Dipole-constrained variational Hirshfeld for electrostatically faithful atomic charges

Density-based atomic partitioning methods provide atomic electron densities that enable the consistent derivation of atomic properties used to model non-bonded interactions, but their atomic charges often fail to accurately reproduce molecular electrostatics. We develop dipole-constrained additive variational Hirshfeld (d-AVH), a partitioning method that exactly reproduces the reference molecular dipole using atomic charges alone. The method extends the AVH framework by introducing dipole constraints into the variational optimization of promolecular densities, which are represented as linear combinations of neutral and charged proatom densities. Two variants are studied: the computationally efficient minimal-basis d-AVH-M and the more flexible bound-proatom d-AVH-B. Across a diverse dataset of more than 760 compounds, d-AVH systematically improves the accuracy of point-charge approximations to the electrostatic potential (ESP) relative to AVH while preserving the conformational stability and interpretability of Hirshfeld-based atomic densities. For several chemically distinct subsets, d-AVH matches the accuracy of ESP-fitted charges and surpasses Charge Model 5. These results establish d-AVH as a broadly applicable density-based framework for constructing electrostatically faithful atomic charges.