidance of the crossing of two potential curves. Thus, the Si=Si bond dissociation energy of Si2H4 is lowered by twice the singlet-triplet gap of SiH2, i.e. 38 kcal mol 1.

In radiolysis, a significant proportion of excited states is produced by ion neutralization. Generally speaking, much more is known about the kinetics of the process than about the nature of the excited states produced. In inert gases at pressures of a few torr or more, the positive ion X+ converts to the diatomic ion X2+ very rapidly. On neutralization, dissociation occurs with production of X. Apparently there is no repulsive He2 state crossing the He2+ potential curve near the minimum. Thus, without He2+ in a vibrationally excited state, dissociative neutralization does not occur instead, neutralization is accompanied by a col-lisional radiative process. Luminescences from both He and He2 are known to occur via such a mechanism (Brocklehurst, 1968). 

In cyclic voltammetry, the current-potential curves are completely irreversible whatever the scan rate, since the electron transfer/bond-breaking reaction is itself totally irreversible. In most cases, dissociative electron transfers are followed by immediate reduction of R, as discussed in Section 2.6, giving rise to a two-electron stoichiometry. The rate-determining step remains the first dissociative electron transfer, which allows one to derive its kinetic characteristics from the cyclic voltammetric response, ignoring the second transfer step aside from the doubling of the current. 

Figure 1.3 Potential curve of a molecule (ground state of HC1). The full curve is the Morse potential of Eq. (1.6). The dashed curve is the harmonic approximation. De is the dissociation energy, and re is the equilibrium separation.

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