We developed a theory of excitation energy transfer (EET) which is applicable to all the values of the coupling strength U in the presence of homogeneous and inhomogeneous broadening. In constructing the theory, we adopted a decoupling procedure corresponding to the factorization by a two-time correlation function of the excitation transfer interaction in the integro-differential equation of a renormalized propagator. We also assumed that the two-time correlation function decreases exponentially with time. Under these assumptions, we could handle our theory nonperturbatively and analytically. We derived formulas of criteria among exciton, intermediate coupling, and Förster mechanisms. We exploited a novel method for determining the EET rate applicable to all the mechanisms from Förster to exciton. Then, we obtained compact formulas for the EET rate and the degree of coherency involved in the EET. We demonstrated how the exciton state is destabilized by the presence of inhomogeneity in the excitation energy of the constituents. The theory was applied to a light-harvesting system LH2 of photosynthetic bacteria.

We investigated the origin of the very rapid and large fluctuation of the electron tunneling matrix element T DA due to the thermal fluctuation of protein conformation which was recently observed by the simulation study (Daizadeh, I.; Medvedev, E. S.; Stuchebrukhov, A. A. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 3703). We made analysis of this phenomena by using the interatomic tunneling current map of Ru-modified azurins. We defined a new index, degree of destructive interference Q, by making an average of the intermediate level for the interatomic tunneling currents. We found an empirical relation that |T DA| is proportional to Q -1 holds true in the course of thermal fluctuation of protein conformation. Comparing maps of the interatomic tunneling currents with different values of Q, we found that the very rapid (in much less than 1 ps) and large amount (maximally 2 orders of magnitude) of fluctuations in T DA are caused by the reconnection and the change in the direction of interatomic tunneling currents with considerable amplitudes. By taking the statistical average for the dynamics effect of log |T DA|, we found that the range of the averaged dynamic modification of electron transfer rate amounts to more than 2 orders of magnitude in the Ru-modified azurins. In the systems with a large range of dynamic modification, this nuclear dynamics effect contributes to enhance the thermally averaged electron transfer rate considerably.

We present a novel method for selecting important electron tunneling pathways in proteins by connecting important interatomic tunneling currents. Then, we constituted an electron tunneling route, called a “worm”, which is formed by averaging over all of the interatomic tunneling currents. The method is applied to six kinds of Ru-modified azurins where the electron transfer takes place from the copper ion to the ruthenium ion linked to the surface of the azurin. We found that the worm is not straight but winds, reflecting the specific role of the microenvironment of the protein structure and ligands in the electron tunneling pathway and rather narrow radius of the worm, ca. 1.5 Å at most. The donor−acceptor distance dependence of the electron-transfer rate k e is examined by taking into account the one-dimensional atomic density in the worm. We found that the Dutton plot, in which the logarithm of k e is in a linear relation with the donor−acceptor distance, which, in turn, depends somewhat on the one-dimensional atom density, is reproduced for a certain level of analysis by the worm model. Thus, we can consolidate the electron tunneling pathway model with the Dutton plot by using the worm model.