Predissociation indirect

These selective transitions (1), (7), and (9) may be achieved by proper optimization of the parameters eo and w, as described elsewhere [13, 18, 21]. Extensions to IR femtosecond/picosecond laser-pulse-induced dissociation or predissociation have been derived in Ref. 16, using either the direct or the indirect solutions of the Schrodinger equation (2) the latter requires extensions of the expansion (5) from bound to continuum states [16,31]. (The consistent derivation in Ref. 16 is based on S. Fliigge in Ref. 31). The same techniques can also be used for IR femtosecond/picosecond laser-pulse-induced isomerization as well as for more complex systems that are two dimensional, three dimensional, and so on, at the expense of increasing numerical efforts due to the higher dimensionality grid representations of the wavepackets f/(t) or the corresponding expansions (5) (see, e.g., Refs. 18, 20, and 21). 

The question arises how does one distinguish experimentally between these two types of photodissociation This question can be answered from consideration of the absorption spectrum. The predissociative state is bound, and, therefore, is characterized by a set of discrete levels. The indirect channel implies the appearance of resonant structure in the photodissociation cross section as a function of the frequency of the incident radiation. Hence, discrete structure in the absorption spectrum indicates the indirect nature of the photodissociation. For example, analysis of the absorption spectrum of C2N2 leads to the conclusion that the process C2N2 (C- -IIu)+ hv -+ CNCX rtj +CN(A II) at V = 164 nm is an indirect photodissociation process (8). 

From this starting point, the authors develop equations leading to the evaluation of the real symmetric K matrix to specify the scattering process on the repulsive surface and propose its determination by a variational method. Furthermore, they show explicitly the conditions under which their rigorous equations reduce to the half-collision approximation. A noteworthy result of their approach which results because of the exact treatment of interchannel coupling is that only on-the-energy-shell contributions appear in the partial linewidth. Half-collision partial linewidths are found not to be exact unless off-the-shell contributions are accidentally zero or (equivalently) unless the interchannel coupling is zero. The extension of the approach to indirect photodissociation has also been presented. The method has been applied to direct dissociation of HCN, DCN, and TCN and to predissociation of HCN and DCN (21b). 

As mentioned in the previous section, indirect photodissociation is a two-step process. The predissociative state undergoes a radiationless transition to the final state of photofragments. The radiationless transition can be caused by a time-independent term of the Hamiltonian (see, e.g., ref. 15), then the transition occurs between states with the same energy. 

The Born-Oppenheimer (BO) description is not exact. The deviation from the BO approximation can be treated as an additional nonadiabatic interaction. This interaction does not depend on time and can be the origin of radiationless transitions. Moreover, the nonadiabatic interaction is a main mechanism for one kind of indirect photodissociation, namely, photopredissociation of Type I (electronic predissociation). 

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). 

Although photochemical reactions of hydrogen and hydrocarbons proceed easily and with high quantum yields, nitrogen photochemistry is not that straightforward. The triple bond within the N2 molecule is extremely difficult to break (E> 9.7 eV). Furthermore, there are no optically allowed excitation paths into repulsive electronic excited states, and dissociation can occur only via indirect paths. Solar radiation below 100 nm can excite predissociating electronic states and constitutes a minor source of N atoms. Dissociative ionization of N2 by either electron impact or solar extreme UV (10-121 nm) radiation produces one N atom and one N+ ion [9] ... 

J or one of the lower-lying singlet states. He further suggests that at 1849 A the sequence is Hg -f O2— 02 PS ] 4- Hg, followed by predissociation of the excited O2 into two translationally excited pP] O atoms. The evidence is again very indirect. The latter proposal would be in conflict with the chain decomposition proposed above. 

