Vibrational, rotational, and translational energy distributions

By following the trajectories to the product asymptotic limit, product vibrational, rotational, and translational energy distributions may also be determined [78]. 

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. 

To obtain the reaction attributes for a particular set of vibrational, rotational and translational energies, many trajectories were simulated at given values of N2 vibrational and rotational quantum numbers and N2-O relative translational energy. The N2 molecular orientation, vibrational phase and impact parameter were chosen randomly for each trajectory. The reaction attributes were then determined by averaging the outcomes of all collisions. The information obtained is state-specific, so for example, the energy distributions of the reactant and product molecules can be determined. The method used to calculate the vibrational and rotational state of the product molecule is outlined in Ref. 67. With the QCT approach, reaction cross sections were determined solely from the precollision state. The method knows nothing of the fluid flow environment and so... 

Experimental product rotational and translational energy distributions derived from energy-selected dissociation reactions can frequently be characterized by a temperature which implies that the distribution is a canonical one. This is found even when rotationally cold reactants are prepared in a state-selective manner. How can this be We illustrate the origin of these canonical distributions by calculating the rotational and vibrational distributions for a system of classical harmonic oscillators. 

Relative distributions of vibrational, rotational and translational energy of products in gas-phase atom abstraction reactions [9]... 

Phase space theory has been able to reproduce experimental distributions of translational energy releases closely for a number of decompositions which do not have energy barriers to the reverse reactions [165, 485] (see Sect. 8). Phase space theory does focus attention on a very late stage of reaction since the degrees of freedom of the loose transition state can be identified as vibrations, rotations and translations. 

For excess energy distributed in the other degrees of freedom, i.e., rotation, translation, and vibration, only collisional degradation is possible. However, it is known that degradation of vibrational energy is a slow process and so a considerable fraction of vibrationally excited species may be expected to persist for some time. On the other hand, rotational and translational energy appear to be exchanged very readily in collisions, so that species thus excited may be expected to be thermalized very rapidly. 

Consider two molecular species in equilibrium, each of which has a different set of energy levels for each isotopic molecule. In the mixture of the isotopic molecules, each isotope distributes between the two molecular species according to the energy levels set for the isotope. This results in uneven distribution of hydrogen isotopes between the two phases. In practice, the contribution of the vibrational energy is dominant over rotational and translational energies in equilibrium isotope effects. 

Thermodynamic data that are suitable for tabulation include standard enthalpies, entropies, and free energies and can be regarded as universally applicable for systems at specified temperature when all participants are at thermal equilibrium. Though such data can also be obtained without thermal equilibrium, compensating experiments, or mathematical corrections are required, sometimes creating difficulties in practice and/or interpretation. A chemical system in the gas phase can reach thermal equilibrium, at a defined temperature, when a sufficient number of intermolecular collisions produce a Boltzmann distribution of energies in all modes, electronic, vibrational, rotational, and translational. In measurements made with an ion trap instrument or Fourier Transform Ion Cyclotron Resonance (FT-ICR) spectrometer at low pressure, hot ions must be cooled, commonly with a pulse of buffer... 

Simulations may be classified as static and dynamic. In a static simulation no explicit account is taken of thermal motions in the system, which is therefore treated as if it were at a temperature of absolute zero. A molecular dynamics simulation, on the other hand, requires the specification of a temperature, which defines the kinetic energy to be distributed between the available degrees of freedom. By solving a set of classical equations of motion, such thermally induced reorientation phenomena as the vibrations, rotations, and translations of the system may be described. The two approaches have their advantages, which become clear in the following sections. 

To study the scalar properties of photodissociation, the energy distribution over the vibrational, rotational, and translational degrees of freedom is experimentally detected. If the photodissociation products are formed in the ground electronic state, the law of energy conservation has the form... 

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.

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