Generalized chirality and symmetry deficiency

Some of the elementary properties of molecular electron densities are studied from the perspectives of generalizations of symmetry, symmetry deficiency, and in particular, chirality. A simple, information-theoretical proof of the Hohenberg-Kohn theorem is discussed, and the information contents of local and global molecular electron densities are compared using a formulation of quantum chemistry on a compact manifold. One result, the "holographic electron density theorem", involving a compactification step combined with analytic continuation, gives a tool for comparing local and global symmetry properties. The compact manifold quantum chemistry approach leads to a precise statement on the role of local molecular regions in determining global properties of complete, boundaryless molecules, resulting in constraints on their symmetry, chirality, and other types of symmetry deficiencies. A special similarity measure, the SLT measure, is used for generalized density domain comparisons, suitable in general for the comparison of semilattices with a tree structure.