What does shape a topological atom?

Joypazadeh, Hamidreza; Shahbazian, Shant

doi:10.1007/s10698-013-9186-0

Cited by 12 publications

(26 citation statements)

References 35 publications

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“…In Figure 6, the −V/T ratio is presented for the H + 2 molecule confined by hard walls, where it is clear that this quantity goes to zero when ξ 0 → 1. [46] The disappearance of the BCP at this point indicates that the chemical bond is lost since the nuclear-electron interaction is not capable of trapping the electron.…”

Section: Resultsmentioning

confidence: 99%

“…Such confinement provides a new "attractor" which can not be associated with any nuclei. [42][43][44][45][46][47] There are other reports where a "single basin" is observed when there are internuclear distance changes, or nuclear masses are varied, or electrons are exposed to non-Coulomb potentials. In Figure 6, the −V/T ratio is presented for the H + 2 molecule confined by hard walls, where it is clear that this quantity goes to zero when ξ 0 → 1.…”

Section: Resultsmentioning

confidence: 99%

“…However, now one question arises; why is the electron density concentrated in the middle of the nuclei for extreme confinements?To answer this www.advancedsciencenews.com www.ann-phys.org question we will use energetic arguments, in fact, the potential energy (V)-kinetic energy (T) ratio will be used in this discussion. [43,46,48] All of them involve physical phenomena quite different to strong confinements. The main reason for this behavior is that T grows up rapidly when ξ 0 is close to 1 and consequently this is much bigger than V. We found that at the catastrophe point, the total electronic energy is equal to zero.…”

Section: Resultsmentioning

confidence: 99%

“…Thus, we have a particle in a prolate spheroidal box and consequently we cannot associate the maximum of the electron density to an attractor, non-nuclear or pseudo atom. [42][43][44][45][46][47] There are other reports where a "single basin" is observed when there are internuclear distance changes, or nuclear masses are varied, or electrons are exposed to non-Coulomb potentials. [43,46,48] All of them involve physical phenomena quite different to strong confinements.…”

Section: Resultsmentioning

confidence: 99%

“…These results coincide with the observation made by Joypazadeh and Shahbazian: "what the local zero-flux equation is really recognizing as a topological atom is a 3D region where electrons cluster with monotonic decaying densities". [46]…”

Section: Resultsmentioning

confidence: 99%

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Electron Density Analysis for the H2+ System Confined by Hard Walls: The Chemical Bond Under Extreme Conditions

et al. 2019

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For the first time, the electron density of the H + 2 molecule is analyzed when this system is confined by spheroidal walls with an infinite potential. Typically, this system is studied to obtain information of the total energy and its components or to gain insight of some expected values when such a system is squeezed by this kind of confinement. However, this is the first report where the electron density and its derivatives, under the quantum theory of atoms in molecules (QTAIM), are analyzed to study the chemical bond involved with this molecule. This confinement induces an unexpected behavior of the chemical bond and gives an idea about atomic interactions under high pressures, where the QTAIM approach indicates that the chemical bond disappears. For strong confinements, there is a significant contribution of the electron kinetic energy and the nuclear-electron energy contribution can be neglected. Under this situation, the confined H + 2 system is another example where the notion of the topological atom given by the QTAIM is no longer suitable.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Electron Density Analysis for the H2+ System Confined by Hard Walls: The Chemical Bond Under Extreme Conditions

et al. 2019

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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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Extending the Topological Analysis and Seeking the Real-Space Subsystems in Non-Coulombic Systems with Homogeneous Potential Energy Functions

Shahbazian

2016

Challenges and Advances in Computational Chemistry and Physics

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It is customary to conceive the interactions of all the constituents of a molecular system, i.e. electrons and nuclei, as Coulombic. However, in a more detailed analysis one may always find small but non-negligible non-Coulombic interactions in molecular systems originating from the finite size of nuclei, magnetic interactions, etc. While such small modifications of the Coulombic interactions do not seem to alter the nature of a molecular system in real world seriously, they are a serious obstacle for quantum chemical theories and methodologies which their formalism is strictly confined to the Coulombic interactions. Although the quantum theory of atoms in molecules (QTAIM) has been formulated originally for the Coulombic systems, some recent studies have demonstrated that most of its theoretical ingredients are not sensitive to the explicit form of the potential energy operator. However, the Coulombic interactions have been explicitly assumed in the mathematical procedure that is used to introduce the basin energy of an atom in a molecule. In this study, it is demonstrated that the mathematical procedure may be extended to encompass the set of the homogeneous potential energy functions thus relegating adherence to the Coulombic interactions to introduce the energy of a real-space subsystem. On the other hand, this extension opens the door for seeking novel real-space subsystems, apart from atoms in molecules, in non-Coulombic systems. These novel real-space subsystems, quite different from the atoms in molecules, call for an extended formalism that goes beyond the orthodox QTAIM. Accordingly, based on a previous proposal the new formalism, which is not confined to the Coulombic systems nor to the atoms in molecules as the sole real-space subsystems, is termed the quantum theory of real-space open subsystems (QTROS) and its potential applications are detailed. The harmonic trap model, containing non-interacting fermions or bosons, is considered as an example for the QTROS analysis. The QTROS analysis of bosonic systems is particularly quite unprecedented, not attempted before.

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What does shape a topological atom?

Cited by 12 publications

References 35 publications

Electron Density Analysis for the H2+ System Confined by Hard Walls: The Chemical Bond Under Extreme Conditions

Electron Density Analysis for the H2+ System Confined by Hard Walls: The Chemical Bond Under Extreme Conditions

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

Extending the Topological Analysis and Seeking the Real-Space Subsystems in Non-Coulombic Systems with Homogeneous Potential Energy Functions

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