Molecule adiabatic collision

During adiabatic collision the molecule completes many rotations. Consequently AJ is oriented isotropically, and the operator (1.9) should be uniformly averaged over F ... 

In this case, during the time of collision, the integrand in (4.42) oscillates many times and the value of the integral is close to zero. Thus, the adiabatic collisions do not lead to excitation of the molecule. 

This relation (Landau Teller, 1936) demonstrates the adiabatic behavior of vibrational relaxation. Usually the Massey parameter at low gas temperatures is high for molecular vibration cox ox k which explains the adiabatic behavior and results in the exponentially slow vibrational energy transfer during the VT relaxation During the adiabatic collision, a molecule has enough time for mai vibrations and the oscillator can actually be considered stractureless, which explains such a low level of energy transfer. An exponentially slow adiabatic VT relaxation and intensive vibrational excitation by electron impact result in the unique role of vibrational excitation in plasma chemistry. Molectrlar vibrations for gases... 

Vibrational relaxation is slow in adiabatic collisions when there is no chemical interaction between colliding partners. For example, the probability of deactivation of a vibrationally excited N2 molecule in collision with another N2 molecule can be as low as 10 at room temperature. The vibrational relaxation process can be much faster in non-adiabatic collisions, when the colliding partners interact chemically. 

Smith and Wood s work also showed that both non-reactive and reactive processes, e.g. chaniwls (a) and (b) in equation (41), could remove vil ationally exdted molecules in electronically adiabatic collisions. However, the non-reactive contribution came almost entirely from trajectories which crossed the surface an even number of times, so that the motions of the three-atom system became strongly coupled. The product vibrational distributions both from these non-reactive trajectories and from reactive collisions were broad, showing that multiquantum transfers, i.e. (v - v ) > 1, are probable. The m ority of trajectories did not, of course, cross = bc °d the transfer of a substantial amount of vibrational energy in these collisions was extremely rare. These general findings have been confirmed in a study modelled on the system Br + HBr with the potential chosen to have a barrier to H atom transfer of 16 kJ mol and one... 

The basis to Nikitin s theory of vibrational energy transfer in electronically non-adiabatic collisions is that any degeneracy, or near degeneracy, associated with spin-orbit terms in an isolated atom or molecule is removed as another species interacts with it in a collision. In several respects, his treatment parallels that outlined above for electronically adiabatic collisions. In particular, it is assumed that the two (or more) intermolecular potentials of concern are not orientation... 

Figure 6 Potential curves representing the interaction of different vibronic states of a molecule with a collision partner whose close approach causes the electronic states j and k, which are nearly degenerate when x oo, to diverge. Vibrational relaxation in electronically adiabatic collisions requires tunnelling between parallel curves as indicated by the horizontal arrows. Electronically non-adiabatic collisions can lead to relaxation via transitions at the crossing points, i.e. at Xa for (J, )- (fc, 0), as indicated by the broken arrows. (Based on figures given in papers by Nikitin...

According to the exact definition (22,IV), the collision diameter is related to the partition function therefore, it has the meaning of a statistical mean value of the distance of closest approach of molecules A and B in a very fast "non-adiabatic" collision. 

To see how we should be able to study the evolution of a collision let us consider first how intermolecular potentials between atoms bound together are studied. This is done, of course, via spectroscopy. One starts with the Born-Oppenheimer approximation for the total molecular wave function this enables one to describe the motion of the nuclei in a potential that depends on the separation between them. This result, the existence of a specific adiabatic potential, rests on there being no appreciable mixing between electronic states. One of its corollaries, the Franck-Condon Principle, enables one to interpret and invert (e.g. using the R.K.R. method) the vibrational spectra in terms of the interatomic potentials in different electronic states. To what extent can we extend such a technique to free-free spectra, in other words, to absorption in the middle of a transient molecule — a collision complex — and deduce information about the potentials between atoms as they collide ... 

The close-coupling equations are also applicable to electron-molecule collision but severe computational difficulties arise due to the large number of rotational and vibrational channels that must be retained in the expansion for the system wavefiinction. In the fixed nuclei approximation, the Bom-Oppenlieimer separation of electronic and nuclear motion pennits electronic motion and scattering amplitudes f, (R) to be detemiined at fixed intemuclear separations R. Then in the adiabatic nuclear approximation the scattering amplitude for ... 

Baer M 1975 Adiabatic and diabatic representations for atom-molecule collisions treatment of the collinear arrangement Chem. Rhys. Lett. 35 112... 

Here p is the radius of the effective cross-section, (v) is the average velocity of colliding particles, and p is their reduced mass. When rotational relaxation of heavy molecules in a solution of light particles is considered, the above criterion is well satisfied. In the opposite case the situation is quite different. Even if the relaxation is induced by collisions of similar particles (as in a one-component system), the fraction of molecules which remain adiabatically isolated from the heat reservoir is fairly large. For such molecules energy relaxation is much slower than that of angular momentum, i.e. xe/xj > 1. 

In the purely non-adiabatic limit the phase (5.52) coincides with that calculated in [203] and for very long flights (rt b,v" v) or high energies (.E e) it reduces to what can be obtained from the approximation of rectilinear trajectories. However, there is no need for these simplifications. The SCS method enables us to account for the adiabaticity of collisions and consider the curvature of the particle trajectories. The only demerit is that this curvature is not subjected to anisotropic interaction and is not affected by transitions in the rotational spectrum of the molecule. 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

A variation on this method, passing the vapors emitted from a heated source or sources through a nozzle, may cause clustering. The gas-phase species, which could be ions or neutral molecules, pass from a region of higher pressure to a region of lower pressure. This process has many collisions and then adiabatic expansion often produces cold clusters. If the clusters have not been ionized, they may be ionized in the low-vacuum region. 

Second, most of the articles cited and the calculations presented are for collisions of diatomic molecules with atoms. The effects of external fields have been studied only for three molecule-molecule collision systems O2-O2 in a magnetic field, NH-NH in a magnetic field, and OH-OH in an electric field. In each case, the calculations are based on significant simplifications of the interaction potential operator. Most of the NH-NH calculations and the O2-O2 studies assume that the collision dynamics occurs on the maximal spin adiabatic potential energy surface of the two-molecule complex. There is only one study that considers the dynamics of NH-NH collisions in a magnetic field with account of transitions to lower spin surfaces [48]. 

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