Excitation transfer induced spectral diffusion and the influence of structural spectral diffusion

The theory of vibrational excitation transfer, which causes spectral diffusion and is also influenced by structural spectral diffusion, is developed and applied to systems consisting of vibrational chromophores. Excitation transfer induced spectral diffusion is the time-dependent change in vibrational frequency induced by an excitation on an initially excited molecule jumping to other molecules that have different vibrational frequencies within the inhomogeneously broadened vibrational absorption line. The excitation transfer process is modeled as Förster resonant transfer, which depends on the overlap of the homogeneous spectra of the donating and accepting vibrational chromophores. Because the absorption line is inhomogeneously broadened, two molecules in close proximity can have overlaps of their homogeneous lines that range from substantial to very little. In the absence of structural dynamics, the overlap of the homogeneous lines of the donating and accepting vibrational chromophores would be fixed. However, dynamics of the medium that contains the vibrational chromophores, e.g., a liquid solvent or a surrounding protein, produce spectral diffusion. Spectral diffusion causes the position of a molecule's homogeneous line within the inhomogeneous spectrum to change with time. Therefore, the overlap of donating and accepting molecules' homogeneous lines is time dependent, which must be taken into account in the excitation transfer theory. The excitation transfer problem is solved for inhomogeneous lines with fluctuating homogeneous line frequencies. The method allows the simultaneous treatment of both excitation transfer induced spectral diffusion and structural fluctuation induced spectral diffusion. It is found that the excitation transfer process is enhanced by the stochastic fluctuations in frequencies. It is shown how a measurement of spectral diffusion can be separated into the two types of spectral diffusion, which permits the structural spectral diffusion to be determined in the presence of excitation transfer spectral diffusion. Various approximations and computational methodologies are explored.