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It has been assumed that the negative divergence of all stress tensors in common use yields the same force. This work finds that this is untrue, and, in fact, can vary wildly. We demonstrate this for the hydrogen atom, the one-particle isotropic harmonic oscillator, and a particle in an infinite spherical well where the exact density, pair-density, and the first order reduced density matrix are known for ground and excited states without any approximation. The Ehrenfest stress-tensor is introduced as any stress-tensor whose negative divergence will yield the corresponding Ehrenfest force for the same system when the exact wave-function is utilized. Stress-tensors within the literature are examined to show those that are Ehrenfest stress-tensors. Those that differ are demonstrated by how they differ within an exact formulation. The proof that the negative divergence of an Ehrenfest stress-tensor yields the Ehrenfest force is summarized. [ABSTRACT FROM AUTHOR]

Accurate restricted Hartree‐Fock (RHF) wave‐functions are used to investigate information theoretic properties of the model problem of two interacting electrons confined within an infinite spherical potential of radius R. Benchmark quality calculations are performed to characterize this system via a range of information measures as a function of the tunable parameter R, across the full electron correlation regime (low to high correlation; small R to large R). Both the Shannon information entropy and a statistical complexity measure provide quantitative insight regarding the onset of the formation of a "Wigner molecule" state for this system. [ABSTRACT FROM AUTHOR]

Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations. [ABSTRACT FROM AUTHOR]

Relationships between third-order reactivity indicators in the closed system [N, v(r)], open system [μ, v(r)], and density [ρ(r)] pictures are derived. Our method of derivation unifies and extends known results. Among the relationships is a link between the third-order response of the energy to changes in the density and the quadratic response of the density to changes in external potential. This provides a link between hyperpolarizability and the system’s sensitivity to changes in electron density. The dual descriptor is a unifying feature of many of the formulas we derive. [ABSTRACT FROM AUTHOR]

We argue that when one divides a molecular property into atom‐in‐a‐molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms‐in‐a‐molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference‐free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an “arbitrary” choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The general-purpose reactivity indicator (GPRI) is utilized to discern the reactive sites of the phenylsulfinate ion, PhSO 2-, both in isolation and with a sodium counterion. While some approaches based on the hard/soft acid/base (HSAB) principle fail to indicate that the oxygens are the hard (electrostatic) sites of the molecule and that the sulfur is the soft (electron-transfer) site of phenylsufinate, the GPRI succeeds. A computer code, written in Fortran, that computes the general-purpose reactivity indicator is released in the supplementary information. [ABSTRACT FROM AUTHOR]

When a molecule is in the presence of a chemical reagent, the external potential and the number of electrons in the molecule change. This leads to perturbative perspectives on chemical reactivity, wherein the response of a molecule to various “model perturbations” of the external potential and number of electrons is used to predict its reactivity. The perturbative perspective allows one to treat indices associated with conceptual density functional theory in a unified way. Here we concentrate on the implications of the perturbative perspective in describing regioselectivity and certain global properties of molecules, specifically, their electrophilicity, nucleofugality, and electrofugality. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [ABSTRACT FROM AUTHOR]

Conceptual density functional theory (CDFT) descriptors were computed to predict the environmental fate of approximately 6,000 widely used industrial chemicals. CDFT descriptors aligned with a molecule's possible bioaccumulation mechanism, i.e., soft chemicals are lipophilic, whereas hard chemicals may bioaccumulate by other mechanisms such as protein binding. The results have provided us with a new "rule of thumb" to guide risk assessment of chemical hazards: suspected persistent organic pollutants are either too hard (η > 0.40 hartree) or too soft (α > 200 Å 3 ). This offers a novel approach to environmental risk assessment using two fundamental properties of a molecule., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

The topology of the molecular electron density of benzene dithiol gold cluster complex Au 4 -S-C 6 H 4 -S'-Au' 4 changed when relativistic corrections were made and the structure was close to a minimum of the Born-Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization., (© 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)