Farnaz Heidar-Zadeh

Constrainng additive variational Hirshfeld (AVH) charges to reproduce the molecular dipole systematically improves their description of the molecular electrostatic potential.

Interacting Quantum Atoms (IQA) is a real-space energy decomposition framework that reveals how individual atoms and their pairwise interactions contribute to the stabilization of molecules, yet its application has been dominated by the Quantum Theory of Atoms in Molecules (QTAIM). Although fuzzy partitioning schemes offer smoother atomic densities, reduce numerical costs, and avoid complications associated with non-nuclear attractors, their influence on IQA energy components has not been systematically assessed. We investigate how the choice of atomic partitioning affects IQA energy components by comparing QTAIM with several variational Hirshfeld-based schemes. To enable direct comparisons between QTAIM- and fuzzy-partitioned IQA energy components, we integrate charge-constrained variational Hirshfeld partitioning with the IQA framework, generating fuzzy analogs of QTAIM atoms with identical atomic charges. Across a diverse set of diatomic and polyatomic molecules, we observe that fuzzy partitioning consistently results in less negative intra-atomic energies and more stabilizing interatomic interactions than QTAIM. These differences are traced to changes in the underlying electron–nuclear attraction and electron–electron repulsion terms. The proposed methodology provides a rigorous basis for comparing QTAIM and fuzzy atoms in IQA, enabling the effects of atomic populations and partitioning schemes to be disentangled for the first time.

We propose a compact, chemically intuitive, and transferable representation of molecular density as a nonnegative linear combination of spherical atom-centered densities corresponding to different atomic charge states. We investigate how far the basis can be reduced without degrading its ability to reproduce the molecular density, measured by the Kullback--Leibler divergence. Using a diverse set of organic molecules, we find that the optimal expansions are very sparse, revealing that only cationic, neutral, and, where bound, anionic atomic densities are required to reproduce the divergence accuracy of the full expansion, which significantly reduces the computational cost. The optimized contributions show limited sensitivity to the electronic-structure method, are transferable across related chemical environments, and accurately reproduce derived atomic properties. These results introduce an efficient and interpretable representation of molecular density that can accelerate the evaluation of atomic properties and intermolecular interactions in large systems and provide a low-dimensional target for developing machine-learning models.

We perform a thorough test of the “ big is good” principle (DMB) using double‐exchange reactions between diatomic molecules. We conclude that DMB is “not bad” at predicting whether or not a reaction will be favorable, but its performance is inferior to alternatives like the maximum hardness principle.

By considering double-exchange reactions between 496 heteronuclear diatomic molecules composed of elements in the first four rows of the periodic table, we test the reliability of the principles of maximum hardness and minimum electrophilicity. Both principles are reasonably robust, especially for reactions that are decisively exothermic, but neither principle is perfectly reliable. Nevertheless, both principles provide good rules-of-thumb for chemical reactions. Removing reactions that violate the hard/soft acid/base rule from the data set enhances the reliability of the maximum hardness principle, offering support for the relationship between the maximum hardness and hard/soft acid/base principles. Both principles are reliable about 80% of the time if near-thermoneutral reactions are removed from the data set. For reactions that follow the hard/soft acid/base rule and that are strongly energetically favored, the maximum hardness principle predicts the correct products nearly 90% of the time.

A unified theoretical framework for interpolating the energy and other molecular properties as a function of the number of electrons is presented. For any smooth interpolatory model of charge transfer, including the ubiquitous quadratic model, the electron density is always negative for some regions of space and some numbers of electrons. This has practical implications; e.g., we observe that parabolic interpolation predicts HF^+0.5 has an unphysical negative population on hydrogen for sufficiently compressed bonds. This suggests that the only sensible model for charge transfer, in most cases, is linear (zero-temperature grand canonical) interpolation.

Chemical hardness is one of the fundamental concepts in chemical reactivity theory, rigorously defined within the framework of Conceptual Density Functional Theory (CDFT). The associated maximum hardness principle (MHP), which postulates that a favorable direction of reaction is toward the state of maximum hardness, has been widely applied as a guiding rule to govern the direction of chemical reactions. However, several studies have questioned its validity. In this work, we investigated the quantitative applicability of the MHP using two reaction datasets, viz, a dipolar cycloaddition dataset of 5269 reaction profiles and the more comprehensive BH9 dataset of 449 reactions. We adopted different approximations to compute the hardness, including Kohn–Sham orbital based frontier molecular orbital (FMO) and the finite difference approximation (FDA). The effect of using different definitions to compute the average hardness of bimolecular reactions is analyzed on the validity of MHP. Our analysis revealed dependence of hardness values on the level of theory, definitions and approximations used which should be kept in mind before criticizing the MHP. Among 5269 cycloaddition reactions, approximately 80% of the reactions are found to obey the MHP. For BH9 dataset, MHP is found to better supported for unimolecular reactions, while remaining strongly dependent on the definition used to compute the average hardness for bimolecular reactions. Reactions in which the individual hardness of the reactants differs significantly are more likely to disobey MHP. Nonetheless, since these electronic structure principles are qualitative in nature, their validity cannot be expected to be universal.

Atomic charges play a central role in the analysis of molecular electronic structure and are widely used in the development of computational models. We introduce a simple and computationally efficient extension of Hirshfeld’s 1977 stockholder partitioning method, called scaled Hirshfeld, in which neutral proatom densities are scaled to construct a promolecular density better adapted to the molecular electron density. We present a fixed-point iterative algorithm to compute the proatom scaling coefficients and show that this formulation is equivalent to the information-theoretic additive variational Hirshfeld method with a minimal basis. This equivalence establishes a rigorous mathematical foundation for the scaled Hirshfeld method and ensures size consistency as well as the existence of a unique solution. Numerical results demonstrate that the proposed approach yields charges larger than those obtained with the original Hirshfeld method, while retaining computational efficiency and providing an improved description of molecular dipole moments and electrostatic potentials.

Charge Model 5 (CM5) refines Hirshfeld charges to better reproduce charge-dependent properties, such as molecular dipole moments. Although it was parametrized using a limited set of molecules in the gas phase, CM5 charges demonstrate broad applicability, computational robustness, and conformational stability. Being merely a charge model, CM5 does not produce atomic densities, limiting its ability to compute other atomic properties and related quantities. We present a novel algorithm to reverse-engineer atomic densities corresponding to a given set of charges and apply it to CM5, by leveraging the recently developed constrained variational Hirshfeld framework. Using these reconstructed atomic densities, we evaluate a range of CM5-consistent atomic properties and compare them with results from similar methods. This computationally efficient approach broadens the utility of the CM5 model, enabling the evaluation of additional atomic properties and molecular interaction terms.