Derivation of the intermolecular interconversion rate

Intermolecular interconversion occurs via the electron-transfer Hamiltonian, f/7. For parallel chains with nearest neighbour electron transfer this is 

If the chains are weakly coupled we may regard H as a perturbation on the approximate Hamiltonian, Hq, where Hq contains the intramolecular Hamiltonians and the remaining interchain interactions - particularly the Coulomb interactions. Thus, we may write the Born-Oppenheimer Hamiltonian for a pair of coupled polymer chains as, 

Within the Born-Oppenheimer approximation the electronic and nuclear degrees of freedom are described by the Born-Oppenheimer states, 

We assume that the stationary electronic states are the eigenstates of the approximate Hamiltonian, Ho- Thus, the perturbation, Hj, mixes these electronic states. In particular, it causes an interconversion from the interchain excitons (or weakly bound polaron pairs) to the intrachain excitons. 

We take the initial electronic state, f), to be a positive polaron on chain 1 and a negative polaron on chain 2, 

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