The spectroscopic channel basis for radiative and radiationless processes: The effective system excited states and interference effects in absorption spectra

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Abstract
By transforming the molecular Hamiltonian, we find a basis, called the spectroscopic channel basis (SCB), in which the individual molecular excited states are coupled in sequence, with the final one having a nonradiative linewidth, which is relatively energy independent. The SCB provides a simple, single‐channel path for the radiationless processes and is a useful basis for analyzing the spectral properties of the molecule in terms of the Green’s operator. We show that the matrix element of the Green’s operator (Green’s function) associated with light absorption obeys certain recurrance relations in the SCB. The spectral density function of each state of the SCB is uniquely determined by the absorption spectrum of the molecule. We describe a rigorous and formally exact method of calculating the spectral density functions and all of the spectroscopic parameters of the SCB from a given absorption spectrum. The absorption spectrum can be expressed as a sum of generalized Lorentzians (Lorentzians modified by interference effects of the Fano type) which correspond to effective excited states and which can be determined from the parameters of the SCB. The interference effects are determined by a new parameter which we term the asymmetry index.