Collision atom-diatom

Let us continue with the atom-diatom collinear collision model, this time allowing for the possibility of the reaction A -r BC —> AB -i- C. We first introduce mass-scaled coordinates, as these are especially convenient to describe rearrangements, using... 

Kaye J A and Kuppermann A 1988 Mass effect in quantum-mechanical collision-induced dissociation in collinear reactive atom diatomic molecule collisions Chem. Phys. 125 279-91... 

Miller W H 1970 Semiclassical theory of atom-diatom collisions path integrals and the classical S matrix J. Chem. Phys. 53 1949-59... 

Baer, M. Adiabatic and diabatic representations for atom-diatom collisions Treatment of the three-dimensional case, Chem.Phys., 15 (1976), 49-57... 

For an atom-diatom collision the initial wavepacket, in body-fixed coordinates, is defined as [47,133]... 

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]. 

We have already mentioned (expressions 30—33) the widely used LEPS surface for atom-diatom reactions. This may be regarded as purely empirical or semi-empirical in any modification in which some integrals are evaluated. Another system for which fairly elaborate potential functions have been used is for non-reactive atom-diatom scattering. The experiment for which the potential is designed is the change of rotational or vibrational state of a diatomic molecule by collision with a third atom, and also the quasi bound states, which may be observed spectroscopically, of van der Waals molecules such as Ar—H2 (133). 

Fig. 13. Coordinates for non-reactive atom-diatom collisions. The position of C is measured relative to the centre of mass of A and B.

The internal coordinates usually chosen to study non-reactive atom-diatom collisions are shown in Fig. 13. If the potential is written... 

The Montroll-Shuler equation can also predict how fast a molecule which is created in a highly excited vibrational state will decay to the equilibrium state. This is of interest in connection with chemiluminescence phenomena. In certain cases one finds experimentally that this relaxation is much faster than what one would expect from the master equation of Montroll and Shuler and improved versions of this equation. One possible mechanism for this fast relaxation is that although most of the collisions in which the diatomic molecule participates are between the diatomic molecule and an inert gas atom, there will also be some collisions between diatomic molecules. In the latter case we have the situation where two diatomic molecules in quantum state n collide producing, with fairly high probability, molecules in quantum states n I and n + 1, respectively. The number of such collisions is, of course quite small compared to the number of collisions of the first kind, but since they are so extremely efficient they may still be of importance. This mechanism, we believe, was first suggested in connection with chemiluminescence by Norrish in a Faraday Society discussion.5 The equations describing this relaxation had, however, been discussed several years earlier by Shuler6 and Osipov.7... 

We will begin with the important case of pairs of linear molecules, such as diatomic molecules the formalism to be developed may be reduced to the case of atom-diatom collisions, or to the case of molecules of arbitrary geometry. 

D A Micha. Few-body processes in atom-diatom collisions. Nuclear Phys., A353 309c, 1981. 

D. Sokolovski, J.N.L. Connor, Semiclassical nearside-farside theory for inelastic and reactive atom-diatom collisions, Chem. Phys. Lett. 305 (1999) 238. 

Kouri, D.J. and Mowrey, R.C. (1987). Close coupling-wave packet formalism for gas phase nonreactive atom-diatom collisions, J. Chem. Phys. 86, 2087-2094. 

Schinke, R. and Bowman, J.M. (1983). Rotational rainbows in atom-diatom scattering, in Molecular Collision Dynamics, ed. J.M. Bowman (Springer, Berlin). 

Jeyes, S.R., McCaffery, A.J. and Rowe, M.D. (1978). Energy and angular moment transfer in atom-diatom collisions from polarized laser fluorescence, Mol. Phys., 36, 1865-1891. 

E.E.Nikitin, Mechanism of atomic fluorescence quenching in collisions with diatomic molecules, J.Quant.Spectr.Rad.Transfer, 5,435 (1965)... 

E.E.Nikitin, J.Troe, and V.G.Ushakov, Adiabatic and post-adiabatic channel description of atom-diatom long-range half-collision dynamics interchannel radial coupling for low-rank anisotropy. J. Chem. Phys. 102,4101 (1995)... 

E.I.Dashevskaya and E.E.Nikitin, On the relation between elastic and inelastic scattering lengths for vibrational relaxation in atom-diatom collisions, Chem.Phys.Lett. 328, 119 (2000)... 

Neuhauser, D., Baer, M., Judson, R.S. and Kotiri, D.J. (1990) A time-dependent wave packet approach to atom diatom reactive collision probabilities - theory and application to H -P H2 (J=0) system,, 7. Chem. Phys. 93, 312-322. 

This asymptotic form is plotted in Fig. 5. A feature of BBM(d>) is that it decreases asymptotically with frequency to zero. If the atom B is involved in vibrational motion at frequency oo (Oq, the coupling with the bath through binary collisions is small and the slow dissipation is the stochastic manifestation of slow vibrational relaxation. The most significant feature of Eq. (3.17) is that the dependence in the exponent of Eq. (3.17) is equivalent to an exponent This is just the form of the Landau-Teller theory of vibration-translation (V-T) energy transfer in atom-diatom collisions, and this form is almost universally used to fit vibrational relaxation rates in such systems. This will be dealt with in more detail in Section V C. The utility of BBM(d>) is that it pertains to atom-atom collisions in which the atom B is bonded to the other atoms by arbitrary potentials. No assumptions have been made about the intramolecular motions, although the use of BBM(d)) implies linear coupling to the displacements of atom B. Grote et al. have alluded to the form of Eq. (3.20) for di = 0 in a footnote. 

The depth of understanding of V-V, V-T, and V-R, relaxation in atom-diatom collisions at low densities is profound. " The advent of state-to- state experiments and of quantum, semiclassical, and classical calculations has provided a wealth of information. Stochastic approaches, which are still under development for polyatomic sys-tems should mimic the essential features of thermally averaged atom-diatom energy transfer when applied to these simple systems. The friction is essentially the characteristic of kinetic energy relaxation. The energy diffusion equation of the energy probability density tr(E, t) is... 

O.I. Tolstikhin and H. Nakamura, Hyperspherical elliptic coordinates for the theory of light atom transfer reactions in atom-diatom collisions. J. Chem. Phys., 108 8899-8921, 1998. 

---