Cross section dissociation

The next step is to consider tire cross-sections of the absorption of radiation by the diatomic halogen molecules in order to decide if the relative effects result from the efficiency of the radiation photon-molecule interactions. These are reflected in the dissociation cross-sections of tlrese interactions. 

The total dissociation cross sections of silane and disilane have been taken from Perrin et al. [201]. An uncertainty in the present knowledge of the silane chemistry is the branching ratio of the silane dissociation channels [192]. Here, the branching ratio is taken from Doyle et al. [197], who suggest using the branching ratio determined by Perkins et al. [202] for photolysis, viz., a branching of... 

In order to discuss predissociation dynamics, it is also important to derive a state-specific rate constant based on the measurements of absorption and dissociation cross sections. 

Figure 27. Cross section for collisional dissociation reactions of N/ ions in X22g and A2nu states as function of incident-ion kinetic energy are indicated by dotted and dashed lines, respectively. Solid line is collisional dissociation cross section for incident-ion beam produced by impact of 50 eV electrons, which includes a mixture of the two states.380...

The enhancement of collisional dissociation cross sections by reactant-ion vibrational excitation is also observed for interactions at relatively low translational energies, particularly in the energy region near threshold. This was demonstrated in studies of dissociation of ( = 0-5) in which... 

In the following we will call the a u,n,j) partial photodissociation cross sections.t They are the cross sections for absorbing a photon with frequency u and producing the diatomic fragment in a particular vibrational-rotational state (n,j). Partial dissociation cross sections for several photolysis frequencies constitute the main body of experimental data and the comparison with theoretical results is based mainly on them. Summation over all product channels (n,j) yields the total photodissociation cross section or absorption cross section ... 

The confluence of theory and experiment achieved in recent years has greatly deepened our understanding of molecular photodissociation. At this point, however, it is important to underline that the cornerstone of realistic dynamical investigations is a multi-dimensional potential energy surface (PES). The interrelation between PESs on one hand and the various dissociation cross sections on the other hand is one prominent topic of this book and therefore we think it is useful to elucidate some qualitative aspects of PESs before we start with the development of the dynamical concepts. 

For energies below the dissociation threshold we can use various coordinate systems to solve the nuclear Schrodinger equation (2.32). If the displacement from equilibrium is small, normal coordinates are most appropriate (Wilson, Decius, and, Cross 1955 ch.2 Weissbluth 1978 ch.27 Daudel et al. 1983 ch.7 Atkins 1983 ch.ll). However, if the vibrational amplitudes increase so-called local coordinates become more advantageous (Child and Halonen 1984 Child 1985 Halonen 1989). Eventually, the molecular vibration becomes unbound and the molecule dissociates. Under such circumstances, Jacobi or so-called scattering coordinates are the most suitable coordinates they facilitate the definition of the boundary conditions of the continuum wavefunctions at infinite distances which we need to determine scattering or dissociation cross sections (Child 1991 ch.l0). Normal coordinates become less and less appropriate if the vibrational amplitudes increase they are completely impractical for the description of unbound motion in the continuum. 

Fig. 3.5. Adiabatic potential curves en(R), defined in (3.31), for the model system illustrated in Figure 2.3. The right-hand side depicts three selected partial photo dissociation cross sections cr(Ef,n) for the vibrational states n = 0 (short dashes), n = 2 (long dashes), and n = 4 (long and short dashes). The vertical and the horizontal arrows illustrate the reflection principle (see Chapter 6). Also shown is the total cross section (Jtot Ef) ...

Calculation and Fourier transformation of the autocorrelation function S(t) in order to yield the total dissociation cross section. 

Which approach offers the better interpretation of the photodissociation dynamics in general and of the dissociation cross sections in particular The answer to this question depends very much on the particular system and cannot be decided in a unique way. There are cases which are better described by the time-independent picture while other systems may be better understood within the time-dependent view. In the course of this monograph we will always attempt to combine both views in order to reveal all facets of a particular system. 

Classical absorption and photo dissociation cross sections... 

