Final rotational state distributions

Figure 11. Final rotational state distributions of CO following the decay of the (0, t>2, 0) resonances...

The final rotational state distributions of the products in the fragmentation of a polyatomic molecule contain additional clues about the intra- and intermolecular dynamics, especially about the coupling in the exit channel. In realistic as well as model studies it has been observed that the rotational state distributions of the photodissociation products reflect the angular dependence of the wave function at the transition state and the anisotropy of the PES in the exit channel [4, 9, 10]. HO2 is no exception. 

In order to calculate final rotational state distributions it is useful to define the so-called rotational excitation function (McCurdy and Miller 1977 Schinke and Bowman 1983 Schinke 1986a,c, 1988a,b)... 

As in Section 6.1 we set the initial momenta, Pq and jo, to zero and with the help of (2.57) we eliminate Ro as initial variable. The (unnormalized) final rotational state distribution for a given energy is thus transformed into a one-dimensional integral,... 

The final rotational state distribution essentially reflects the square of the bending wavefunction of the parent molecule the mapping is mediated by the rotational excitation function J(yo). 

However, we must underline that this simple relation is only valid in the sudden limit, Erot excitation function and therefore the final state distribution depends on the energy E, the reduced mass m, and last but not least the anisotropy parameter 0(7).+ More of the interrelation between the anisotropy of the PES and the final rotational state distribution follows in Chapter 10. 

Fig. 6.7. Left-hand side Rotational excitation function J(70) and weighting function W(70) for the dissociation of ClNO(Si). Right-hand side Calculated final rotational state distribution of NO for an excess energy of 1 eV. The dashed curves represent the same quantities calculated, however, within the so-called impulsive model (IM) which we will discuss in Section 10.4. Reproduced from Schinke et al. (1990).

A much clearer picture evolves when one decomposes the total spectrum into the partial photodissociation cross sections a(, n,j) for absorbing a photon with wavelength A and producing NO in a particular vibrational-rotational state with quantum numbers (n,j). Experimentally this is accomplished by measuring so-called photofragment yield spectra. The idea is, in principle, simple the NO product is probed by laser-induced fluorescence (LIF). However, instead of scanning the wavelength Alif of the probe laser (in order to determine the final rotational state distribution) one fixes Alif to a particular transition NO(2n, nj) —>... 

Rotational excitation as a consequence of overall rotation of the parent molecule before the photon is absorbed does not reveal much dynamical information about the fragmentation process. It generally increases with the magnitude of the total angular momentum J and thus increases with the temperature of the molecular sample. In order to minimize the thermal effect and to isolate the dynamical aspects of photodissociation, experiments are preferably performed in a supersonic molecular beam whose rotational temperature is less than 50 K or so. Broadening of final rotational state distributions as a result of initial rotation of the parent molecule will be discussed at the end of this chapter. 

In analogy to Section 9.1 and Equations (9.4) and (9.5) the (unnormalized) final rotational state distribution becomes... 

The final rotational state distribution in the elastic limit is approximately proportional to the rotational FC factors f(j). 

The initial state of H20(X) contains, in addition to bending excitation, some quanta of stretching excitation this does not, however, noticeably affect the present discussion of final rotational state distributions because stretching and bending vibrations separate to a very good approximation. 

Inserting the appropriate parameters yields a temperature of approximately 400 K in reasonable accord with the average of the two measured values. A linear Boltzmann plot of the final rotational state distribution usually indicates that the torque in the exit channel is weak. 

Fig. 10.9. Left-hand side Rotational excitation functions Ja and Jb for the dissociation of H2O2 through the lowest two excited states, A and B, as functions of the initial torsional angle tpo- IFa and Wb represent the corresponding weighting functions. For definitions see Section 6.3. Right-hand side The resulting final rotational state distributions of the OH products. Reproduced from Schinke and Staemmler (1988).

Fig. 10.10. Final rotational state distribution of the OH products following the photodissociation of H2O2 at 193 nm for three initial temperatures, 7h2o2 = 0 (beam, lower curve), 150 K (middle curve), and 300 K (bulk, upper curve). The experimental data (open circles) for dissociation in the beam and in the bulk are taken from Grunewald, Gericke, and Comes (1988) and Jacobs, Wahl, Weller, and Wolfrum (1987), respectively. The theoretical results (filled circles) for the dissociation in the A and in the B states are averaged according to a ratio of 3 1. Adapted from Schinke (1988c).

Do the final rotational state distributions of NO depend on the particular bending resonance excited in the complex and, if yes, how does the distribution reflect the degree of bending excitation ... 

Bending excitation of the parent molecule transforms into rotation of the fragment molecule and therefore it is plausible to expect a relationship between the initial excitation and the final rotational state distribution. 

The final rotational state distributions of NO can be qualitatively interpreted as a reflection of the stationary wavefunction at the transition state mediated by the dynamics in the exit channel. Figure 10.13 depicts the total stationary wavefunctions 7 E) corresponding to the en-... 

The final rotational state distributions qualitatively reflect the shape of the resonance wavefunctions along the transition line, i.e., along a line which is roughly perpendicular to the minimum energy path. 

Fig. 10.16. Final rotational state distributions of NO following the dissociation of C1NO through the T state. The quantum numbers n and k specify the initial vibrational and bending excitation of the ClNO(Ti) complex. The undulations for the excited bending states reflect the nodal structures of the dissociation wavefunction at the transition state. The open and the filled circles indicate different P and Q branches. The corresponding absorption spectrum is depicted in Figure 7.14. Adapted from Qian, Ogai, Iwata, and Reisler (1990).

A very small torque in the exit channel implies a comparatively large effect of overall rotation of the parent molecule on final rotational state distributions. 

Figure 11.2 illustrates the scheme of rotational energies for H2O in the electronic ground state and J = 4. In Section 11.3 we will elucidate the photodissociation of single rotational states and the resulting final rotational state distributions of the OH fragment. For this purpose it is important to stress that ... 

Each initial rotational state yields a distinct final rotational state distribution. This holds true even if the total angular momentum J is the same and merely the projection quantum numbers K- and K+, are different. 

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