Force field and potential due to the Fermi-Coulomb hole charge for nonspherical-density atoms

Slamet, Marlina; Sahni, Viraht; Harbola, Manoj K.

doi:10.1103/physreva.49.809

Cited by 27 publications

(10 citation statements)

References 26 publications

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“…The local one-electron potential (7) can be considered as the path-independent work done in moving an electron belonging to a system from infinity to the reference point r against the electric field created by the total charge and the Fermi-Coulomb hole charge and a correlation-kinetic field. That means we follow a simple electrostatic interpretation of effective potential given by Slamet et al (1994), Liu et al (1999) and Sen et al (2002). It allows us to avoid the functional derivation and to facilitate a computation of the inner-molecule/crystal forces.…”

Section: Methodsmentioning

confidence: 99%

Orbital-free quantum crystallography: view on forces in crystals

Tsirelson

Stash

2020

Acta Crystallogr B Struct Sci Cryst Eng Mater

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Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic F kin( r ) and potential forces F ( r ). The critical points of both potentials are analyzed and they are recognized as the points at which forces F kin( r ) and F ( r ) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F ( r ) force pushes electrons to the atomic nuclei, while the kinetic force F kin( r ) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential v kin( r ) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

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Section: Methodsmentioning

confidence: 99%

Orbital-free quantum crystallography: view on forces in crystals

Tsirelson

Stash

2020

Acta Crystallogr B Struct Sci Cryst Eng Mater

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“…Here 𝜇(𝒓) is the chemical potential, i.e., the path-independent work that needs to be done for moving any electron belonging to a system from infinity to a reference point against the kinetic force field and the static Coulomb force field corrected for exchange. 22,[32][33][34] Functional 𝐸 𝑘 [𝜌] describes the noninteracting kinetic energy of electrons. In one-determinant approximation, the latter can be presented as the sum of Pauli 𝐸 𝑃 [𝜌] and von Weizsäcker 𝐸 𝑊 [𝜌] kinetic energy functionals.…”

Section: 𝜇[𝜌(𝒓)] = 𝛿𝐸 𝑘 [𝜌(𝒓)] 𝛿𝜌(𝒓) + 𝜑 𝑒𝑚 (𝒓)mentioning

confidence: 99%

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Shteingolts

Stash

Tsirelson

et al. 2022

Preprint

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Intricate behavior of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Bosonic and fermionic quantum potentials were utilized in bonding analysis as descriptors of the localization of electrons and electron pairs. Channels of locally enhanced kinetic potential and the corresponding saddle Lagrange points were found between chemically bonded atoms linked by the bond paths. Superposition of electrostatic φ_es (r) and kinetic φ_k (r) potentials and electron density ρ(r) allowed partitioning any molecules and crystals into atomic ρ- and potential-based φ-basins; the φ_k-basins explicitly account for electron exchange effect, which is missed for φ_es-ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between ρ- and φ-zero-flux surfaces. The gap between φ_es- and ρ-basins represents the charge transfer, while the gap between φ_k- and ρ-basins is proposed to be a real-space manifestation of sharing the transferred electrons. The position of φ_k-boundary between φ_es- and ρ-ones within an electron occupier atom determines the extent of electron sharing. The stronger an H‧‧‧O hydrogen bond is, the deeper hydrogen atom’s φ_k-basin penetrates oxygen atom’s ρ-basin. For covalent bonds, a φ_k-boundary closely approaches a φ_es-one indicating almost complete sharing the transferred electrons, while for ionic bonds, the same region corresponds to electron pairing within the ρ-basin of an electron occupier atom.

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“…For spherically symmetric densities, as used in atomic sphere approximation (ASA) in LMTO-ASA, this E is curl free. For nonspherical charge densities, the solenoidal part of E is related to the difference in kinetic energies between the HF and the HS approaches [88] and the contribution is numerically insignificant [89]. The HS potential can directly be derived from Schrödinger equation [90].…”

Section: Orbital Based Exchange Correlationmentioning

confidence: 99%

Semiconductor Physics: A Density Functional Journey

Datta¹,

Jana²

2020

Preprint

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The journey of theoretical study of semiconductors is reviewed in nonconventional way. We have started with the basic introduction of Hartree-Fock method and introduce the fundamentals of Density Functional Theory (DFT). From the oldest Local density approximations (LDA) to the most recent developments of semi-local corrections [Generalised Gradient Approximation (GGA), Meta-GGAs], Hybrid functionals and Orbital dependent methodologies are discussed in detail. During this discussion, we have defined the relevant and widely used terms in methodological and applicational DFT. To showcase the performance of DFT, results obtained via different approximations are compared. We indicate the success of semilocal approximations in structural properties prediction. We also show how less computationally costly but withstand architecture of some semi-local DFT methods can solve the long riddle of bandgap underestimation. In semiconductor physics, the importance of not only the band structure prediction, but also proper calculation of Fermi energy and exact finding of band alignment is argued. This provides the guideline for the proper choice of methods for investigation of structural, electronic and optical properties. The comparison of Fermi energy dependent properties can channelize the theoretical studies on modern age environment-friendly researches on semiconductors, like artificial photocatalysis, energy efficient opto-electronic devices, etc. This prescription on proper choice of DFT method is potential competent to complement the experimental findings as well as can open up a pathway of advanced semiconducting material discoveries.

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Force field and potential due to the Fermi-Coulomb hole charge for nonspherical-density atoms

Cited by 27 publications

References 26 publications

Orbital-free quantum crystallography: view on forces in crystals

Orbital-free quantum crystallography: view on forces in crystals

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Semiconductor Physics: A Density Functional Journey

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