The Polytope Formalism for Constitutional Isomerism and Isomerization

The principles of the Polytope Formalism as developed for stereoisomerism can also be applied to constitutional isomerism reflecting a deep connection between the two and thereby opening the way for describing all isomerism including nuclearspin isomerism. Further, the conceptual framework and methodology can accommodate other discrete molecular-state aspects not typically considered “isomerism”, such as rovibrational and electronic states. The formalism thus provides a universal framework for the abstract description of chemical entities, their naming, and digital representation. Of greater importance, by accommodating a multidimensional implementation of transition-state theory, the results of the formalism meaningfully describe the landscape of the associated chemical space. This provides a powerful and essential tool for its exploration. Novel features of the Polytope Formalism of constitutional isomerism are that it is based upon atom connectivity and the explicit inclusion of subvalent and hypervalent species. The resulting comprehensive sets of possible species include isomers and their related interconversion intermediates (transition states, higher-order saddle points, etc.) providing a powerful tool for elucidating isomerisation mechanisms. The networks of species and interconversion pathways map onto the corresponding potential-energy surfaces and thus represent an “encoding” of these surfaces. Implementation of the formalism is demonstrated through worked examples of H-tautomerism, illuminating applications more broadly.