For instance, if we treat the coupling as a global phase V LC = |V 0 |e iθ (i.e., corresponding to the case where V x = V y = V 0 ), the populations are predicted to be independent of the phase angle. As expanded upon in the Supporting Information, when the initial state of the system is localized on one of the molecules, the factor will merely act as an overall phase in the evolution of the site-basis probability amplitudes, c i (t). On the other hand, the imaginary part of the off-diagonal elements of the density matrix, I[ρ ij ], contains information about the quantum coherence and therefore the direction of the exciton flux. As seen in Fig. , the coherences for the V x = V y case do depend on the phase θ.