Theoretical calculations of the dissociative recombination of Hj using the same approach as for the predissociation problem give cross sections that are smaller than all experimental results given in Table 1. However, these are only restricted, two-dimensional theoretical results, and cannot be used to draw definitive conclusions. Three-dimensional calculations, including all relevant electronic states, will be needed in the future. What seems clear at this point is that direct dissociative recombination, (X Ui) + e H3 (X E ) H + H + H or H + H2, is very slow. " For HeH" " it was found that the indirect mechanism, which involves vibrationally excited Rydberg states as intermediates, enhances the cross section.According to the preliminary calculations, the effect of the indirect mechanism is even more pronounced for Hj. Model calculations have shown that channel mixing effects can enhance the DR cross section substantially when the indirect mechanism is taken into... 

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). 

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 ... 

The effect of predissociation on spectral features depends on whether it is the initial or final state of the transition that is predissociated. Predissociation can be detected either by direct measurements of lifetimes (r), linewidths (T), or level shifts (5E), or indirectly by observation of fragments. Table 7.2 surveys the range of predissociation rates sampled by different methods. Erman (1979) has reviewed the experimental methods for characterizing predissociation phenomena. 

Anomalous isotope effects occur at accidental or indirect predissodations, which are discussed in Section 7.13. The accidentally predissociated v, J-level is perturbed by a v, 7-level that is directly predissociated by a third (unbound) state. The accidentally predissociated level, having acquired an admixture of the perturber s wavefunction, borrows part of the characteristics of the perturber,... 

Indirect or accidental predissociation, which is treated in the following section. 

In Section 7.8 the possibility of predissociation of isolated lines was mentioned. This is usually called accidental predissociation and can be interpreted as perturbation of a nominally bound rotational level by a predissociated level that lies nearby in energy for this value of J. This type of predissociation should more generally be called indirect predissociation, since the predissociation takes place through an intermediate state (or doorway state, see Section 9.2). 

Figure 7.38 The potential energy curves of some states of N2. The indirect predissociation of b1nu(u = 3) by the C,3n continuum via the C3II (u = 8) level is shown. The widths of the directly and indirectly predissociated levels are indicated.

Figure 7.39 Schematic mechanism of the indirect or accidental predissociation described in Fig. 7.38.

Figure 7.40 Comparison between the Budo-Kovacs (dashed line) and coupled equations (solid line) models for indirect predissociation. The width of the indirectly predissociated N2 b1nu(ii = 3) level is plotted versus the energy separation from the C3IIu(u = 8) intermediate predissociated perturbing level. The electronic coupling between the C and C states is taken as 400 cm-1. [Courtesy J.M. Robbe from data of Robbe (1978).]...

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) ... 

While the use of direct absorption methods has grown, indirect action spectroscopic methods continue to be widely and successfully used in the study of neutral molecular clusters. As mentioned earlier, there are two commonly used detection methods, mass spectrometers and bolometers. Because of the variety of mass-spectroscopic methods, there is an equally wide range of techniques used in neutral cluster spectroscopy. One of the oldest among these involves electron-impact mass spectrometry of a cw neutral beam combined with vibrational predissociation spectroscopy using a tunable cw or pulsed laser. The advent of continuously tunable infrared sources (such as color center lasers and LiNbOa optical parametric oscillators) allowed for detailed studies of size and composition variation in neutral clusters. However, fragmentation of the clusters within the ionizer of the mass spectrometer, severely limited the identification of particular clusters with specific masses. Isotopic methods were able to mitigate some of the limitations, but only in a few cases. 

Band and Freed have criticized the quasi-diatomic approximation and emphasized that any complete theory of dissodation must involve the use of the correct sets of normal modes Q and O of the molecule in the initial and final states (> and /> respectively. The two sets are not independent, but are related by a co-ordinate transformation. A detailed, quantum mechanical description has been developed in which the set Q in state ( > are taken to be the normal modes of the unexdted parent molecule for direct photodissodation, or the metastable photo-excited molecule for indirect predissociation, and the set Q ) in the state /> are separated into QUQi, wh e Qi is the reaction co-ordinate on the final repulsive surface and IQi are the normal modes in the photofragments. For a linear, triatomic molecule, Qi is simply the vibrational mode of the diatomic fragment and Q) indudes the symmetric and antisymmetric stretching modes (if collinearity is preserved). The matrix elements for the transition from... 

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