Pseudo-point groups and chronality in enumeration of reaction pairs

Abstract

The pseudo-point group $$\tilde D_{6h}$$ is constructed to characterize the symmetry of a basic pair of hexagonal reaction graphs having no par-bonds on its edges. Any pairs of reaction graphs (reaction pairs) are considered to be obtained by adding par-bonds to the edges of the basic pair; they are counted by the USCI (unit-subduced-cycle-index) approach. Thus, the six edges of the basic pair are assigned to the coset representation $$\tilde D_{6h}$$ (/C 2v ). After the subduction of the $$\tilde D_{6h}$$ is calculated, the partial-cycle-index method of the USCI approach is applied to the combinatorial enumeration of reactions pairs. Reaction pairs are classified to two categories, i.e. isoenergetic and anisoenergetic. An isoenergetic pair is concluded to be a self-reaction pair, while an anisoenergetic pair corresponds to a non-self-reaction pair. The concept of chronality is also discussed to clarify the symmetrical nature of the resulting orbits.