Cross reactions quantum-mechanical treatment

This expression differs by a factor of 2 from the corresponding semiclassical formula (159.11). This factor arises because in the quantum-mechanical treatment of the nuclear motion, there are two fluxes, corresponding to the incident and reflected waves, which are almost equal if the transition probability is small hence, the nuclear system crosses twice the coupling region in two opposite directions. Therefore, the formula (174.11) gives a "two-way transition probability for non-adiabatic reactions. 

The quantum mechanical treatment of a three-dimensional atom-diatom reactive system is one of the main subjects of theoretical chemistry [1]. About a decade ago when the first numerical results for the H + H2 reactions appeared in print [2] it seemed that the problem was solved. However, difficulties associated with numerical instabilities and with the bifurcation into two nonsyrametric product channels slowed progress with this kind of treatment. This situation caused a change in the order of priorities whereas previously most of the effort was directed toward developing algorithms for yielding "exact cross sections, now it is mostly aimed at developing reliable approximations. 

In accord with our interest we restrict our exposition in this section to statistical treatments which contain as an element the quantum mechanical cross-section or transition probability discussed in Section IV. Such statistical approaches which have been applied to chemical reactions may be conveniently divided into three categories those based on the Pauli equation or similar considerations (Section V-A), a modified Boltzmann equation (Section V-B), or a quantum statistical formulation of the Onsager theory (Section V-C). These treatments have not had notable success in comparison with experiment, probably because of the implicit Born approximation or its equivalent. It is therefore of considerable importance to extend this type of treatment to cross-sections other than that derived with the Born approximation. The method presented in Section V-C would seem to offer the best hope in this direction. 

For recent treatments of a classical bent see References 47, 15, 14, 58. An interesting quantum mechanical discussion has been given in Reference 93 in the language of the scattering matrix, from which the reaction cross-section may be derived. 

In this review, almost all of the simulations we have described use only classical mechanics to describe the nuclear motion of the reaction system. However, a more accurate analysis of many reactions, including some of the ones that have already been simulated via purely classical mechanics, will ultimately require some infusion of quantum mechanical methods. This infusion has already taken place in several different types of reaction dynamics electron transfer in solution, > i> 2 HI photodissociation in rare gas clusters and solids,i i 22 >2 ° I2 photodissociation in Ar fluid,and the dynamics of electron solvation.22-24 Since calculation of the quantum dynamics of a full solvent is at present too time-consuming, all of these calculations involve a quantum solute in a classical solvent. (For a system where the solvent is treated quantum mechanically, see the quantum Monte Carlo treatment of an electron transfer reaction in water by Bader et al. O) As more complex reaaions are investigated, the techniques used in these studies will need to be extended to take into account effects involving electron dynamics such as curve crossing, the interaction of multiple electronic surfaces and other breakdowns of the Born-Oppenheimer approximation, the effect of solvent and solute polarization, and ultimately the actual detailed dynamics of the time evolution of the electronic degrees of freedom. 

ABSTRACT. Calculation of the rate constant at several temperatures for the reaction +(2p) HCl X are presented. A quantum mechanical dynamical treatment of ion-dipole reactions which combines a rotationally adiabatic capture and centrifugal sudden approximation is used to obtain rotational state-selective cross sections and rate constants. Ah initio SCF (TZ2P) methods are employed to obtain the long- and short-range electronic potential energy surfaces. This study indicates the necessity to incorporate the multi-surface nature of open-shell systems. The spin-orbit interactions are treated within a semiquantitative model. Results fare better than previous calculations which used only classical electrostatic forces, and are in good agreement with CRESU and SIFT measurements at 27, 68, and 300 K. ... 

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