Sampling reactive pathways with random walks in chemical space: Applications to molecular dissociation and catalysis

Automatically generating chemical reaction pathways is a significant computational challenge, particularly in the case where a given chemical system can exhibit multiple reactants and products, as well as multiple pathways connecting these. Here, we outline a computational approach to allow automated sampling of chemical reaction pathways, including sampling of different chemical species at the reaction end-points. The key features of this scheme are (i) introduction of a Hamiltonian which describes a reaction "string" connecting reactant and products, (ii) definition of reactant and product species as chemical connectivity graphs, and (iii) development of a scheme for updating the chemical graphs associated with the reaction end-points. By performing molecular dynamics sampling of the Hamiltonian describing the complete reaction pathway, we are able to sample multiple different paths in configuration space between given chemical products; by periodically modifying the connectivity graphs describing the chemical identities of the end-points we are also able to sample the allowed chemical space of the system. Overall, this scheme therefore provides a route to automated generation of a "roadmap" describing chemical reactivity. This approach is first applied to model dissociation pathways in formaldehyde, H2CO, as described by a parameterised potential energy surface (PES). A second application to the HCo(CO)3 catalyzed hydroformylation of ethene (oxo process), using density functional tight-binding to model the PES, demonstrates that our graph-based approach is capable of sampling the intermediate paths in the commonly accepted catalytic mechanism, as well as several secondary reactions. Further algorithmic improvements are suggested which will pave the way for treating complex multi-step reaction processes in a more efficient manner.