While the absolute magnitude of the tilt parameters may exhibit large differences, we see that if the ratio of s x /s y is similar, then the composite parameters P and B, defined in Eq. 15, may be similar. For example, although the DFT/MRCI(2) tilt parameters for ethylene are significantly smaller than their ab initio MRCI counterparts, the predicted P and B values fall under the same category. That is, they both predict peaked and singlepath intersections. On the other hand, for butadiene, not only are the DFT/MRCI(2) tilt parameters a lot smaller, the ratio is also significantly different. As a result, DFT/MRCI(2) predicts a bifurcating intersection, whereas MRCI predicts a single-path intersection, These differences in the intersection topography discussed above do not translate, however, into significant differences in the respective branching spaces. As shown in Table , the Finally, to confirm that the surrogate potentials accurately reproduce the DFT/MRCI(2) potential surfaces within the branching space, Fig. shows DFT/MRCI(2) single point energies computed along the branching space directions, with the origin corresponding to the MECI geometry, for ethylene, butadiene and fulvene. Fig. shows that the GPR surrogates Additionally, Fig. shows the eigenvalues of the c z 0 Hessian, with the number of non-zero (zero) eigenvalues corresponding to the branching (seam) space dimension. The first point of note is that the eigenvalues of the seam space coordinates should be strictly zero. For DFT/MRCI(2), the seam space eigenvalues show small deviations from zero, but is within the uncertainty of the GPR surrogate model, which will be discussed in Section 4.3. In practice, Fig. shows that DFT/MRCI(2) is able to correctly capture the branching and seam space dimensions. to MR-CISD for a range of molecules. The methods examined included SA-CASSCF, ensemble DFT approaches, and the orthogonalization-corrected (OM2) semi-empirical configuration interaction method. As that study demonstrated, the branching spaces furnished by different electronic structure approaches can vary widely, with, for example, spin-flip TDDFT (SF-TDDFT) yielding r IJ overlaps with the benchmark MRCI ranging from 0.64 for a twisted-bond-alternating methylimine MECI to near quantitative agreement and a 0.986 overlap for methylimine MECI. Thus, the average overlap between the DFT/MRCI (2) and MR-CISD branching spaces of 0.98 for the examples considered should be considered near quantitative agreement.