Second, the calculated (as well as the measured) distributions are remarkably smooth although often more than fifty or so rotational states are populated. If so many quantum states take part in a collision, one intuitively expects pronounced interference oscillations. The reason for the absence of interferences is the uniqueness between 70 and j one and only one trajectory contributes to the cross section for a specific final rotational state. If two trajectories that lead to the same j had comparable weights, the constructive and destructive interference, within a semiclassical picture, would lead to pronounced oscillations (Miller 1974, 1975 Korsch and Schinke 1980 Schinke and Bowman 1983). These so-called supernumerary rotational rainbows are well established in full collisions (Gottwald, Bergmann, and Schinke 1987). If the weighting function W (70) is sufficiently wide that both trajectories contribute to the dissociation cross section, similar oscillations may also exist in photodissociation (see, for example, Philippoz, Monot, and van den Bergh 1990 and Miller, Kable, Houston, and Burak 1992). 

Fig. 7.7. Comparison of the different energy behavior of partial dissociation cross sections a(E,j) for the production of NO(j) in indirect, HONO(iS i), and in direct, ClNO(Si), photofragmentation. Note the quite different energy scales The results for HONO are obtained from a two-dimensional model (Schinke, Untch, Suter, and Huber 1991) and the cross sections for C1NO are taken from a three-dimensional wavepacket calculation (Untch, Weide, and Schinke 1991b).

The matrix elements (4>i(.E,n) pio f of(Ef)) are just the partial photodissociation amplitudes (2.68) which are required in the calculation of dissociation cross sections for vibrationally excited parent molecules. The actual calculation proceeds in the following way ... 

The main features of the early kinetics could be reproduced using a five-level rate equation which included convolution with the pump and probe pulse shapes. These levels represent five locations, or time windows (L1-L5), describing five discrete time zones in the evolution of the Cr(CO)6 excited state and ultimate formation of Cr(CO)5 and Cr(CO)4 in the gas phase. These levels are consecutively populated and differ in the nature and ratio of the fragment ions they produce. Their populations are modeled by rate equations providing the lifetimes (x. for Li) and the ionization-dissociation cross section ("a. for Cr(CO)n+) for a particular fragment in Li. This five-level model is represented in Fig. 12 and Table 2 contains the optimized... 

Table 2 The lifetimes x and effective ionization dissociation cross sections "a for the various fragment ions following excitation of Cr(CO)6 with X = 270 nm (From [15])...

Table 6 Lifetimes (xy) and effective ionization-dissociation cross sections (

Fig. 9. a Electrospray mass spectrum of a 10 4 mol l"1 solution of HC1 in H20 under mild declustering conditions, showing the presence of different clusters [(H30)(H20)n]+, the clusters with n=l, 2, and 3 being most prominent, b CID threshold curve (collision gas Ar), showing the dependence of the dissociation cross section against collision energy, and fit to Ar-mentrout s threshold function... 

An example of this modeling procedure is shown in Fig. 4 for the total dissociation cross section of the Cr+(CO)6 complex [9]. The energy at which the Cr+(CO)5 product signal first deviates from zero clearly depends on the sensitivity of the experiment, but certainly rises above the background at about 0.5 eV (Fig. 1). This apparent threshold energy differs appreciably from the E0 value obtained from modeling with Eq. (3), 1.59 0.09 eV, as indicated by where the dashed line deviates from zero in Fig. 4. The convolution of Eq. (3) over the... 

Fig. 1. Maxwell-Boltzmann electron energy distribution for 3 and 8 eV electrons, compared to experimental data for f(Ec) in CHF . Also shown is the total dissociation cross section of CHFj (reproduced with permission from Phys. Rev., A25 (1982) 1420 [7]).

Figure 1 also shows an MBD for 8 eV electrons and the typical variation with energy of the total electron impact dissociation cross section for CHF3 [7], This points out that the fraction of the electron population which has enough energy to initiate gas phase chemistry is extremely dependent upon Te. 

Numerical calculation of two-photon dissociation cross-sections for HJ. Cross-sections are small for low vibrational levels but increase rapidly with increasing vibrational excitation Spectroscopic study of ion photofragments resulting from the 193 nm photodissociation of H2, HD, DJ, 020", OD, ND3, and NDJ... 

J. C. Keck, Statistical Investigation of Dissociation Cross-Section for Diatoms, Discuss. Faraday Soc., 33 (1962) 173. 

It should be noted that dissociation cross sections used in JVE refer to excitation to the b 32u state only. Actual dissociation cross sections include excitation to all triplet H2 states. Use of experimental cross sections and of edf s which take into account the simultaneous presence of vibrational disequilibrium and of atoms yield values of k, also reported in Table 1, which are in better agreement with kexp. Further details can be found in Ref.2 ... 

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