Vibrationally unbound states

Rates for nonradiative spin-forbidden transitions depend on the electronic spin-orbit interaction matrix element as well as on the overlap between the vibrational wave functions of the molecule. Close to intersections between potential energy surfaces of different space or spin symmetries, the overlap requirement is mostly fulfilled, and the intersystem crossing is effective. Interaction with vibrationally unbound states may lead to predissociation. 

Bound electronic states exhibit a discrete spectrum of rovibrational eigenstates below the dissociation energy. The interaction between discrete levels of two bound electronic states may lead to perturbations in their rovibrational spectra and to nonradiative transitions between the two potentials. In the case of an intersystem crossing, this process is often followed by a radiative depletion. Above the dissociation energy and for unbound states, the energy is not quantized, that is, the spectrum is continuous. The coupling of a bound state to the vibrational continuum of another electronic state leads to predissociation. 

The second type of predissociation observed for diatomic molecules is known as electronic predissociation the principles are illustrated in figure 6.28. A vibrational level v of a bound state E lies below the dissociation asymptote of that state, but above the dissociation asymptote of a second state E2. This second state, E2, is a repulsive state which crosses the bound state E as shown. The two states are mixed, and the level v can predissociate via the unbound state. It is not, in fact, necessary for the potential curves of the two states to actually cross. It is, however, necessary that they be mixed and there are a number of different interaction terms which can be responsible for the mixing. We do not go into the details here because electronic predissociation, though an important phenomenon in electronic spectroscopy, seldom plays a role in rotational spectroscopy. Since it involves excited electronic states it could certainly be involved in some double resonance cases. 

Figure 24.22 Left energetic diagram for the l2 - -Ne system both I-I and l2 - Ne distances are considered. Notice how vibrationaLLy excited states are isoenergetic with continuum states of the unbound fragments, which leads to vibrational predissociation. Right pump and probe scheme to estimate the lifetime of the excited l2- Ne complex. Reproduced from WiUberg et al, 3. Chem. Phys., 1992, 96 198, with permission of the American Institute of Physics...

FI 12.42 When absorption occurs to unbound states of the upper electronic state, the molecule dissociates and the absorption is a continuum. Below the dissociation hmit the electronic spectrum has a normal vibrational structure. 

The free energy of association of two molecules in solution is driven by a balance of enthalpic and entropic contributions, The entropic contributions are both positive and negative. Solvent entropy favors the combined solute since it has a smaller surface area. The loss of three degrees of translational and three degrees of rotational entropy upon dimerization favors the unbound state. These lost translational and rotational modes are recovered, however, in the form of six new vibrational modes for the system. 

Dissociation occurring by tunneling from a bound to an unbound rovibronic state (i.e., a state corresponding to a particular rotational energy level of a vibrational level of an electronic state). 2. The appearance of a diffuse band region within a series of sharp bands of an absorption spectrum. 

A rather controversial proposal of a concerted CO loss from a Fe(CO)5 excited state (Fe(CO)5 ) was used to explain these observations. In this description Fe(CO)5, formed following the absorption of two 400 nm photons, is launched onto a steep unbound surface and loses four CO s within the time scale of the vibrational period of a Fe-CO bond (100 fs). The time shift in the signals for the Fe(CO) (n = 4-2) is explained by the time taken for the fragments to move away from their force field attraction. 

The phase-space model has been applied to triple collisions by F. T. Smith (1969) in a detailed study of termolecular reaction rates. He classified 3-body entry or exit channels into two classes, of pure and indirect triple collisions, and introduced kinematic variables appropriate to each class. These variables were then used to develop a statistical theory of break-up cross-sections. A recent contribution (Rebick and Levine, 1973) has dealt with collision induced dissociation (C1D) along similar lines. Two mechanisms were distinguished in the process A + BC->A + B + C. Direct CID, where the three particles are unbound in the final state, and indirect CID, where two of the particles emerge in a quasi-bound state. Furthermore, a distinction was made in indirect CID, depending on whether the quasi-bound pair is the initial BC or not. Enumeration of the product (three-body) states was made in terms of quantum numbers appropriate to three free bodies (see e.g. Delves and Phillips, 1969) the vibrational quantum number of a product... 

The fact that AH in Scheme 5.25 is actually measured to be endothermic by this amount for the Cr complex implies that zero-point and excited-state vibrational energies for the tj2-H2 species determine the EIE.189 Furthermore, one must consider more than just the lowering of rHh versus vDD on coordination. The favoring of the left-hand side of Scheme 5.25 is the inverse of that predicted from simple changes in fun alone, where deuterium should favor the stronger force constant that is, D2 should prefer to remain unbound compared to H2. 

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