Directed graphs of structurally stable potential energy surfaces representing a-priori reaction pathways

An intrinsic property of potential energy surfaces (PES) that holds within the adiabatic approximation is established: its structural stability.We derive the condition that ensures this property: There cannot be any integral curve of the gradient field of the PES that connects two classical transition state configurations without passing through another critical configuration in between.Under this situation, we can establish a one-to-one correspondence: a whole class of adiabatic PES defining one reaction mechanism is associated to a directed graph. Thus, the problem of finding a-priori pathways involving a given number m of chemical species narrows down to a classifying certain directed graphs with m sinks. The combinatorial method is derived in this paper.Detailed examples on a-priori pathways for degenerate thermal rearrangements and on 1-2 hydrocarbon shifts are worked out and found in agreement with experimental evidence.