The equilibrial path concept is further developed.
Special attention is spent the symmetry conservation along equilibrial paths and symmetry-breaking.
Symmetry-breaking can occur only at singular points. The simple singular points of an equilibrial path are valley-ridge inflection points. In contrast to the intrinsic reaction paths and the gradient extremal paths, the equilibrial paths enable to describe the branching of reaction channels. O ab initio potential energy surface with equilibrial paths are presented. In particular four minimizers associated with the product of an elimination reaction and 26 saddle points, among these 14 saddle points of first order, have been located.