Reaction Networks and the Metric Structure of Chemical Space(s)

In this paper, we develop a formal definition of chemical space as a discrete metric space of molecules and analyze its properties. To this end, we utilize the shortest path metric on reaction networks to define a distance function between molecules of the same stoichiometry (number of atoms). The distance between molecules with different stoichiometries is formalized by making use of the partial ordering of stoichiometries with respect to inclusion. Calculations of fractal dimension on metric spaces for individual stoichiometries show that they have low intrinsic dimensionality, about an order of magnitude less than the dimension of the underlying reactive potential energy surface. Our findings suggest that efficient search strategies on chemical space can be designed that take advantage of its metric structure.