Indirect photodissociation

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). 

Another possibility for distinguishing between direct and indirect channels arises from an analysis of the angular dependence of the fragments. If the photodissociation is direct, there will be a correlation between the angular distribution and and direction of the radiation. For indirect photodissociation the correlation vanishes, because the appearance of the photofragments is a result of the radiationless transition. 

Takatsuka and Gordon (21a) have developed a "full collision" formulation of photodissociation which describes a multichannel process on the repulsive surface for both direct and indirect events. The scattering wavefunctions that are used to generate the T-matrix and the FC overlaps are not zeroth-order uncoupled functions, but solutions of the coupled-channel problem. 

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). 

We now turn to the analysis of indirect photodissociation. We shall see that this case can also be reduced to the analysis of nuclear dynamics. The problem of the evaluation of the nuclear wavefunctions and the FC factors will be discussed below in Sections III.C and III.D. 

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. 

Despite the fact that both states belong to the same pes, an approach has been developed that enables this type of indirect photodissociation to be described as a quantum transition (33). The method is analogous to Bardeen s theory of tunneling (34)... 

Indirect photodissociation of type II can be treated as a quantum transition between the Q and D states (see eqs. 41 and 42) which are eigenstates of the Hamiltonian H this transition is governed by AH. The term AH does not depend on time and can cause transitions between states of the same energy (see, e.g., ref. 15). This property is relevant because energy is conserved in the elementary step. Following the usual theory of quantum transitions, the solution is sought in the form y(t) =... 

According to the dressed oscillator model, the normal modes describing the dissociative state are assumed to be part of the set of normal modes for the initial bound state. However, the initial and final states (G and D for direct photodissociation, or Q and D for indirect photodissociation) are each characterized by their own set of normal modes, that are related to each other by a linear transformation (2,40). 

This expression has been analyzed for the dissociation of ICN. The initial thermal distribution corresponds to large j. A distribution peaked around j 25 was obtained, in good agreement with experimental data. The analysis has been generalized to describe the case of a bent triatomic molecule (53,5A). Moreover, these authors consider the scalar coupling which corresponds to indirect photodissociation. 

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). 

In addition to the direct methods, in which one calculates first the continuum wavefunctions and subsequently the overlap integrals with the bound-state wavefunction, there are also indirect methods, which encompass the separate computation of the continuum wavefunctions the artificial channel method (Shapiro 1972 Shapiro and Bersohn 1982 Balint-Kurti and Shapiro 1985) and the driven equations method (Band, Freed, and Kouri 1981 Heather and Light 1983a,b). Kulander and Light (1980) applied another method, in which the overlap of the bound-state wavefunction with the continuum wavefunction is directly propagated. The desired photodissociation amplitudes are finally obtained by applying the correct boundary conditions for R —> oo. 

In indirect photofragmentation, on the other hand, a potential barrier or some other dynamical force hinders direct fragmentation of the excited complex and the lifetime amounts to at least several internal vibrational periods. The photodissociation of CH3ONO via the 51 state is a representative example. The middle part of Figure 1.11 shows the corresponding PES. Before CH30N0(5i) breaks apart it first performs several vibrations within the shallow well before a sufficient amount of energy is transferred from the N-0 vibrational bond to the O-N dissociation mode, which is necessary to surpass the small barrier. 

In contrast to indirect dissociation, which is the topic of Chapter 7, direct photodissociation is relatively simple to understand. The reflection principle describes qualitatively the fully state-resolved photofragmentation cross sections a E, n, j) as a multi-dimensional mapping of the initial coordinate distribution in the electronic ground state ... 

The main characteristics of indirect dissociation are resonances in the time-independent picture and recurrences in the time-dependent approach. Resonances and recurrences are the two sides of one coin they reveal the same dynamical information but provide different explanations and points of view. To begin this chapter we discuss in Section 7.1, on a qualitative level, indirect photodissociation of a one-dimensional system. A more quantitative analysis follows in Section 7.2. The time-dependent and the time-independent views of indirect photodissociation are outlined and illustrated in Sections 7.3 and 7.4, respectively, with emphasis on vibrational excitation of the NO moiety in the photodissociation of CH30N0(S i). Section 7.5 accentuates the relation between... 

Fig. 7.1. Schematic illustration of indirect photodissociation for a one-dimensional system. The two dashed potential curves represent so-called diabatic potentials which are allowed to cross. The solid line represents the lower member of a pair of adiabatic potential curves which on the contrary are prohibited to cross. The other adiabatic potential, which would be purely binding, is not shown here. More will be said about the diabatic and the adiabatic representations of electronic states in Chapter 15. The right-hand side shows the corresponding absorption spectrum with the shaded bars indicating the resonance states embedded in the continuum. The lighter the shading the broader the resonance and the shorter its lifetime.

In this section we consider indirect photodissociation of systems with more than one degree of freedom in the time-dependent approach. We will use the results of Section 7.2 to derive approximate expressions for the wavepacket evolving in the upper electronic state, the corresponding autocorrelation function, and the various photodissociation cross sections. 

The photodissociation of methyl nitrite in the first absorption band, CH30N0(Si) — CH3O + NO(n, j), exemplifies indirect photodissociation (Hennig et al. 1987). Figure 1.11 shows the two-dimensional potential energy surface (PES) of the S electronic state as a function of the two O-N bonds. All other coordinates are frozen at the equilibrium values in the electronic ground state. Although these two modes suffice to illustrate the overall dissociation dynamics, a more realistic picture... 

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