3. A third criterion is smoothness. For dynamics, it will be essential that we obtain smooth DW-SA-cCASSCF energies and wavefunctions. and the ne = 0 diabatic state (i.e. the diabatic state whose number of electrons on the impurity is 0). Far away from the crossing point, the onsite energy ϵ d (x) is so much larger energy than the fermi level that for a good algorithm, the asymptotic behavior of the S 2 energy should approach the ne = 0 diabatic state energy. Note that these two metrics favor opposite ζ parameters, and so have we chosen ζ = 40 as a compromise so as to keep the ground state as accurate as possible without sacrificing the excited state asymptotic behavior entirely. Luckily, the excited states are smooth for all ζ parameters (not shown here). The parameter set is the one-site model with mω 2 = 0.003, g = 0.0075, e d 1 = 0.05, U = 0 with 101 metal states evenly distributed with energy spacing dE = Γ 10 (i.e. the full band width is 10Γ).