In the systematic approach , we attempt to systematically sample all possible products that are connected to the reactant with a transition state, as outlined in Figure ). We start by generating the atom connectivity matrix (AC, also known as an adjacency matrix) for the reactant: R. This is a binary N atom × N atom symmetric matrix where the presence and absence of bonds are indicated by 1's and 0's, respectively. The corresponding AC for product i (P i ) is derived from R through a conversion matrix