Unified Generation of Conformations, Conformers, and Stereoisomers: A Discrete Mathematics-Based Approach

In this feasibility study we propose an approach to a unified generation of stereoisomers including conformers of a molecular structure. The method is based on discrete mathematics, it recognizes and varies the orientation of in principle each quadruple of atoms. The method has potential to also generate stereoisomers that are not describable in terms of stereocenters or single bond rotations. Fundamentals such as the concept of a (partial) orientation function are discussed, and mathematical tools such as Radon partitions and binary Grassmann-Plücker relations are used to construct tests for realizability of abstract orientation functions. Simple examples are treated in detail.