Dissociative continuum

The preceding discussion was limited mostly to VP processes occurring by direct coupling of the quasibound state of the complex to the dissociative continuum, which is the simplest and most commonly observed decay route for the complexes. However, these systems also serve as ideal venues for studying an array of more complicated dynamical processes, including IVR, and electronic predissociation. This brief section will focus on the former, underscoring some of the inherent dynamical differences between Rg XY complexes by discussing the IVR behavior of a few systems. 

Figure 7. Potential energy diagram for HI, showing the two lowest ionization states (2n3//2 and 2 IT j, ) coupled to a neutral dissociative continuum (3Ao) at the three-photon (3

Tiffany78,78 has employed a tuned, pulsed ruby laser to excite Br2 to within 500-800 cm-1 below the dissociation continuum of the 3IIlu state (correlating with ground state atoms) and has observed the reaction of the bromine atoms resulting from the dissociation. By contrast with the collisional release mechanism, Tiffany has proposed a process in which the energy for dissociation for a small number of the Br IIm) molecules into ground state atoms is provided by collisions. 

The most extensive potential obtained so far with experimental confirmation is that of Le Roy and Van Kranendonk for the Hj — rare gas complexes 134). These systems have been found to be very amenable to an adiabatic model in which there is an effective X—Hj potential for each vibrational-rotational state of (c.f. the Born Oppenheimer approximation of a vibrational potential for each electronic state). The situation for Ar—Hj is shown in Fig. 14, and it appears that although the levels with = 1) are in the dissociation continuum they nevertheless are quasi bound and give spectroscopically sharp lines. 

The beginning of the continuum in the absorption spectrum of simple gas-phase molecules implies the dissociation of the bond in question. (Figure 4.3). In some molecules a blurring of the spectrum appears i before the dissociative continuum suggesting dissociation at a lower energy requirement- This is known as predissociation. An understanding of the... 

Feshbach or compound resonances. These latter systems are bound rotovibra-tional supramolecular states that are coupled to the dissociation continuum in some way so that they have a finite lifetime these states will dissociate on their own, even in the absence of third-body collisions, unless they undergo a radiative transition first into some other pair state. The free-to-free state transitions are associated with broad profiles, which may often be approximated quite closely by certain model line profiles, Section 5.2, p. 270 If bound states are involved, the resulting spectra show more or less striking structures pressure broadened rotovibrational bands of bound-to-bound transitions, e.g., the sharp lines shown in Fig. 3.41 on p. 120, and more or less diffuse structures arising from bound-to-free and free-to-bound transitions which are also noticeable in that figure and in Figs. 6.5 and 6.19. At low spectroscopic resolution or at high pressures, these structures flatten, often to the point of disappearance. Spectral contributions of bound dimer states show absorption dips at the various monomer Raman lines, as in Fig. 6.5. 

Photodissociation experiments have become one of the most valuable tools in chemical physics for the purpose of understanding how excited electronic states couple to the dissociation continuum. These experiments, and the the-... 

Examples of the latter two sources of the channel phase are illustrated in Fig. 11. From an independent knowledge that the channel phase for ionization of H2S is zero (or 7i), it is deduced that the phase lags A8(I, H2S+) and A8(HI+, H2S+) are equal, respectively, to the channel phases (modulo tv) for the dissociation (< [3) and ionization (< /+) of HI. The nearly flat, nonzero values of 8[3 (triangles in Fig. 11a) is indicative of coupling in the dissociation continuum, whereas the peak in 8(diamonds)... 

From the point of view of chemical reaction dynamics, the most interesting case is that of unbound excited states or excited states coupled to a dissociative continuum that is, photodissociation dynamics. The dissociative electronically excited states of polyatomic molecules can exhibit very complex dynamics, usually involving nonadiabatic processes. The TRPES and TRCIS may be used to study the complex dissociation dynamics of neutral polyatomic molecules, and below we will give two examples of dissociative molecular systems that have been studied by these approaches, NO2 and (NO)2. 

Franck-Condon dissociative continuum. At long times (Af = 3500 fs), a sharp photoelectron spectrum of the free NO(A, 3,v) product is seen. The 10.08 eV band shows the decay of the (NO)2 excited state. The 9.66 eV band shows both the decay of (NO)2 and the growth of free NO(A, 3,v) product. It is not possible to fit these via single exponential kinetics. However, these 2D data are fit very accurately at all photoelectron energies and all time delays simultaneously by a two-step sequential model, implying that an initial bright state (NO)2 evolves to an intermediate configuration (NO)2f, which itself subsequently decays to yield free NO(A, 3s) products [138]... 

