There is a central minimum, M , which is surrounded by five SPs. Five VRI points are shown between the SPs through Xi, where i is a consecutive number. The boundaries of the convex-concave regions are enclosed by green lines. They are given by the condition det(H) = 0. These lines also cross the VRI points. Normally they are curvilinear, so that the points of a molecule on a higher dimensional PES with det(H) = 0 form curved hypersurfaces (not 'hyperplanes' as claimed in ). Each VRI is intersected by its own singular NT, all of which are represented by thin blue lines. For example, the dashed blue curve is the singular NT through the VRI point X1. Singular NTs are the boundaries of families of NTs that connect the minimum, M , with different SP s. Two singular NTs each form a corridor for all NTs connecting the minimum, M , with the same SP i .