A unifying geometric framework for computational representation of stereoisomers based on mixed product

Analyzing molecular chirality, encompassing the determination of stereoisomers' configurations and quantification of the degree of chirality, is critical for drug discovery. However, current methods struggle with complex chirality and lack quantification capabilities. We propose a unifying geometric solution based on mixed product representation for chirality quantification. This approach unifies chiral stereoisomer discrimination by directly mapping molecular symmetry breaking to a 3D algebraic space. Unlike conventional qualitative rules such as the Cahn-Ingold-Prelog rules, this method provides quantitative descriptors for each stereogenic element. We implement this approach in ChiralFinder, a computational tool that achieves high accuracy in differentiating conformations and automates the analysis of central and axial chirality. The benchmarking results demonstrate that ChiralFinder effectively detects and distinguishes stereogenic elements and integrates with machine learning models to enhance spectra prediction. This rigorous geometric framework establishes a foundation for comprehensive stereoisomer representation, with potential for expansion to include planar and helical chirality.