Rotationally predissociating levels

Comparison with experiment (solid points) of calculated widths (open points) of rotationally predissociating levels of HD(1,2)-Ar. Reproduced with permission from Ref.(24). Copyright 1983, American Institute of Physics. 

One obvious conclusion from the above study is that calculated vibrational and rotational predissociation levels widths are extremely sensitive to the quality of the wave function used to represent the "initial" and "final" states, as well as to the coupling function itself. While this makes it difficult to use observations of this type to obtain new information about the potential energy surface, it also means that they should provide an extremely stringent constraint on the properties of a surface so determined. We have also seen that while they sometimes give useful qualitative information, none of the approxioiate methods considered herein are reliable enough chat they may be used in a quantitative analysis of experimental level widths. 

Photolysis of CO occurs by absorption of stellar UV radiation in the wavelength range 90-100 nm. The reaction proceeds by a predissociation mechanism, in which the excited electronic state lives long enough to have well-defined vibrational and rotational energy levels. As a consequence, the three isotopic species—C O, C O, and C O—absorb at different wavelengths, corresponding to the isotope shift in vibrational frequencies. Because of their different number densities, the abundant C O becomes optically thick in the outermost part of the cloud (nearest to the external source of UV radiation), while the... 

Figure 5. A typical SFCCCC a-trajectory for the complex eigenvalue associated with the rotational predissociation of the metastable level (j = Jl=2, J M 0) of the Ar...H2 vdW molecule (with potential LJ(III)), The numbers on the dots shown in the figure indicates the rotational angles (in radians) used. Reproduced with permission from Ref. 19. Copyright 1982, American Institute of Physics.

Interaction between a bound rotation-vibration level of one electronic state and the vibrational continuum of another electronic state (predissociation, Chapter 7). 

The mechanism of a predissociation may be characterized by measurements of the lifetime, rv, of each vibrational level or, even better, tvj, of every rotational level, carefully extrapolated to zero pressure. When the two unknown rates that appear in Eq. (7.4.6) have similar magnitudes, it is necessary to partition the observed total decay rate into tt and rnr. If the radiative lifetime is known for a non-predissociated level of the same electronic state, rT can be calculated for predissociated levels assuming an //-independent value for the electronic transition moment. The nonradiative lifetime is then deduced by subtraction of 1 /tt from the experimental 1/t value as follows ... 

Measurements by photographic photometry require careful calibration due to the nonlinear response of photographic plates saturation effects can lead to erroneous values. Line profiles can be recorded photoelectrically, if the stability of the source intensity and the wavelength scanning mechanism are adequate. Often individual rotational lines are composed of incompletely resolved spin or hyperfine multiplet components. The contribution to the linewidth from such unresolved components can vary with J (or TV). In order to obtain the FWHM of an individual component, it is necessary to construct a model for the observed lineshape that takes into account calculated level splitttings and transition intensities. An average of the widths for two lines corresponding to predissociated levels of the same parity and J -value (for example the P and R lines of a 1II — 1E+ transition) can minimize experimental uncertainties. A theoretical Lorentzian shape is assumed here for simplicity, but in some cases, as explained in Section 7.9, interference effects with the continuum can result in asymmetric Fano-type lineshapes. 

In Section 7.8 the possibility of predissociation of isolated lines was mentioned. This is usually called accidental predissociation and can be interpreted as perturbation of a nominally bound rotational level by a predissociated level that lies nearby in energy for this value of J. This type of predissociation should more generally be called indirect predissociation, since the predissociation takes place through an intermediate state (or doorway state, see Section 9.2). 

Internal rotational energy transfer may also cause predissociation. For example the internal rotational energy of N2 within N2 Ar may be transfered to the weak van der Waals bond and cause its rupture. This will occur when the energy of the J level populated exceeds the van der Waals bond strength. Theoretical models for this process, rotational predissociation, have been offered. 

Figure 12. Potential energy contour plots for He + I Cl(B,v = 3) and the corresponding probability densities for the n = 0, 2, and 4 intermolecular vibrational levels, (a), (c), and (e) plotted as a function of intermolecular angle, 0 and distance, R. Modified with permission from Ref. 40. The I Cl(B,v = 2/) rotational product state distributions measured following excitation to n = 0, 2, and 4 within the He + I Cl(B,v = 3) potential are plotted as black squares in (b), (d), and (f), respectively. The populations are normalized so that their sum is unity. The l Cl(B,v = 2/) rotational product state distributions calculated by Gray and Wozny [101] for the vibrational predissociation of He I Cl(B,v = 3,n = 0,/ = 0) complexes are shown as open circles in panel (b). Modified with permission from Ref. [51].

Gray and Wozny [101, 102] later disclosed the role of quantum interference in the vibrational predissociation of He Cl2(B, v, n = 0) and Ne Cl2(B, v, = 0) using three-dimensional wave packet calculations. Their results revealed that the high / tail for the VP product distribution of Ne Cl2(B, v ) was consistent with the final-state interactions during predissociation of the complex, while the node at in the He Cl2(B, v )Av = — 1 rotational distribution could only be accounted for through interference effects. They also implemented this model in calculations of the VP from the T-shaped He I C1(B, v = 3, n = 0) intermolecular level forming He+ I C1(B, v = 2) products [101]. The calculated I C1(B, v = 2,/) product state distribution remarkably resembles the distribution obtained by our group, open circles in Fig. 12(b). 

Dimers. It is well known that H2 pairs form bound states which are called van der Waals molecules. The discussions above based on the isotropic interaction approximation have shown that for the (H2)2 dimer a single vibrational state, the ground state (n = 0), exists which has two rotational levels f = 0 and 1). If the van der Waals molecule rotates faster ( > 1), centrifugal forces tear the molecule apart so that bound states no longer exist. However, two prominent predissociating states exist which may be considered rotational dimer states in the continuum (/ = 2 and 3). The effect of the anisotropy of the interaction is to split these levels into a number of sublevels. 

Besides a transition to a continuum level of an excited electronic state, dissociation can occur by another mechanism in electronic absorption spectroscopy. If the potential-energy curve of an excited electronic state A that has a minimum in UA(R) happens to be intersected by the U(R) curve of an unstable excited state B with no minimum in U, then a vibrational level of A whose energy lies near the point of intersection of UA and UB has a substantial probability to make a radiationless transition to state B, which then dissociates. This phenomenon is called predissociation. Predissociation shortens the lifetimes of those vibrational levels of A that are involved, and therefore by the uncertainty principle gives broad vibrational bands with rotational fine structure washed out. 

D. M. Neumark We make no effort to produce vibrationally cold O2, since the B < — X transitions to predissociating upper state levels are rotationally resolved and completely understood. In the case of CH3O, we detach the CH3O- just above the detachment threshold so that we do not produce vibrationally excited CH3O. 

In some molecules there is another, slower dissociation path known as predissociation. In this case the crossing to the dissociative state is the rate-limiting step, and this may take place after many vibrations in the absorption spectrum the vibrational sub-levels remain sharp, but the rotational levels are blurred (Figure 4.28). 

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