Translational energy, after

With the various experimental techniques, the actual measurement concerns product ions after they have been extracted from the source. That is to say, the decomposition occurs in a source before acceleration, but what is actually measured is translational energy after the product ion has been accelerated. To be still more precise, it is, in most cases, the distribution of the component of velocity along the axis of the mass spectrometer (i.e. in the direction in which the ions were accelerated out of the source) which is, in effect, measured. The measured quantity is, therefore, distinct from the translational energy distribution of the product ion (called the laboratory distribution ) as it was upon its formation in the source (i.e. before acceleration). The measured distribution needs to be analysed to obtain the laboratory distribution. Working with means or averages is much simpler, but there are possible pitfalls (see the discussion of the time-of-flight technique below). 

There are many examples of energy transfer to or from the solvent. Caging dissipates the translational energy after bond breaking and conversely, the solvent must provide the energy required to cross an activation barrier to a chemical... 

The impact operator corrected in such a way still remains semiclassical though the requirements of detailed balance are satisfied. It is reasonable provided that the change of rotational energy is small on average, relative to translational energy ey — ej < ikT, where the overbar means averaging performed over the distribution of products after collision. 

If a charge exchange process, A + + B- A -f- B +, occurs when the distance between the two particles is large, we expect that no transfer of translational energy takes place in the reaction and that the same selection rules govern the ionization as in spectroscopic transitions. This means that if the molecule B is in a singlet state before the ionization, the ion B + will be formed in a doublet state after ionization of one electron without rearrangements of any other electrons, at least for small molecules. 

Figure 8. Translational energy distributions of CO(v = 0) after dissociation of H2CO at hv = 30,340.1 cm for the CO product rotational levels (a) Jco = 40, (b) 7co = 28, and (c) Jco = 15. The internal energy of the correlated H2 fragment increases from right to left. Dashed lines are translational energy distributions obtained from the trajectory calculations. Markers indicate H2 vibrational thresholds up to v = 4, and in addition odd rotational levels for v = 5—7. Reprinted from [8] with permission from the American Association for the Advancement of science.

In cases where both the system under consideration and the observable to be calculated have an obvious classical analog (e.g., the translational-energy distribution after a scattering event), a classical description is a rather straightforward matter. It is less clear, however, how to incorporate discrete quantum-mechanical DoF that do not possess an obvious classical counterpart into a classical theory. For example, consider the well-known spin-boson problem—that is, an electronic two-state system (the spin) coupled to one or many vibrational DoF (the bosons) [5]. Exhibiting nonadiabatic transitions between discrete quantum states, the problem apparently defies a straightforward classical treatment. 

Fig. 1.1.1 Schematic illustration of the probability density, x(R,t) 2, associated with a chemical reaction, A + BC — AB + C. The contour lines represent the potential energy surface (see Chapter 3), and the probability density is shown at two times before the reaction where only reactants are present, and after the reaction where products as well as reactants are present. The arrows indicate the direction of motion associated with the relative motion of reactants and products. (Note that, due to the finite uncertainty in the A-B distance, Rab, there is some uncertainty in the initial relative translational energy of A + BC.)...

It is observed that excitation of the stretching vibrations in HOD enhance the rate more than the increase resulting from an equivalent amount of relative translational energy. In addition, the branching ratio between the two product channels can be controlled by appropriate vibrational pre-excitation of HOD. Thus, it is found that after excitation of the H-OD stretch with one or more vibrational quanta, the reaction produces almost exclusively H2 +OD, whereas after excitation of the HO-D stretch, only the HD + OH products are formed. 

The El fragmentation pattern of exo- (108) and endo- (109) 5-chloronorbornan-2-ones and of exo- (110) and endo- (111) 6-chloronorbornan-2-ones is stereo-dependent220. Information on the ion structures have been obtained by energy-resolved mass spectrometry (ERMS), (ERMS is obtained in a triple quadrupole instrument by plotting the relative abundance of the ions after collisional activation as a function of the parent ion translational energy). 

The impulse model is applied to the interpretation of experimental results of the rotational and translational energy distributions and is effective for obtaining the properties of the intermediate excited state [28, 68, 69], where the impulse model has widely been used in the desorption process [63-65]. The one-dimensional MGR model shown in Fig. 1 is assumed for discussion, but this assumption does not lose the essence of the phenomena. The adsorbate-substrate system is excited electronically by laser irradiation via the Franck-Condon process. The energy Ek shown in Fig. 1 is the excess energy surpassing the dissociation barrier after breaking the metal-adsorbate bond and delivered to the translational, rotational and vibrational energies of the desorbed free molecule. 

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