For the one-site calculations below, we start with such an initial guess: we use the identity matrix and switch its first column with the N e 2 -th column (N e is the total number of electrons). The parameter set is: mω 2 = 0.003, g = 0.0075, e d 1 = 0.05, and we discretize the bath with 101 metallic states evenly distributed with energy spacing dE = Γ 10 . We set the dynamical weighting parameter to be ζ = 40. And we set the convergence threshold for the norm of gradient to be 1 × 10 -4 . In Table and Table , we report total number of orbital optimization cycles needed to converge the calculation. We observe that (i) convergence is harder when Γ is large; and (ii) converge is also more difficult when the electron-electron repulsion is finite (U = 0.1). Clearly, for Γ = 0.01, our algorithm for finding a cCASSCF solution is suboptimal and can be improved (the number in the bracket is calculated by reading the CI coeffcients for Γ = 0.001). Nevertheless, we have been able to converge the solutions and, as we show below, the final states are illuminating.