Understanding the full range of configurations available to coordination centres is central to stereochemistry, reactivity, and molecular design. While classical coordination chemistry treats geometries such as tetrahedral, square planar, trigonal bipyramidal, and octahedral as discrete categories, no general framework exists for describing all possible configurations of coordination centres of arbitrary valence ABn in a unified and mathematically complete way.
In this talk, a general formalism for constructing the complete configuration space of arbitrary coordination centres as a structured topological object is presented. Using a polytopal representation, configurations are treated as vertices in abstract configuration spaces, with edges corresponding to feasible rearrangement pathways. This approach generates not only classical coordination geometries and stereoisomers, but also all interconversion intermediates, including transition states and higher-order saddle configurations.
The resulting configuration spaces possess well-defined topologies, symmetry structures, and connectivities, allowing direct mapping onto potential-energy surfaces and reaction networks. This provides a rigorous, system-independent framework for understanding coordination geometry, stereochemical interconversion, fluxionality, and rearrangement mechanisms within a single mathematical structure. Surprisingly, these configuration spaces are revealed to be unexpectedly complex and indicate that surprising phenomena are possible inviting experimental confirmation.
Beyond classification, the formalism enables automated enumeration, systematic organisation, and algorithmic exploration of coordination chemistry, establishing a foundation for integrating stereochemistry, reaction dynamics, and digital chemical representation into a unified configuration-space theory of coordination centres.