Mixing of Frenkel and charge-transfer excitons in a finite molecular chain

2 Mixing of Frenkel and charge-transfer excitons in a finite molecular chain 

For the discussion of the excitonic spectrum in a one-dimensional molecular crystal (with one molecule per unit cell) we use the following Hamiltonian  

In these relations the operator B (Bn) describes the creation (annihilation) of a molecular excitation at lattice site n. We assume below that n 1,2,. ..,Ar, where N is the number of molecules in the chain and we consider one electronically excited molecular state. Then E-p is the on-site energy of a Frenkel exciton and Mnni is the hopping integral for molecular excitation transfer from molecule n to molecule n. In the summation in HF the terms with n = n are omitted. The Hamiltonian HF describes the Frenkel excitons in the Heitler-London approximation. 

In the same way as in the theory of Frenkel exciton mixing (Ch. 3), we have to diagonalize the total Hamiltonian H to consider the mixing of Frenkel and CT states and to find the new mixed states. We use the linear transformation to new operators ( and where 

In this relation, the terms with Cy-i and are absent, because the corre- 

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