Excitation function rotational

Figure 3.24. The rotational quadrupole alignment AJ asa function of translational energy /i ralls = Ef of D2 desorbing from Cu(lll) in the D2(v = 0, J = 11) quantum state (points connected by solid line) and in the D2(v = 1, J = 6) quantum state (points connected by dashed lines). The inset shows the same results plotted against Ef — E0(v, J), where E0(v, J) is the center of the S -shaped state-resolved translational excitation function obtained from unpolarized Df(Ef, v, J, Ts) measurements. From Ref. [421].

R. W. Field I must apologize for not being sufficiently clear about the excitation scheme we use for our acetylene experiments. Although the initial and final states are both on the acetylene X1 g surface, the final state we prepare is the result of two electronic transitions (A X followed by A —X) rather than one vibrational-rotational infrared or Raman transition. There is a profound difference between the knowledge of the excitation function needed to describe electronic versus vibrational processes. 

In chemiluminescence experiments such as those described previously in the experimental section, emission spectra characteristic of the excited products of ion-neutral collisions are obtained, that is, intensities of the emitted radiation as a function of wavelength. This permits identification of the electronically excited states produced in the reaction as well as determination of the relative populations of these states. In addition if the luminescence measurements are made using beam techniques, excitation functions (intensity of a given transition as a function of the translational energy of the reactants) can be measured for certain transitions. As is discussed later, some of the observed transitions exhibit translational-energy thresholds. In the emission spectra from diatomic or polyatomic product molecules, band systems are sometimes observed from which the relative importance of vibrational and rotational excitation accompanying electronic excitation may be assessed. 

The photo-dissociation dynamics at 193 nm was analyzed in detail and the observed rotational state distribution was obtained by using the rotation reflection principle by Schinke and Stasemler [53]. All rotational state distributions depend sensitively on the anisotropy of the dissociative potential energy surface. These are interpreted as a mapping of the bound state wave function onto the quantum number axis. The mapping is mediated by the classical excitation function determined by running classical trajectories onto the potential energy surface within the dissociative state. This so-called rotation-reflection principle... 

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)... 

J(ro) is the classical counterpart of the rotational quantum number j of the fragment molecule. (Note that J(to) is defined as a dimensionless quantity.) It represents the final angular momentum of the fragment molecule as a function of all initial variables to- In the same way, we define the vibrational excitation function (Miller 1974, 1975, 1985)... 

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). 

The value of the excitation function at the ground-state equilibrium angle ye determines approximately the maximum of the rotational distribution the breadth of the initial coordinate distribution together with the gradient dJ/yo control the width of P(j). 

In order to relate the rotational excitation function directly to the potential parameters we consider a potential of the form... 

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).

Because of the lack of quantum mechanical interference effects classical mechanics is well suited for the treatment of direct dissociation. Very few trajectories actually suffice to construct the rotational and the vibrational excitation functions which establish the unique relation between (ro,7o) and (n,j). /(70) and N(ro) are the links between the multi-dimensional PES on one hand and the final state distributions on the other. 

The photodissociation of H2O2 represents an instructive example of the rotational reflection principle, which was outlined in detail in Section 6.3. Figure 10.9 depicts the rotational excitation functions Ja(po) and Jb(p0) obtained in five-dimensional classical trajectory calculations including the 0-0 bond distance, the two polar angles at and the two azimuthal angles Pi of each OH rotamer (i = 1,2) (Schinke and Staemmler 1988). po is the initial torsional angle of the trajectory. The excitation functions have the same qualitative behavior although the p dependences of the A- and the 5-state PES differ remarkably. 

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).

Construct the rotational excitation function J(70) by starting classical trajectories on the transition line with initial angle 70. 

To account for quantum mechanical effects, an approximate quantum model that reproduces the findings of the two classical spin-based approaches was constructed in a next step.37 One foundation of this model was the finding that several (nonfmstrated) molecular antiferromagnets of N spin centers 5 (which can be decomposed into two sublattices) have as their lowest excitations the rotation of the Neel vector, that is, a series of states characterized by a total spin quantum number S that runs from 0 to N x 5. In plots of these magnetic levels as a function of S, these lowest S states form rotational (parabolic) bands with eigenvalues proportional to S(S +1). While this feature is most evident for nonfmstrated systems, the idea of rotational bands can be... 

The 0( D) +H2 reaction has been widely investigated both experimentally and theoretically and has become the prototype of insertion reactions [1, 10, 11, 12, 13, 14, 15, 16. 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], The combination of high r( sohition experiments and high accuracy of the theoretical calculations has allowed remarkable improvement in understanding of the reaction dynamics of this system. Many experimental results are available such as differential cross section (DCS), product translational energ - distribution, excitation function and product rotational angular momentum polarization [15, 17, 18, 23]. Two complementary detailed experiments have recently been performed. 

An application of the above model to FNO(5,) dissociation (Ogai et al., 1992) is illustrated in figure 9.19. The left-hand side of this figure depicts the rotational excitation function and the weighting function for four bending resonance states. 

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