The dimer shifts of the LUMO orbital energies were examined as a function of 𝛥 5643 . The (𝛽 #' 5643 ) + values were also looked at as a function of Δ 5643 . Analogous relationships were explored for the monomer and dimer HOMO orbitals. These models are shown in Figure . Figure (b) and (d) offer some insight into the origins of the complex 𝛽 values that were generated by Equation 2. As Δ 2343 and Δ 5643 increase in the secular determinant shown in Equation 1 does an increasingly poor job at describing the molecular orbital interactions of the monomers after dimer formation. Once the difference in monomer LUMO energies is greater than 1.5 eV, nearly all calculated #' 5643 values are complex numbers. This is also the case for large differences in monomer HOMO energies (Δ 2343 ≥ 1.3 eV).