An extended theoretical formulation of the circular dichroism band shape of chromophore aggregates by use of the ensemble-averaged resolvent matrix method

A new theoretical formulation is given to the circular dichroism band shape of chromophore aggregates by means of the ensemble-averaged resolvent matrix method. This formulation can be used to calculate the circular dichroism band shape of chromophore aggregates having arbitrary strengths of the excited-state interactions between chromophores. Using the resolvent expansion rule, thermal and static effects upon the circular dichroism band shape are incorporated as the mean-frequency shifts of the normalized band shape functions used for ensemble averaging the resolvent matrix of chromophore aggregates. This formulation is applied to derive a generalized band shape expansion formula which gives a theoretical justification to the practical first-order Taylor expansion equation used to calculate the circular dichroism band shape of chromophore aggregates. Basic properties of the generalized band shape expansion formula are investigated by comparing it with the usual perturbation expansion equation for the circular dichroism band shape of chromophore aggregates.