Predissociation by rotation

There are two complementary ways of looking at the phenomenon of predissociation time-dependent and time-independent pictures. 

Time-dependent picture. Experimental observations can be discussed in terms of a competition between two processes the radiative process (absorption or emission), characterized by a radiative rate r 1, and a nonradiative process, predissociation, characterized by a nonradiative rate. There are two possible decay pathways for the excited state, 

Predissociation is a nonradiative process because some of the internal energy of the predissociated state is transformed into kinetic energy of the fragment atoms rather than into radiation. 

Only the total lifetime r of a level can be measured, r is related to the rate of decrease of the number of molecules initially in a given level via both radiative and nonradiative routes. Let kr be the radiative rate constant (the probability per unit time that a molecule will leave the level as a result of emission of a quantum of light) and knr the predissociation rate (the dissociation probability per unit time). Recall that the pressure is assumed to be low enough that the rates are not affected by collisions. The number of molecules leaving the initial state during the time interval dt is given by 

Nq being the initial population, and the emitted radiation has intensity proportional to N(t). The lifetime is defined by 

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In closing the section on non-Hermitean approaches to continuum processes in atomic and molecular physics, we will also mention accurate examinations on resonance parameters in molecular predissociation displaying unexpected resonance overlapping [46,89]. The phenomenon of predissociation by rotation in HgH was analyzed via an isotopically combined potential due to Stwalley [120]. The potential, i.e., a relatively shallow energy curve with a nonzero /-value giving rise to a rotational barrier, supported novel metastable states above the dissociation limit. The Weyl s method was able to resolve the closely lying vibrational states v = 3 and v = 4 for the rotational quantum number K = 9. 

M. Hehenberger, B. Laskowski, E. Brandas, Weyl s Theory Applied to Predissociation by Rotation. I. Mercury Hydride, J. Chem. Phys. 65 (1976) 4559. 

This is generally known as Case I of predissociation it concerns an electronic transition. Case II, predissociation by vibration, can only take place in polyatomic molecules. Case III is predissociation by rotation, and concerns transitions in the same electronic level. The question is treated in detail by Herzberg i, ... 

Figure 7.12 Predissociation by rotation. The J 0 potential is obtained by adding the centrifugal energy, fi2 J(J + l)/2fj,R2, to the J — 0 potential.

Even more so than for perturbations, the isotopic dependence of predissociations is useful for identifying the electronic symmetry of the unbound state. The naive assertion that the lightest isotopic molecule is predissociated most rapidly must be examined with caution. It is valid only in the cases of gyroscopic predissociation and predissociation by rotation through a centrifugal barrier. In Eq. (7.5.17), the matrix element... 

As noted in Section 7.3, shape resonances also occur in the spectrum of vibrational transitions. They correspond to predissociation by rotation (resonances stabilized behind the nuclear motion centrifugal barrier, Vj(R)). Here the name shape resonance comes from the shape of the barrier on Vj(R). 

Both electronic and vibrational shape resonances arise from a direct process and can be explained by a single potential (McKoy, et al., 1984). Shape resonances (single Vi(r) or Vj(R)) differ from autoionization resonances and predissociation (with the exception of predissociation by rotation), which involve two potentials or two states with different quantum numbers. 

O. Goscinski and O. Tapia Predissociation by Rotation and Long-Range Interactions Mol. Phys. 24, 647 (1972). 

Fig. 12.5. Zeroth-order potentials Veff(R-,j,Sl,J) defined in (12.7) for fl = 0 and several total angular momentum quantum numbers J. The excited rotational states can decay either by tunneling (shape resonances) or by rotational predissociation ( Feshbach resonances) as indicated by the horizontal arrows. The excitation through the IR photon originates from the vibrational ground state n = 0 which is not shown in the figure.

FIGURE 9 Potential energy curves of HI. The insert shows the rotational structure of the b3n- Rydberg state, which is predissociated by the A1 n valence state. [Reproduced with permission from Fiss, J. A., Khachatrian, A., Truhins, K., Zhu, L., Gordon, R. J., and Seideman, T. (2000). Phys. Rev. Lett. 85, 2096.]... 

