Incorporating nuclear vibrational energies into the “atom in molecules” analysis: An analytical study

Gharabaghi, Masumeh; Shahbazian, Shant

doi:10.1063/1.4979994

Cited by 10 publications

(14 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to consider the positronic bond we employ the recently developed multi-component quantum theory of atoms in molecules (MC-QTAIM), [52][53][54][55][56][57][58][59] which is an extended version of the QTAIM proposed originally by Bader and coworkers. [60] The MC-QTAIM is the only available chemical theory specially designed to deal with the bonding analysis of the exotic species.…”

Section: Resultsmentioning

confidence: 99%

On the Nature of the Positronic Bond

Goli

Shahbazian

2019

ChemPhysChem

Self Cite

View full text Add to dashboard Cite

Recently it has been proposed that the positron, the anti‐particle analog of the electron, is capable of forming an anti‐matter bond in a composite system consists of two hydride anions and a positron [Angew. Chem. Int. Ed. 57, 8859–8864 (2018)]. In order to dig into the nature of this novel bond the newly developed multi‐component quantum theory of atoms in molecules (MC‐QTAIM) is applied to this positronic system. The topological analysis reveals that this species is composed of two atoms in molecules, each containing a proton and half of the electronic and the positronic populations. Further analysis elucidates that the electron exchange phenomenon is virtually non‐existent between the two atoms and no electronic covalent bond is conceivable in between. On the other hand, it is demonstrated that the positron density enclosed in each atom is capable of stabilizing interactions with the electron density of the neighboring atom. This electrostatic interaction suffices to make the whole system bonded against all dissociation channels. Thus, the positron indeed acts like an anti‐matter glue between the two atoms.

show abstract

Section: Resultsmentioning

confidence: 99%

On the Nature of the Positronic Bond

Goli

Shahbazian

2019

ChemPhysChem

Self Cite

View full text Add to dashboard Cite

show abstract

“…Accurate TC-DFT(ee+eµ) results also offer the opportunity to deduce reliable chemical indices, based on the multicomponent quantum theory of atoms in molecules, [141][142][143][144][145][146][147][148] through analyzing the multi-component KS wavefunctions, which may provide new insights into detailed bonding modes and interatomic interactions in complex muonic systems as demonstrated previously. [114][115][116][117] This line of research also will be considered in detail in a future computational study.…”

Section: Discussionmentioning

confidence: 95%

Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional

Goli,

Shahbazian

2021

Preprint

Self Cite

View full text Add to dashboard Cite

It is well-known experimentally that the positively-charged muon and the muonium atom may bind to molecules and solids, and through muon's magnetic interaction with unpaired electrons, valuable information on the local environment surrounding the muon is deduced. Theoretical understanding of the structure and properties of resulting muonic species requires accurate and efficient quantum mechanical computational methodologies. In this paper the two-component density functional theory, TC-DFT, as a first principles method, which treats electrons and the positive muon on an equal footing as quantum particles, are introduced and implemented computationally. The main ingredient of this theory, apart from the electronic exchange-correlation functional, is the electron-muon correlation functional which is foreign to the purely electronic DFT. A Wigner-type local electron-muon correlation functional, termed eµc-1, is proposed in this paper and its capability is demonstrated through its computational application to a benchmark set of organic muonic molecules. The TC-DFT equations containing eµc-1 are not only capable of predicting the muon's binding site correctly but they also reproduce muon's zero-point vibrational energies and the muonic densities much more accurately than the TC-DFT equations lacking eµc-1. Thus, this study set the stage for developing accurate electron-muon functionals, which can be used within the context of the TC-DFT to elucidate the intricate interaction of the positive muon with complex molecular systems.

show abstract

“…There have been some attempts to extend the analysis beyond equilibrium geometries when the HF forces are not null and these have been summarized by Keith (see chapter 3 in ). But, none of the proposed schemes is satisfying as stressed by the author himself (a possible tentative route to solve this problem have been proposed by present author recently that needs to be worked out in detail). Throughout present analysis, we will restrict our analysis only to the equilibrium geometries and do not try to consider the more involved problem of generalizing the analysis to nonequilibrium geometries.…”

Section: Open Problems and Corresponding Backgroundmentioning

confidence: 92%

“…The case of

n = - 2

at first glance may seem problematic but it is well known that in the case of attractive interactions, corresponding total system does not have well‐behaved bound states (see subsection 35 in ). The energy of a real‐space quantum subsystem is now easily derivable from the integration of the energy density within the atomic basin,

E_{normalΩ} = \int_{normalΩ} d \overset{q}{true} E true(\overset{r}{true} true)

, and the net zero‐flux equation is assumed to be satisfied for any real‐space subsystem, then:

E_{normalΩ} = true(1 + 2 / n true) K_{normalΩ} = - true(1 / 2 + 1 / n true) true{V_{normalΩ}^{B} + V_{normalΩ}^{S} true}

(for applications of the formalism to non‐coulombic systems see ). Finally, topological atom's energy in the coulombic systems is recovered as a special case:

E_{normalΩ} = - K_{normalΩ} = true(1 / 2 true) true{V_{normalΩ}^{B} + V_{normalΩ}^{S} true}

.…”

Section: Open Problems and Corresponding Backgroundmentioning

confidence: 99%

“…Starting from a decade ago, inspired by these exchanges, the present author and his coworkers reconsidered the mathematical foundations of the QTAIM in detail trying to resolve some issues put forward by critics of the QTAIM formalism . Interestingly, as a byproduct, this reconsideration eventually gave rise to an extended version of the QTAIM, finally termed the multi‐component QTAIM, which widens the applications of the AIM analysis beyond the Born‐Oppenheimer paradigm as well as exotic molecular species …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Shahbazian

2018

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

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

show abstract

Incorporating nuclear vibrational energies into the “atom in molecules” analysis: An analytical study

Cited by 10 publications

References 74 publications

On the Nature of the Positronic Bond

On the Nature of the Positronic Bond

Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional

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

Contact Info

Product

Resources

About