We examined reaction 93 in detail (Figure ), in which IDPP provides an undesired path (Section 2.1). Key structural elements highlighted in Figure or 8a, such as the C-O distance (Figure ), C-C-C angle (Figure ), and H-C-C-H dihedral angle (Figure ), were calculated for each energy evaluation point/image structure. If the constraint violations of FB-ENM or IDPP were ideally zero, these values would be nearly constant. However, as noted in Section 2.1, they vary significantly along the IDPP path, while remaining nearly constant along the FB-ENM path. DFT energies along both paths (Figure ) show that the FB-ENM path energy remains low up to the vicinity of the TS energy, reflecting the absence of undesired molecular distortions or bond breakings. To demonstrate that reaction 93 is not a special case, we calculated DFT energies along the FB-ENM and IDPP paths for all 121 reactions, and the difference between their highest energies (Tables ). Figure shows the distribution of these differences, excluding reaction 102 due to IDPP path divergence caused by a severe atomic collision on the initial path. IDPP paths have lower energies than FB-ENM in only 17 out of 120 reactions (14%), with 6 and 13 reactions having slight differences within 2 kcal/mol and 10 kcal/mol, respectively. Only reaction 34 has a large difference of over 1 eV (= 23.1 kcal/mol), which will be examined next. In contrast, FB-ENM provides lower-energy paths in 103 reactions (86%), with 25 and 9 reactions having differences over 1 eV and 2 eV, respectively. This suggests that the combination of FB-ENM and the direct MaxFlux method yields favorable results even when IDPP does not work well, such as in reaction 93.