Predissociation vibrational

For energies below the first threshold, Ar + H2(n = 0), both vibrational channels are asymptotically closed and the coupled equations must be 

The rigorous calculation of the absorption spectrum now proceeds in exactly the same way as outlined in Section 3.1.2 [see Equation (3.14)] with the exception that the transition dipole function is replaced by the dipole function [i.e., the diagonal element of the dipole matrix defined in Equation (2.35)] because the absorption takes place in the same electronic state. Below the first threshold, the spectrum is discrete because both vibrational states are true bound states. Above the n = 0 threshold, however, the system becomes open and can dissociate yielding Ar and H2(n = 0). The spectrum is consequently a continuous spectrum with sharp resonances near the quasi-bound states temporarily trapped by the 

V potential curve. The inclusion of higher vibrationally excited states is straightforward.  

Predissociation of van der Waals molecules is ideally suited for the application of the general expressions for the decay of resonance states derived in Section 7.2, especially Equation (7.12) for the dissociation rate. The reason is that the coupling is so small that we can rigorously define accurate zero-order states 

For the sake of simplicity we assume that the interaction potential has the form Vj(R, r) = Vo(R) + Vi(ii) (r — re). Only the second term can induce vibrational-translational coupling and therefore initiate the decay of the quasi-bound state. With W = V R) (r — re) inserted in Equation (7.12) the dissociation rate becomes 

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Another example of current interest is the vibrational predissociation of hydrogen bonded complexes such as (HF) ... 

Pine A S, Lafferty W J and Howard B J 1984 Vibrational predissociation, tunneling, and rotational saturation in the HF and DF dimers J. Chem. Phys. 81 2939-50... 

Ewing G E 1980 Vibrational predissociation in hydrogen-bonded complexes J. Cham. Phys. 72 2096-107... 

Huang Z S, Jucks K W and Miller R E 1986 The vibrational predissociation lifetime of the HF dimer upon exciting the free-H stretching vibration J. Cham. Phys. 85 3338-41... 

The temi action spectroscopy refers to those teclmiques that do not directly measure die absorption, but rather the consequence of photoabsorption. That is, there is some measurable change associated with the absorption process. There are several well known examples, such as photoionization spectroscopy [47], multi-photon ionization spectroscopy [48], photoacoustic spectroscopy [49], photoelectron spectroscopy [, 51], vibrational predissociation spectroscopy [ ] and optothemial spectroscopy [53, M]. These teclmiques have all been applied to vibrational spectroscopy, but only the last one will be discussed here. 

A nice example of this teclmique is the detennination of vibrational predissociation lifetimes of (HF)2 [55]. The HF dimer has a nonlinear hydrogen bonded structure, with nonequivalent FIF subunits. There is one free FIF stretch (v ), and one bound FIF stretch (V2), which rapidly interconvert. The vibrational predissociation lifetime was measured to be 24 ns when excitmg the free FIF stretch, but only 1 ns when exciting the bound FIF stretch. This makes sense, as one would expect the bound FIF vibration to be most strongly coupled to the weak intenuolecular bond. 

For complexes such as Ar-H2, Ar-HF and Ar-lTCl, vibrational predissociation is a very slow process and does not cause appreciable broadening of the lines in the infrared spectmm. Indeed, for Ar-ITF, ITuang et al [20] showed that... 

Figure C 1.3.5. Spectra of two different infrared bands of HF dimer, corresponding to excitation of the bound (lower panel) and free (upper panel) HF monomers in the complex. Note the additional line width for the bound HF, caused by vibrational predissociation with a lifetime of about 0.8 ns. (Taken from 1211.)...

Figure 2. Laser-induced fluorescence and action spectra acquired in the ICl B—X, 2-0 spectral region. The LIF spectrum, panel (a), is dominated by the intense I Cl and I Cl transitions at lower energies. Features associated with transitions of the T-shaped He I C1(X, v" = 0) and hnear He I C1(A, v" = 0) and He I C1(X, v" = 0) conformers are observed to higher energy and are rs 100 times weaker than the monomer features. The action spectra, (b), was recorded by probing the I Cl E—B, 10-1 transition, or the Av = — 1 vibrational predissociation channel.

Zewail and co-workers performed a series of time-resolved experiments characterizing the vibrational predissociation dynamics of He I2(B, v ). 

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). 

U. Buck and I. Ettischer, Vibrational predissociation spectra of size selected methanol clusters New experimental results../. Chem. Phys. 108, 33 38 (1998). 

One major focus of these experiments has been the excited OH vibration population lifetime. This is currently interpreted as being dominated by either vibrational predissociation [2], i.e. the breaking of the hydrogen bond of an excited OH stretch [9], or by vibrational relaxation of the excited OH without such IR-induced bond breaking [7,10,11] (see Ref. 12 for a recent review). 

Vibrational Predissociation, in this section we discuss the case of a transition from a predissociative state to the photofragment state that occurs on a single adiabatic pes. Such processes cannot occur for diatomic molecules, but they can be observed for polyatomic systems. The transition is caused by intramolecular energy transfer, that is, by internal redistribution of vibrational energy. 

Thus, we can use the same derivation as that carried out for vibrational predissociation (see Section III) to obtain an expression for the probability of obtaining product energy distributions. The functions Tp = andTp = ilptfp describe... 

Usually tunneling through a potential barrier is considered on the basis of the stationary Schroedinger equation with the use of matching conditions. A different approach has been developed by Bardeen (34). Bardeen s method enables one to describe tunneling as a quantum transition and to use the Golden Rule in order to evaluate the probability of penetration through the barrier. A similar method has been used in Section III to describe vibrational predissociation. This section contains a short description of Bardeen s method (see refs. 39,82-84). 

The Si PES, calculated by Nonella and Huber (1986), has a shallow minimum above the ground-state equilibrium, or expressed differently, a small potential barrier hinders the immediate dissociation of the excited S complex. Although the height of the barrier is less than a tenth of an eV, it drastically affects the dissociation dynamics, even at energies which significantly exceed the barrier. The excited complex lives for about 5-10 internal NO vibrational periods before it breaks apart. The photodissociation of CH3ONO through the Si state exemplifies indirect photodissociation or vibrational predissociation (Chapter 7). 

In this section we will explain the essential mechanism of vibrational predissociation by virtue of a linear atom-diatom complex such as Ar H2. Figure 12.1 illustrates the corresponding Jacobi coordinates, t In particular, we consider the excitation from the vibrational ground state of H2 to the first excited state as illustrated in Figure 12.2. The close-coupling approach in the diabatic representation, summarized in Section 3.1, provides a convenient basis for the description of this elementary process. For simplicity of presentation we assume that the coupling between the van der Waals coordinate R and the vibrational coordinate r is so weak that it suffices to include only the two lowest vibrational states, n = 0 and n = 1, in expansion (3.4) for the total wavefunction,... 

Fig. 12.4. ln(r/n) plotted versus [m(en - en i)]x 2 for the vibrational predissociation of HeCl2. m is the reduced mass of the van der Waals molecule and en — en i is the energy spacing between adjacent levels of the Morse oscillator. Note that n increases from the right- to the left-hand side Adapted from Cline, Evard, Thommen, and Janda (1986). 

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