To characterize the conical intersection topography at the optimized MECI geometry, we first determine the intersection adapted x and y (Eq. 5) coordinates that span the branching space. When the derivative coupling vector is not available, the branching space vectors can also be obtained from the curvature information of the energy difference squared surface ∆E 2 (R). Specifically, for a two-state CI, the eigenvectors associated with the non-zero eigenvalues of the energy difference squared Hessian form the branching space. In the ω-CP model, this Hessian is equivalent to taking the Hessian of c z 0 (R). This was the approach employed here to determine the branching space vectors at MECIs optimized on DFT/MRCI(2) derived GPR-surrogates. The intersecting potentials are described by a firstorder two-state model given by: 1