Rotational reflection principle

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... 

The reflection principle, outlined in Sections 6.1 and 6.2, explains the energy dependence of absorption spectrum as a mapping of the initial coordinate distribution in the electronic ground state onto the energy axis. Rotational state distributions of diatomic photofragments in direct dissociation can be explained in an analogous manner. 

Equation (6.27) manifests the rotational reflection principle (Schinke 1986c Schinke and Engel 1986) as illustrated in Figure 6.6 ... 

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. 

Schinke, R. (1986c). The rotational reflection principle in the direct photodissociation of triatomic molecules. Close-coupling and classical calculations, J. Chem. Phys. 85, 5049-5060. 

Schinke, R. and Engel, V. (1986). The rotational reflection principle in photodissociation dynamics, Faraday Discuss. Chem. Soc. 82, 111-124. 

Schinke, R. and Staemmler, V. (1988). Photodissociation dynamics of H2O2 at 193 nm An example of the rotational reflection principle, Chem. Phys. Lett. 145, 486-492. 

Figures 7.5 and 7.6 show the experimental absorption spectra of HCl and DCl, respectively, together with the spectra calculated using wavepacket propagation and the reflection principle. It can be seen that the wavepacket method is in good agreement with the experimental results. For both HCl and DCl the wavepacket propagation method yields the correct frequency for the absorption peak. The wavepacket propagation method is exact and the deviation from the experimental spectrum must be attributed to the use of only two electronic states and/or inaccurate transition dipole moments and/or potential energy curves and/or not treating the rotations of the molecule. The experimental results are quite accurate.

A general statement of this argument is that in an isotropic system flows and forces of different tensorial orders are not coupled. This is known as the Curie principle. Systems that are anisotropic often have some elements of symmetry which reduce the number of nonzero coefficients from the maximum of n2. To prove these relations one must apply the arguments of Chapter 11 involving parity, reflection symmetries, rotational symmetries, and time-reversal symmetries. 

In principle, rotations around three axis (one of them 6) would be sufficient to bring any lattice plane into an orientation satisfying the Bragg condition (see above) and to intercept the resulting diffracted beam with the detector. However, the fourth degree of freedom makes possible an azimuthal scan of a reflection, during which the plane remains in a reflecting position but the crystal rotates around the normal to this plane (so-called ijr axis). 

Rotational state distributions like the one in Figure 9 have been measured for many systems. If the initial wave function has nodes along the angular coordinate, these nodes will be reflected as undulations in the state distribution. If the decay proceeds through a transition state, instead of the bending wave function of the parent molecule it is the wave function at the TS that is reflected. The rotational reflection principle not only provides a very simple explanation of final rotational state distributions, it also shows that complicated brute force calculations are not always necessary sometimes simple mechanistic pictures can provide simple insight as well as quantitative agreement with full quantum mechanical calculations. ... 

A striking experimental result is that the speed distribution of S (or the rotational distribution of CO) is bimodal (8,14,15). Since the bending wavefunction of a parent molecule and the rotational distribution of a diatomic fragment can be related by the rotational reflection principle (16), a Gaussian-shaped rotational distribution of CO may be anticipated for a single dissociation channel. The observed bimodal distribution implies that there is bifurcation in dissociation dynamics. The scattering distribution of S atoms observed by ion imaging indicates that the bimodal distribution occurs only for dissociation from the A ( A) state and not for the A ( 2 ) state. The question is why does it occur only from the A ( A) state ... 

We performed wave packet calculations on the 2A and lA adiabatic ab initio surfaces. As is easily understood from the similarity of the 2A and lA PES s and from the rotational reflection principle, dissociation on these two surfaces produce ahrost identical product distributions, i.e. singly-peaked Gaussians. This is clearly at odds with the observed bimodality in the product distribution and the specificity observed for 2A , suggesting that bimodality cannot be explained by adiabatic dissociation dynamics. Close inspection of Fig. 3 reveals that both the 2A ( A) and 1 A ( S ) surfaces approach the ground state around 0 = 65 , where non-adiabatic transition from 2A to 1 A might be anticipated. 

In this work, a microwave interferometric method and apparatus for vibration measurements is described. The principle of operation is based on measurement of the phase of reflected electromagnetic wave changing due to vibration. The most important features of the method are as follows simultaneous measurement of tlie magnitude and frequency of the rotating object high measurement accuracy weak influence of the roll diameter, shape and distance to the object under test. Besides, tlie reflecting surface can be either metallic or non-metallic. Some technical characteristics are given. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

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