Variational Hirshfeld partitioning is a powerful framework for constructing approximate models of the electronic density of molecules and materials. While its attractive features have been derived from its mathematical definition,1 this talk explores the reverse direction: what is the minimal set of properties, or axioms, that uniquely define the variational Hirshfeld framework?
We show that four intuitive axioms are sufficient: locality, additivity, coordinate invariance, and normalization. Beyond clarifying the mathematical foundation of variational Hirshfeld partitioning, these axioms carry two significant implications. First, within a broad family of partitioning schemes, every alternative method must violate at least one of these four basic axioms. Second, the axioms constrain the set of admissible model densities for atomic fragments. These results establish theoretical guardrails for density partitioning and offer clear guidance for designing future atoms-in-molecules methods.
