Derivation of the Singlet Kinetic Equation

The kinetic equation description of the reaction A-(-B =iC-l-B at the sing-let-doublet level involves the set of fields 5n (a = A,B,C), 5n s(o = A, B,C). The doublet fields are generated by the action of + on 8n (Appendix B). If we restrict our calculations to forward reaction terms, we need to calculate only matrix elements involving the reduced set of fields Sn, 5 ab as bsI- singlet A, B, and C fields are orthogonal 

The static memory function that couples the and fields is also 

Using these results, the kinetic equation for the A singlet phase-space correlation function takes the form 

We have made an addition approximation in writing (C.9) the coupling between the singlet A and singlet B fields has been dropped. This coupling is due to elastic collisions between A and B molecules, and it gives rise to cross-diffusion coefficients, which can be neglected in a dilute system. Most elastic collisions are with solvent molecules. 

To complete the kinetic equation description, equations for the correlation functions involving doublet fields must be constructed. Once again, we calculate some of the matrix elements as an illustration. Consider first the coupling matrix element ab,a(12, T) 

---