PNNL

Abstract

A reduced set of reaction coordinates are often employed in chemistry to describe the collective change between reactants and products within the context of rare event theories and in the exploration of energy landscapes. While incredibly powerful, use of these collective variables becomes increasingly challenging as the systems under study become more complex. Recent advancement of new descriptions of collective molecular coordinates have included PageRank (PR) analysis of the network of interactions about molecules and atoms within a system. Herein, PR is developed as a continuous variable that not only captures chemical transformations but can also be employed as a collective variable for a process that could span a highly dimensional energy surface. The derivatives of PR with respect to atomic coordinates are presented, and subsequently combined with forces during a chemical transformation within biased molecular dynamics sampling simulations to create the potential of mean force (PMF). This technique is demonstrated for two reactions: 1) the transformation of tetrahedral [Al(OH)4]-(aq) to octahedral [Al(OH)4(H2O)2]-(aq), and 2) the formation of contact ion pairs (CIPs) and solvent separated ion pairs (SSIPs) of Na+ and OH- in bulk water. Comparison of the behavior of the PR collective variable in both examples reveals that the ability of the PR to resolve local versus extended configurational attributes is tuned by the size of the network employed. This is a unique feature of PageRank that enables control over the resolution of the PMF that is produced.