In this article we propose a new topology, based on the stable attractors of the gradient field of the potential energy hypersurface, that may be used as a general definition of a stable chemical structure. We further construct two examples of particular realizations of this abstract topology. One of them is closely related to the catchment-region topology of Mezey and the other one to the molecular-graph model of Bader. A particularly interesting point is that both topologies lead to equivalent definitions of molecular structure; in particular, they permit us to differentiate between cis-trans isomers and rotational conformers, that had equivalent structures in the definition proposed by Bader.

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