Development and Application of Constrained Variational Hirshfeld Atoms in Molecules Methods

Abstract

Chemists have long relied on fundamental concepts such as atomic charges, chemical bonding, electrophilicity, and aromaticity to interpret and predict molecular properties and their transformations. Although these concepts often lack clear definitions within the framework of quantum mechanics, they remain indispensable for interpreting experimental results and developing computational models. Translating these chemical concepts into a rigorous mathematical definitions derived from quantum mechanics typically requires defining atoms within molecules. However, because atomic properties are not quantum-mechanical observables, their definitions are inherently ambiguous. Nevertheless, their practical utility has driven the development of numerous real-space partitioning schemes. This thesis advances these efforts by developing and applying novel methods for partitioning electron density into atomic regions, with a particular focus on variational Hirshfeld approaches, and by integrating both new and existing partitioning schemes with energy decomposition analysis. We introduce two novel methods for computing atomic densities under chemical and physical constraints and present extensive numerical results to support their chemical significance and computational performance. The constrained Iterative Hirshfeld (c-HI) method extends the popular Iterative Hirshfeld partitioning scheme by introducing a variational formulation that incorporates charge constraints. The dipole-constrained Additive Variational Hirshfeld (d-AVH) method builds on the additive variational Hirshfeld framework to enforce a dipole constraint, ensuring that the atomic charges exactly reproduce the molecular dipole moment. A detailed analysis highlights the distinctive features of d-AVH relative to existing schemes. In addition, we present a general-purpose and modular implementation of the Interacting Quantum Atoms (IQA) energy decomposition method, enabling the calculation of atomic and pairwise energy components for any partitioning scheme. Building on these developments, we introduce Origin-Independent Constrained Population (OICP) decomposition, which is a novel origin-independent method for decomposing molecular polarizabilities into atomic contributions. Compared with other origin-dependent decompositions, OICP provides numerically stable, additive, and transferable atomic polarizabilities across diverse chemical environments. Collectively, these contributions deepen the chemical insight obtainable from quantum chemical calculations and offer new pathways for improving the description of non-covalent interactions in molecular mechanics force fields and physics-based machine-learning models.