Monotonicity properties of the atomic charge density function

Angulo, J. C.; Yáñez, R. J.; Dehesa, J. S.; Romera, E.

doi:10.1002/(sici)1097-461x(1996)58:1<11::aid-qua2>3.0.co;2-0

Cited by 11 publications

(8 citation statements)

References 37 publications

(4 reference statements)

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“…The benefits of working with V ( r ) have been demonstrated. For example: Although it is known empirically that ρ ( r ) decreases monotonically with radial distance from the nucleus of a ground‐state neutral atom,11,62 proving this remains a challenge. But demonstrating that V ( r ) must behave in this manner is straightforward, using Poisson's equation 11,12…”

Section: The Diverse Aspects Of the Electrostatic Potentialmentioning

confidence: 99%

The electrostatic potential: an overview

Murray

Politzer

2011

WIREs Comput Mol Sci

1,207

698

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The electrostatic potential V(r) that is created by a system of nuclei and electrons is formulated directly from Coulomb's law and is a physical observable, which can be determined both experimentally and computationally. When V(r) is evaluated in the outer regions of a molecule, it shows how the latter is 'seen' by an approaching reactant, and thus is a useful guide to the molecule's reactive behavior, especially in noncovalent interactions. However, V(r) is a fundamental property of a system, the significance of which goes beyond its role in reactivity. For example, the energy of an atom or molecule can be expressed rigorously in terms of the electrostatic potentials at its nuclei. These and other features of V(r) are discussed in this overview. C

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Section: The Diverse Aspects Of the Electrostatic Potentialmentioning

confidence: 99%

The electrostatic potential: an overview

Murray

Politzer

2011

WIREs Comput Mol Sci

1,207

698

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“…In ref 19 this is shown to be true for the electron density outside a sphere with a certain radius r and for r f ∞. For the region close to the core the Kato cusp condition states that the density is monotonic in this region, and although there is still no formal proof, 8 there exists further computational evidence that the atomic density is indeed a monotonically decaying function for all values of r. [1][2][3][4][5][6][7]9 Therefore, many functions derived from the total electron density have been proposed as a tool to recover the shell structure and to visualize the Aufbau principle. The first studies focused on the radial density distribution function D(r) which was shown to exhibit maxima that correspond to the electronic shells of atoms.…”

Section: Introductionmentioning

confidence: 99%

The Shell Structure of Atoms

Eickerling

Reiher

2008

J. Chem. Theory Comput.

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The total electron density distribution of an isolated atom or an atom in a molecule does not reveal an atomic shell structure. Many localization functions, such as the radial averaged electron density, the Laplacian of the electron density, or the electron localization function have been proposed to visualize and analyze the shell structure of atoms. It was found that for light main group elements the correct number of shells is revealed by such functions. Later it was recognized that for heavy main group elements and for transition metals many of these diagnostic tools fail to reveal the full set of electronic shells as expected from the periodic table. In this work we focus on the radial structure of isolated atoms as revealed by the Laplacian of the electron density. We will demonstrate that it is the nodal structure of the orbitals of the inner shells which is responsible for the diminishing of at least one valence shell of third row transition metal atoms. Particular attention is paid to the effect of different electronic configurations on the shell structure of atoms and the question if the changes observed in the Laplacian of the radial density are sufficiently large for experimental studies on the topology of the electron density. Our presentation is as general as possible and, hence, employs a fully relativistic, i.e., four-component picture and a multiconfigurational ansatz for the wave function, which is thus valid for the whole periodic table of elements.

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“…To answer this question, it seems legitimate to consider the one‐electron density of free atoms at first step. It is well‐known computationally that the ground state

\vec{\nabla} {normalρ}_{atom} true(\overset{r}{true} true)

of a free atom reveals a single attractor, a (3, −3) critical point, at the position of nucleus while

{normalρ}_{atom} true(\overset{r}{true} true)

decays “monotonically” far from the nucleus (check Figure ), however, from theoretical viewpoint, this is not a proven conjecture yet . On the other hand, if the free atom's one‐electron density is perturbed marginally in a molecule because of interaction with other AIM, it seems reasonable to assume that the one‐electron density of a molecule is nearly the sum of the one‐electron densities of the constituent free atoms,

{normalρ}_{mol} true(\overset{r}{true} true) \approx \sum_{i} {normalρ}_{atom, i}^{} true(\overset{r}{true} true)

, which is officially called the promolecule model of the one‐electron density (for examples as well as a recent bibliography on this model see ).…”

Section: Open Problems and Corresponding Backgroundmentioning

confidence: 99%

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

Shahbazian

2018

Int J of Quantum Chemistry

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In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011, 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi-component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013, 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi-component version. K E Y W O R D S holographic principle, quantum theory of atoms in molecules, subsystem quantum mechanics, topological atom, virial partitioning

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Monotonicity properties of the atomic charge density function

Cited by 11 publications

References 37 publications

The electrostatic potential: an overview

The electrostatic potential: an overview

The Shell Structure of Atoms

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

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