Energy migration as related to the mutual position and orientation of donor and acceptor molecules in LH1 and LH2 antenna complexes of purple bacteria

Many approaches to discovering the interaction energy of molecular transition dipoles use the well-known coefficient ξ(φ, ψ1ψ2) = (cos φ − 3 cos ψ1 cos ψ2)2, where φ, Ψ1, and Ψ2 are inter-dipole angles. Unfortunately, this formula often yields rather approximate results, in particular, when it is applied to closely positioned molecules. This problem is of great importance when dealing with energy migration in photosynthetic organisms, because the major part of excitation transfers in their chlorophyllous antenna proceed between closely positioned molecules. In this paper, the authors introduce corrected values of the orientation factor for several types of mutual orientation of molecules exchanging with electronic excitations for realistic ratios of dipole lengths and spacing. The corrected magnitudes of interaction energies of neighboring bacteriochlorophyll molecules in LH2 and LH1 light-absorbing complexes are calculated for the class of photosynthetic purple bacteria. Some advantageous factors are revealed in their mutual positions and orientations in vivo.