Predissociation Dissociation occurring by tunnelling from a bound to an unbound rovihronic state. In an absorption spectrum of a molecular entity, the appearance of a diffuse band region within a series of sharp bands, is called predissociation, since irradiation with frequencies within the diffuse region leads to effective dissociation. The energy of the band is smaller than that of the dissociation continuum of the bound state. 

It is pertinent to mention here that from the convergence limit of the dissociation continuum, in the flash spectrum of SO, a value of 127.1 kcal./mole was obtained for Z)(S—0). ... 

In this chapter, we discussed the principle quantum mechanical effects inherent to the dynamics of unimolecular dissociation. The starting point of our analysis is the concept of discrete metastable states (resonances) in the dissociation continuum, introduced in Sect. 2 and then amply illustrated in Sects. 5 and 6. Resonances allow one to treat the spectroscopic and kinetic aspects of unimolecular dissociation on equal grounds — they are spectroscopically measurable states and, at the same time, the states in which a molecule can be temporally trapped so that it can be stabilized in collisions with bath particles. The main property of quantum state-resolved unimolecular dissociation is that the lifetimes and hence the dissociation rates strongly fluctuate from state to state — they are intimately related to the shape of the resonance wave functions in the potential well. These fluctuations are universal in that they are observed in mode-specific, statistical state-specific and mixed systems. Thus, the classical notion of an energy dependent reaction rate is not strictly valid in quantum mechanics Molecules activated with equal amounts of energy but in different resonance states can decay with drastically different rates. 

A predissociation is an indirect dissociation. It manifests itself by decomposition of the molecule when it is excited into a state that is quasi-bound with respect to the dissociation continuum of the separated atoms ... 

In the preceding sections, we have assumed that an absorption line has a Lorentzian shape. If this is not true, then the linewidth cannot be defined as the full width at half maximum intensity. Transitions from the ground state of a neutral molecule to an ionization continuum often have appreciable oscillator strength, in marked contrast to the situation for ground state to dissociative continuum transitions. The absorption cross-section near the peak of an auto-ionized line can be significantly affected by interference between two processes (1) direct ionization or dissociation, and (2) indirect ionization (autoionization) or indirect dissociation (predissociation). The line profile must be described by the Beutler-Fano formula (Fano, 1961) ... 

SO and OH. ° In the first two cases, the quenching is due to the collision-induced intersystem crossing, in the third one, to the collision-assisted transition into a dissociative continuum. In the case of SO2, both S, r, and processes seem to be important, while for OH the final... 

Compound-state resonances are important in quantal theories of unimolecular decomposition. They are prepared in low-energy atom (molecule)-molecule collisions when part of the relative kinetic energy of the motion becomes temporarily converted into excitation of the internal (rotational and/or vibrational) degrees of freedom of either partner. When this excitation occurs, the molecular system has insufficient energy in its relative motion to separate. One can also prepare compound-state resonances by using electromagnetic radiation (e.g., a laser) to excite the molecule. Thus, it is proper to view these resonances as the natural extension of the bound vibration-al/rotational eigenstates into the dissociative continuum. 

The RRKM rate for dimer dissociation must be treated with some care. For instance, it is not clear whether the van der Waals modes (six in the case of aniline—CH4) are more strongly coupled to the dissociation continuum than they are to the aniline or the CH4 modes. Kelley and Bernstein (1986) assume that the coupling between van der Waals modes and the rest of the dimer modes is weak so that the RRKM calculation includes only van der Waals modes. If on the other hand, the rest of the modes are coupled to the van der Waals modes, then all of them must be included in the RRKM density and sums of states calculations. In some cases it will make little difference which mechanism is assumed because the dissociation limit is often below an energy at which the molecular modes will contribute much density. In the case of aniline, only a few modes are below the dimer binding energy so that they contribute very little to the density of states. 

There are molecules which, in the Born-Oppenheimer approximation, can be bound only in excited states, such as the "excimer" molecules (HeH), (NeH), (ArH), and (HeF). These excited bound states decay to the dissociative continuum of the ground state either via radiative transitions or via radiationless transitions, each having its characteristic probability. Suppose we look at the collision of the (ground repulsive state) free atoms in the... 

The collinear A+BC dissociative collision can be treated in a straightforward manner,using the Time Dependent WavePacket (TDWP) method. The reason is that the dissociative continuum of the BC molecule is handled automatically within the space discretization scheme of the grid. As the basic method has already been described in detail elsewhere ,it will be only outlined here,emphasizing the technical points and some new features which lead to a significant reduction in computation time. 

Rydberg states is probably due to coupling to the dissociation continuum... 

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