  From studying the time evolution of the single electron density matrix within
a density functional tight-binding formalism we study in a fully atomistic
picture the electronic excitation transfer between two photosynthetic pigments
in real time. This time-dependent quantum dynamics is based on fully atomistic
structural models of the photosynthetic pigment. We analyze the dependence of
the electronic excitation transfer with distance and orientation between
photosynthetic pigments. We compare the results obtained from full quantum
dynamics with analytical ones, based on a two level system model were the
interaction between the pigments is dipolar. We observed that even when the
distance of the photosynthetic pigment is about $30$ \AA\ the deviation of the
dipolarity is of about $15$ percent.