The experimental results for v = 7 [37] showed that the lowest ( 15) rotational levels exhibited single exponential decay with a decay constant that was essentially independent of J. These levels were then assumed to be stable and unaffected by the predissociation. For much higher initial rotational states, J > 28, the observed lifetime was dramatically shortened. A very rapid initial decay was observed followed after a few microseconds by a slower decay. On increasing the pressure, the initial fast decay was hardly affected but the intensity of the longer-lived decay component increased as more molecules were transferred by rotational relaxation out of the initially formed predissociated state into lower-lying stable states. 

Predissociation By Internal Rotation Vibrational Predissociation With Av=0... 

Results and Predictions. Detailed close coupling calculations for "real" Av<0 vibrational predissociation of weak-coupling systems such as the hydrogen-inert gas complexes are more difficult and computationally more expensive than those for predissociation by internal rotation. The computational expense arises simply from the very large increase in the nvmber of channels which must be included in order to obtain converged results. The difficulty, on the other hand, arises from the fact that these resonances have very small widths, usually 10 cm , %jhich makes them very difficult to find. 

Calculations analogous to those of Table V have not yet been reported for complexes of hydrogen with other inert gases. However, our experience with the case of predissociation by internal rotation and our understanding of the potential energy surfaces involved should allow us to make reliable predictions reqarding the trend from one system to the next. 

The distinction between direct dissociation processes discussed in the present section and indirect dissociation or predissociation processes discussed in Section 7.3 to Section 7.14 is that in a direct process photoexcitation occurs from a bound state (typically v = 0 of the electronic ground state) directly to a repulsive state (or to an energy region above the dissociation asymptote of a bound state) whereas in an indirect process the photoexcitation is to a nominally bound vibration-rotation level of one electronically excited state which in turn is predissociated by perturbative interaction with the continuum of another electronic state. Direct dissociation, often termed a half collision is much faster and dynamically simpler than indirect dissociation. In a direct dissociation process the distance between atoms increases monotonically and the time required for the two atoms to separate is shorter than a typical vibrational or rotational period (Beswick and Jortner, 1990). 

If a predissociation is strong, the observed widths can often be explained in terms of a single-configuration picture for the two states. Consider, for example, the OD A2X+ state (see Fig. 7.31). The v >7 vibrational levels of the A2X+ state of OD are strongly predissociated. The rotational lines of the B2X+ — A2X+ emission system are broadened by predissociation of A2X+, the lower state of the transition, and the linewidth is found to vary rapidly with v and N. Figure 7.21 shows this variation for the v = 11 level of OD A2X+. 

The collision-assisted predissociation in iodine B O + state merits a detailed discussion. It is well known that B state is weakly coupled to the dissociative A 1m state by rotational and hyperfine-structure terms in the molecular Hamiltonian. The natural predissociation rate strongly depends on the vibrational quantum number (pronounced maxima for o=5 and u = 25, a minimum for u= 15), this dependence being due to a variation of the Franck-Condon factor. " The predissociation rate is enhanced by collisions. In absence of a detailed theoretical treatment of the colhsion-assisted 12 predissociation, one can suppose that the asymmetric perturbation (breakdown of the orbital symmetry) in the collisional complex affects electronic and rotational wavefimctions but does not change the nuclear geometry. 

Figure 6 shows a higher resolution spectrum of the fluorescence from another excited state, l Ag (N-31, Fi) to the v=0 level of b IIu. Because these are both good Hund s case(b) states, due to small spin-orbit coupling, large rotational constants, and high J, the spectrum exhibits a P,Q,R pattern. The weaker features are due to collisional relaxation in the upper state, as in Na2 (Figure 1). The Q(N=31) line in this fluorescence scan is broader than the instrumental resolution of about 0.8 cm due to predissociation by the a Ey" vibrational continuum. The R(30) and P(32) lines are sharp. However, the collisionally relaxed Q(30) and Q(32) lines are sharp and the R and P lines adjacent to R(30) and P(32) are broad. The reason for this selectivity in the predissociation of the b II rotational levels is explained by examining Figure 7.

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