using 𝛽 2 𝜎 𝑝𝑎𝑟 𝜎 𝑝𝑒𝑟𝑝 𝜎 𝑝𝑎𝑟 2𝜎 𝑝𝑒𝑟𝑝 (8) In eqn ( ) and ( ), Φ is the left Dyson orbital and Φ is the right Dyson orbital (for Hermitian methods the two are identical). Averaging over molecular orientations is performed numerically in ezDyson using orientations computed with REPULSION. The results of these calculations are represented by the ℓ ∞ curve in Fig. (b). Again, using the exact expression for the plane wave gave almost identical results as using the partial wave expansion with ℓ = 10 or 5. In fact, the ℓ = 5 (blue) curve is difficult to discern in Fig. (b), because it coincides almost exactly with the other two curves in the figure. This demonstrates that using the partial wave expansion with terms up to ℓ = 5 is sufficient for describing the near-threshold photoelectron anisotropy in SO  .