Graph theory for automatic structural recognition in molecular dynamics simulations

Graph theory algorithms have been proposed in order to identify, follow in time, and statistically analyze the changes in conformations that occur along molecular dynamics (MD) simulations. The atomistic granularity level of the MD simulations is maintained within the graph theoric algorithms proposed here, isomorphism is a key component together with keeping the chemical nature of the atoms. Isomorphism is used to recognize conformations and construct the graphs of transitions, and the reduction in complexity of the isomorphism has been achieved by the introduction of "orbits" and "reference snapshots." The proposed algorithms are applied to MD trajectories of gas phase molecules and clusters as well as condensed matter. The changes in conformations followed over time are hydrogen bond(s), proton transfer(s), coordination number(s), covalent bond(s), multiple fragmentation(s), and H-bonded membered rings. The algorithms provide an automatic analysis of multiple trajectories in parallel, and can be applied to ab initio and classical MD trajectories alike, and to more coarse grain representations.