Vibrationally excited coordinatively

The degree of vibrational excitation in a newly formed bond (or vibrational mode) of the products may also increase with increasing difference in bond length (or normal coordinate displacement) between the transition state and the separated products. For example, in the photodissociation of vinyl chloride [9] (reaction 7), the H—Cl bond length at the transition state for four-center elimination is 1.80 A, whereas in the three-center elimination, it is 1.40 A. A Franck-Condon projection of these bond lengths onto that of an HCl molecule at equilibrium (1.275 A) will result in greater product vibrational excitation from the four-center transition state pathway, and provides a metric to distinguish between the two pathways. 

The higher energy features can indeed be associated with transitions of He lCl(K,v" = 0) ground-state complexes with rigid He I—Cl linear geometries. In contrast to the T-shaped band that is associated with transitions to the most strongly bound intermolecular vibrational level in the excited state without intermolecular vibrational excitation, n = 0, the transitions of the linear conformer access numerous excited intermolecular vibrational levels, n > 1. These levels are delocalized in the angular coordinate and resemble hindered rotor levels with the He atom delocalized about the l Cl molecule. 

As we have reviewed here, the linear region is not fully repulsive, and transitions of the ground-state, linear conformer access vibrationally excited intermolecular levels that are delocalized in the angular coordinate. As depicted in Fig. 1, however, the internuclear distance is significantly longer in the excited state at the linear geometry. Consequently, there is favorable Franck-Condon overlap of the linear conformer with the inner-repulsive wall of the excited-state potential. It is therefore possible for the linear Rg XY conformers to be promoted to the continuum of states just above each Rg - - XY B,v ) dissociation limit. 

For reactants having complex intramolecular structure, some coordinates Qk describe the intramolecular degrees of freedom. For solutions in which the motion of the molecules is not described by small vibrations, the coordinates Qk describe the effective oscillators corresponding to collective excitations in the medium. Summation rules have been derived which enable us to relate the characteristics of the effective oscillators with the dielectric properties of the fi edium.5... 

These data led to the model already described several times above. The enzyme executes a search for a tunneling sub-state, apparently 13 kcaFmol in energy above the principal state from this state the hydrogen atom tunnels with no further vibrational excitation. Probably motion of the secondary center is coupled into the tunneling coordinate. The result is large, temperature-independent primary and secondary isotope effects in the context of an isotope-independent activation energy. 

CD2CH2CD2 and CH2CD2CH2 diradicals decay at somewhat longer lifetimes, in 183 and 129 fs, respectively. Torsional motions of the terminal methylene groups are obviously critical to the reaction coordinate leading to vibrationally excited cyclopropane-dj products. 

Overtone band. Similar induced dipole matrix elements for the H2-He system have been derived from Table 4.5 for the overtone bands [61]. In that case, the numerical accuracy of the resulting B coefficients is limited for large vibrational excitations unless the data are supplemented by larger variations of the vibrational coordinate r. 

This suggests that there is a H0N0 coplanar transition state formed during this reaction. The initial parent vibrational excitation in -N=0(V2) has no effect on the energy content of the OH product, suggesting that dissociation is so rapid that the >2(-N=0 stretch) vibration does not interact effectively with the fragmentation coordinate v),(0-N stretch), that is, the vibration is localized. 

Fig. 6.9. Left-hand side Vibrational excitation function N(ro) and weighting function W(ro) versus the initial oscillator coordinate ro for three values of the coupling parameter e. The equilibrium separation of the free BC molecule is f = 0.403 A and the equilibrium value within the parent molecule is re = 0.481 A. Right-hand side Final vibrational state distributions P(n) for fixed energy E the quantum mechanical and the classical distributions are normalized to the same height at the maxima. The classical distributions are obtained with the help of (6.32). The lowest part of the figure contains also the pure Franck-Condon (FC) distribution (

The free BC oscillator is assumed to be harmonic with force constant k and equilibrium separation r the parameter e controls the coupling between the dissociation coordinate R and the vibrational coordinate r. For e = 0 (elastic limit) the equations of motion for (R, P) and (r, p) decouple and energy cannot flow from one degree of freedom to the other. As a consequence, the vibrational energy of the oscillator remains constant throughout the dissociation and the corresponding vibrational excitation function, which for zero initial momentum po is given by... 

Fig. 7.12. Comparison of the measured and the calculated absorption spectra for the So — Si transition in CH3ONO. The quantum number n denotes vibrational excitation of the NO moiety in the complex. The theoretical spectrum is obtained in a three-dimensional wavepacket calculation including the ONO bending angle in addition to the two N-0 stretching coordinates. The spectrum is convoluted with a Gaussian function with width AEres = 0.02 eV in order roughly to mimic thermal broadening and is artificially shifted along the energy axis. Reproduced from Untch, Weide, and Schinke (1991a).

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