In these equations, we find that the effect of the alignment angle ϕ is to impose a global phase on the evolution of the |+⟩ basis state. Excitation with a LCP pulse imposes an analogous phase shift on the |-⟩ basis state. Numerical solutions to these equations for θ = 0 and θ = π/3 are presented in Fig. as dashed lines. The coherences, I[c i c j ] for ϕ = π/3 compare to those for a perfectly aligned system with ϕ = 0 and θ = 0. Populations |c i | 2 for an arbitrary alignment given by ϕ will be identical to those of the ϕ = 0 dimer.