The Polytope Formalism: application to molecular constitution and the prospect of a complete description of Chemical Space

), providing a powerful tool for elucidating isomerisation mechanisms. This is demonstrated through increasingly complex examples of H-tautomerism. The corresponding networks of species and interconversion pathways map directly onto their associated potential-energy surfaces and thus function as a "discretised encoding" of them. Because this framework accommodates a multidimensional implementation of transition-state theory, it describes and organises the behaviour of the chemical system. Beyond stereoisomerism and molecular constitution, the same mathematical and conceptual principles may be applied to the quantum chemical aspects (nuclear, electronic, and rovibrational states), yielding a fully discretised and physically grounded representation of molecular systems. In doing so, the Polytope Formalism provides a universal framework for the automated exploration of chemical behaviour and Chemical Space - integrating rigorous theory, digital representation, and data-driven discovery within a single coherent framework.