Selection rule, vibrational predissociation

Ewing, G.E. (1987). Selection rules for vibrational energy transfer Vibrational predissociation of van der Waals molecules, J. Phys. Chem. 91, 4662-4671. 

In gas-phase dynamics, the discussion is focused on the TD quantum wave packet treatment for tetraatomic systems. This is further divided into two different but closed related areas molecular photofragmentation or half-collision dynamics and bimolecular reactive collision dynamics. Specific methods and examples for treating the dynamics of direct photodissociation of tetraatomic molecules and of vibrational predissociation of weakly bound dimers are given based on different dynamical characters of these two processes. TD methods such as the direct projection method for direct photodissociation, TD golden rule method and the flux method for predissociation are presented. For bimolecular reactive scattering, the use of nondirect product basis and the computation of the initial state-selected total reaction probabilities by flux calculation are discussed. The descriptions of these methods are supported by concrete numerical examples and results of their applications. 

More precisely the two energy surfaces A and B will intersect each other along a curve. The chance of predissociation for a vibration-rotation level of B will be great—apart from the fulfilment of selection rules perhaps introduced by the symmetry properties of the molecule—if its energy is about the same as that of a point on the intersection curve. For then the vibratory motion of the molecule represented by a sort of Lissajous figure on the surface V pa) come somewhere near the line of intersection with the surface V (p, pa) of A, making it easy for the molecule to jump from the former to the latter surface. 

Not only do the experimental vibrational predissociation lifetimes require interpretation, so do the increasingly sophisticated theoretical calculations whose results often fall out of a web of coupled differential equations or the convoluted algebra of quantum mechanics. In order to offer a qualitative overview of dynamical processes in van der Waals molecules, we shall introduce a selection rule which can provide insight into possible relaxation channels of vibrationally excited molecules. This selection rule concerns the change in a quantum number, Anj., which is to remain small for efficient vibrational predissociation processes. It bears a close analogy to the selection rules of optical spectroscopy which require small changes in quantum numbers Au, AJ, AS, etc. for efficient transitions between molecular states. Let us review the origin of the vibrational predissociation selection rule which has been developed in more detail elsewhere. ... 

We are now prepared to set down the effective quantum numbers for use of the selection rule expression of eq. 5. Application of the analytical expression for vibrational predissociation rates of A-B C for a wide variety of van der Waals molecules bound by Morse intermolecular potential functions like those shown in Fig. 2 reveals the effective translational quantum number change... 

Figure 3. The total quantum number change, An, and lifetimes, r, for vibrational predissociation. The line is the selection rule expression of eq. 5. Experimental measurements are indicated by the open circles described in the text.

The problem lies in the assumption required to derive the selection rule that the u=l and u=0 surfaces are the same shape and are merely displaced vertically as we have illustrated in Fig. 2. For HF HF on the contrary, the intermolecular potential is highly anisotropic and rotational excitation of the fragments results in an effective potential which is shallow and may actually cross other surfaces. This has been demonstrated in calculations of Halberstadt et al.. The surfaces taken from their work are shown in Fig. 4. The curve crossing yields relaxation times orders of magnitude more efficient than those calculated by our selection rule. It is a challenge to the theorists to model the predissociation process, consistent with experiment, that allows both HF molecules to rotate on fragmentation. Clearly anisotropic effects will play an important role in understanding vibrational predissociation in other systems as well-for example, in the electronically excited state of OH Ar by Lester et al.. ... 

It has been shown that Fermi resonances between chemical bond vibrational levels and van der Waals modes can dramatically reduce vibrational predissociation lifetimes. The selection rule becomes altered because the definitions of the quantum numbers become blurred by the Fermi resonances. This is illustrated in the recent study of Tiller, Peet and Clary and shown in Fig. 5. Here 5 0,0,0> mixes with nearby 17 0,0,10> whose vibrational predissociation lifetime is calculated to be two orders of magnitude shorter than the prepared state. 

Here NaCl(lOO) is the face of a single crystal of salt and the dots represent the physisorbed bond dominated by electrostatic contributions as in the case of van der Waals molecules. The vibrational energy in CO of 2100 cm exceeds the physisorbed bond strength of 1500 cm so predissociation is possible and relaxed CO flies away with kinetic energy AE 600 cm. For the same reason vibrational predissociation is inefficient for N2 -N2 so it is for the relaxation of eq. 12. Indeed attempts to photodesorb CO from NaCl(lOO) have failed and the quantum yield for this relaxation channel is < 10". Theory to account for relaxation channels from excited molecules physisorbed to surfaces is developing but the paucity of experimental data prevents a calibration of the calculations. The selection rule of eq. 5 can be easily extended to qualitatively account for photodesorption and becomes... 

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