p(TP|q) peak maximization: Necessary but not sufficient for reaction coordinate accuracy

Free energy hysteresis errors and other problems can arise from coordinates that are only optimized to accurately parameterize the separatrix. In this sense, an accurate separatrix is necessary but not sufficient to ensure reaction coordinate accuracy. For diffusive dynamics we prove that maximizing the peak in the projected transition path probability p(TP|q) is equivalent to separatrix optimization. Thus methods based on this criterion [27] may find coordinates that accurately parameterize the separatrix, but not earlier and later stages along the reaction pathway.