Large-amplitude vibration

Modem photochemistry (IR, UV or VIS) is induced by coherent or incoherent radiative excitation processes [4, 5, 6 and 7]. The first step within a photochemical process is of course a preparation step within our conceptual framework, in which time-dependent states are generated that possibly show IVR. In an ideal scenario, energy from a laser would be deposited in a spatially localized, large amplitude vibrational motion of the reacting molecular system, which would then possibly lead to the cleavage of selected chemical bonds. This is basically the central idea behind the concepts for a mode selective chemistry , introduced in the late 1970s [127], and has continuously received much attention [10, 117. 122. 128. 129. 130. 131. 132. 133. 134... 

Technology developments are revolutionizing the spectroscopic capabilities at THz frequencies. While no one teclmique is ideal for all applications, both CW and pulsed spectrometers operating at or near the fiindamental limits imposed by quantum mechanics are now within reach. Compact, all-solid-state implementations will soon allow such spectrometers to move out of the laboratory and into a wealth of field and remote-sensing applications. From the study of the rotational motions of light molecules to the large-amplitude vibrations of... 

Resonance is defined as a large-amplitude vibration caused by a small periodic stimulus having the same, or... 

In the scenario just sketched, the large amplitude vibration along s is governed by the following equation ... 

Furthermore, large amplitude vibrational motions are characterized by fundamental changes in the nature of the electronic structure of the system. Dissociation of many closed shell molecules, for example HC1, transforms two atoms cohabitating in a fashion that repels electrons into a non-interacting pair of electron-attractors . c This picture suggests that molecules subjected to the rigors of large amplitude vibrational motion... 

Experimental probes of Born-Oppenheimer breakdown under conditions where large amplitude vibrational motion can occur are now becoming available. One approach to this problem is to compare theoretical predictions and experimental observations for reactive properties that are sensitive to the Born-Oppenheimer potential energy surface. Particularly useful for this endeavor are recombinative desorption and Eley-Rideal reactions. In both cases, gas-phase reaction products may be probed by modern state-specific detection methods, providing detailed characterization of the product reaction dynamics. Theoretical predictions based on Born-Oppenheimer potential energy surfaces should be capable of reproducing experiment. Observed deviations between experiment and theory may be attributed to Born-Oppenheimer breakdown. 

Fig. 4. Accumulating evidence is starting to show that molecules which undergo large amplitude vibration can interact strongly with metallic electrons in collisions and reactions at metal surfaces. This suggests that the Born-Oppenheimer approximation may be suspect near transition states of reactions at metal surfaces.

Fig. 9. Incidence energy dependence of the vibrational state population distribution resulting when NO(u = 12) is scattered from LiF(OOl) at a surface temperature of (a) 480 K, and (b) 290 K. Relaxation of large amplitude vibrational motion to phonons is weak compared to what is possible on metals. Increased relaxation at the lowest incidence energies and surface temperatures are indicators of a trapping/desorption mechanism for vibrational energy transfer. Angular and rotational population distributions support this conclusion. Estimations of the residence times suggest that coupling to phonons is significant when residence times are only as long as ps. (See Ref. 58.)...

GPa indicate the presence of a bcc lattice undergoing large amplitude vibrations, even though each RDF in Figure 10 has width similar to that of a liquid or a glass. The RDFs for the amorphous phase (not shown) are similar to those of the solid phase obtained in the S simulations. 

Wallace, R. (1984), Large Amplitude Vibration in Polyatomic Molecules. I. A Polar Representation of Orthogonal Relative Coordinates, Chem. Phys. 88, 247. 

The experimental data for the Fe2Cl6 molecules could be best approximated by a model with a puckered four-membered ring (Cjy symmetry). However, the deviation from the Z)2h symmetry may be a consequence of large-amplitude vibrations around the imaginary axis connecting the two bridging chlorine atoms (cf. 

Cyclohexane derivatives with hetero atoms. Electron diffraction studies have been made for many molecules with hetero atoms. These molecules are analogous to cyclohexane derivatives. Principal findings pertaining to large amplitude vibration are summarized in Table 9. 

Several alkali halides have been studied at elevated temperatures394 and dimeric species forming four-membered rings have been found to predominate. There are indications of rather large amplitude vibrations in these dimers. It should be pointed out that monomeric species are also present in addition to the predominating dimers and several of these have been indentified by microwave spectroscopy44 ... 

The ratio of yHF to yDF was assumed to be 21/4 in deriving Eqn. (10). For yHF — 20-30°,Eqn.(10)givesadipolemomentdifferenceof0.03-0.08 D, as observed. Thus, the dipole moment data and the hyperfine interactions support a nearly linear equilibrium hydrogen bond, with large amplitude vibrational displacements from equilibrium. It must be emphasized that none of the experimental evidence discussed so far, including this, precludes the hydrogen bond from having a small departure, on the order of 5°, from linearity at equilibrium. 

The second problem concerns the convergence of the expansion of the coefficients Hap. Until recently this problem has not been studied to the same extent as the effect of the anharmonicity of the large-amplitude vibrations in the expansion of V. However, the role of the large-amplitude motions in the expansion of Hap may be equally important, especially in the ab initio approach to the calculation of the rotational energy levels of a non-rigid molecule [cf. ]. 

However, molecular parameters obtained in this way are often only effective quantities without physical significance. Furthermore, if the molecule executes large-amplitude vibrations, the number of these parameters becomes unmanageably large. 

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