Adiabatic collisions

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

Because non-adiabatic collisions induce transitions between rotational levels, these levels do not participate in the relaxation process independently as in (1.11), but are correlated with each other. The degree of correlation is determined by the kernel of Eq. (1.3). A one-parameter model for such a kernel adopted in Eq. (1.6) meets the requirement formulated in (1.2). Mathematically it is suitable to solve integral equation (1.2) in a general way. The form of the kernel in Eq. (1.6) was first proposed by Keilson and Storer to describe the relaxation of the translational velocity [10]. Later it was employed in a number of other problems [24, 25], including the one under discussion [26, 27]. 

It is necessary to get insight into the kernel of the integral equation (3.26). Since frequency exchange is initiated by non-adiabatic collisions, it is reasonable to use the Keilson-Storer model. However, before employing kernel (1.16) it should be integrated over the angle... 

However, this equality does not hold in general. It holds if the factor ei(wu+com )s jn Eq (4.27) is omitted as if it were 1. The integrals over s and t are then trivial and the evolution matrices reduce to S-matrices (4.6). This limit is justified for non-adiabatic collisions [181], which occur at (< / + (OmkK < 1. 

Let us consider first quantum J-diffusion. It is carried out by purely non-adiabatic collisions realized for anc is the average rotational frequency. A semiclassical analogue of the infinite-order sudden... 

The rotational phase shift 5, which cannot exceed a mean angle of a molecular rotation during collisional time (anc), is certainly small in the case of non-adiabatic collisions. This condition is exactly that needed for anisotropic scattering (or IR absorption) spectrum narrowing, just as vibrational dephasing must be weak for an isotropic spectrum to narrow. 

In the MF equation (A7.20) can be simplified essentially only in the particular case of non-adiabatic collisions, which do not change the molecular orientation y(g) = <5(g). In this case operator T = /, and the relaxation part of (A7.20) can be diagonalized over index q ... 

Such local point-group quantum numbers may change during a non-adiabatic collision. A simple example is7,18... 

Figure 34, Schematic illustration of body-fixed adiabatic collisions of atomic 2), II+), and n ) states,...

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. 

W. R. Thorson and J. B. Delos, Phys. Rev., A18, 135 (1978). Theory of Near-Adiabatic Collisions. II. Scattering Coordinate Method. 

H. D. Meyer and W. H. Miller. Classical analog for electronic degrees of freedom in non-adiabatic collision processes. J. Chem. Phys., 70(7) 3214-3223, 1979. 

When X impinges on the core of M at R R2 the angular velocity increases and this causes transitions between the components, thus leading finally to transitions between 2P1/2 and 2P3/2 atomic states (mechanism 2). This mechanism is operative at smaller distances compared to those involved in mechanism 1. The transition probability for mechanism 2 is proportional to ratio (< /w)2, which does not appear in mechanism 1, Both factors tend to decrease the importance of mechanism 2 compared to mechanism 1. Nevertheless, the difference in steepness of the repulsive interaction between X and M in B 22 and A 2II states can lead to preference of mechanism 2 for nearly adiabatic collisions when the mixing cross section is very small. 

E.E.Nikitin, Inelastic transitions between fine-stracture components of alkalies in adiabatic collisions. I.General theory, Optika i Spektr. 22, 689 (1967)... 

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. 

Although reactive collisions in which a system switches between electronic states are unusual, electronically non adiabatic collisions can provide a quite efficient... 

The Dynamics of ElectronicaUy Adiabatic Collisions.— There are three parts to a detailed rate theory of processes occurring in electronically adiabatic collisions. First, the potential describing the molecular interaction must be calculated or estimated. Secondly, the equations of motion have to be solved for individual, fully specified, collisions. Finally, the results of calculations on single collisions must be averaged correctly to yield the required result for example, a reactive cross-section or a detailed rate constant. The procedures for the third stage were outlined in Section 2. In the forward direction, i.e. from o(n ln 6) to ic(T), this averaging presents no problems, but it is the difficulty of reversing this process which makes it impossible to obtain detailed information about the collision dynamics or potential from experimental measurements of thermal rate constants. 

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...

This certainly seems to preclude formation of NjO( S+) in collisions between N2(v) and 0 i ) - at least, for low values of v and moderate temperatures. An alternative is that energy transfer occurs as a result of electronically adiabatic collisions on the triplet hypersurface across which the reaction... 

For an electronically adiabatic reaction (X= 1), this equation turns into the expression (24.IV) of the simple collision theory. In this case the "diatomic" model will be valid only if, after the very fast "non-adiabatic" collision of the radicals CH, the reaction is com-... 

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. 

The probability of producing ions, 2P(1 - P), cannot exceed 1/2 regardless of the magnitude of v. When v is small (large, adiabatic collision), P is small and the behavior is adiabatic. When v is large (low f), 1 - P is small. Thus, there will be a maximum in the energy dependence of the cross-section for collisional ionization, as shown in Figure 9.11. From the position of the maximum one can estimate Vm-... 

W. H. Miller and C, W. McCurdy, Classical trajectory model for electronically non-adiabatic collision phenomena, J. Chem. Phys. 69 5163 (1978). 

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