Eq. A14 is evaluated as The above expression in Eq. A21 is equivalent to plugging the discrete spectral density expression J eff (ω) = π 2 j C2 j Ωj δ(ω -Ωj ) into Eq. A7 then explicitly evaluate the integral, which is not surprising. Instead of just using evenly distributed grid points in ω to evaluate the integral, the integral converges faster if one can efficiently sample the distribution of the frequencies { Ωj } and coupling coefficients { Cj } in the spectral density (Eq. 11) using strategies in Ref. 96 (or related earlier approaches in Ref. 47 and Ref. 97).