Theoretical treatment of bimolecular reactions

Abstraction reactions are typical bimolecular gas phase processes and as such can be treated using standard theoretical tools for such systems. Broadly speaking the theoretical treatment of bimolecular reactions can be divided into two categories dynamical and statistical. These categories can be further sub-divided into techniques that are based on quantum or classical mechanics. 

Of the dynamical techniques available the most rigorous and informative are the quantum mechanical dynamics methods. These methods are, however, the most sophisticated and computationally intensive to employ. Two of the most widely used quantum dynamics techniques are quantum scattering (QS) [35] and wavepacket (WP) [125] analysis. 

In the quantum scattering approach the collision is modelled as a plane wave scattering off a force field which will in general not be isotropic. Incident and scattered waves interfere to give an overall steady state wavefunction from which bimolecular reaction cross-sections, cr, can be obtained. The characteristics of the incident wave are determined from the conditions of the collision and in general the reaction cross-section will be a function of the centre of mass collision velocity, u, and such internal quantum numbers that define the states of the colliding fragments, represented here as v and j. Once the reactive cross-sections are known the state specific rate coefficient, can be determined from. 

In WP analysis the time evolution of an initial wavefunction (or wave-packet) is obtained by the solution of the appropriate time-dependent Schrbdinger equation. The initial wavefunction is determined by the conditions of the collision. The Schrbdinger equation is then integrated, which given the complexity of the potentials usually has to be performed numerically. Information about the crossections can be obtained from this technique and again canonical rate coefficients obtained by the above averaging procedure. 

Apart from the complex nature of these techniques and their intense computational demands a detailed knowledge of the potential energy surface is required, which is in itself a demanding problem for ab initio quantum chemistry. As a consequence these techniques are limited in the systems to which they can be applied - rigorous calculations involving four atoms have only recently started to appear - and so direct application to reactions of importance in combustion is not possible at present. One important exception is the reaction. 

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