One of the most useful pieces of information extracted from quantum mechanical calculations is the atomic properties like charges and multipole moments. These are commonly used in force field development, conceptual density functional theory, and dispersion interaction energy calculations, just to name a few. Because atomic properties do not correspond to a quantum mechanical observable, there is an inherent ambiguity in calculating them. However, their effectiveness and practical utility have driven the development of various methods for decomposing a molecule into atomic components. One of the most established family of partitioning schemes, inspired by Hirshfeld [1], uses reference proatom densities to compute the share of an atom in the molecular density. Characterizing the mathematical, chemical, and computational features of these schemes is an active topic of research [2,3,4].

Iterative Hirshfeld is one of the most commonly used variants of Hirshfeld scheme[5], which self-consistently updates each proatom so that they have the same number of electrons as the corresponding atom. We recently developed a variational procedure for the iterative Hirshfeld method. This not only provides an elegant mathematical framework for iterative Hirshfeld, but also provides a straightforward approach for adding constraints when computing atomic densities. This has many applications, for example in force-field parameterization, one often wants to constrain a portion of an amino acid residue to have a specific charge. In this presentation, the constrained iterative Hirshfeld is introduced and compared to the information-theoretic approaches, like constrained scaled Hirshfeld and constrained additive variational Hirshfeld. In addition, we present our assessment of the chemical and computational quality of these methods for different representative systems.

[1] F. L. Hirshfeld. Bonded-atom fragments for describing molecular charge densities.Theoretica Chimica Acta, 44(2):129–138, 1977. [2] Toon Verstraelen, et.al. Minimal BasisIterative Stockholder: Atoms in Molecules for Force-Field Development. Journal of Chemical Theory and Computation, 12(8):3894–3912, 2016. [3] Farnaz Heidar-Zadeh, et.al . Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes. Journal of Physical Chemistry A, 122(17):4219–4245, 2018. [4] Minsik Cho, et.al. The atomic partial charges arboretum: Trying to see the forest for the trees. ChemPhysChem, 21(8):688–696, 2020 [5] Bultinck, P. et.al. Critical Analysis and Extension of the Hirshfeld Atoms in Molecules. J. Chem. Phys. 2007, 126,9