A simple measure of electron localization in atomic and molecular systems

Becke, Axel D.; Edgecombe, Kenneth E.

doi:10.1063/1.458517

Cited by 6,107 publications

(4,461 citation statements)

References 22 publications

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“…The geometry optimizations for the atomic site occupancy in the cell were performed on the experimental lattice parameters using the Broyden-Fletcher-Goldfarb-Shanno minimization scheme 53 . The ELF 43 , as an indicator of the electron-pair distribution in terms of inter-atomic bonding, is introduced to represent the conditional probability of finding a second like-spin electron near the reference position. It is a local, relative measure of the Pauli repulsion effect on the kinetic energy density.…”

Section: Magnetic Measurementsmentioning

confidence: 99%

Stable magnetostructural coupling with tunable magnetoresponsive effects in hexagonal ferromagnets

et al. 2012

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The magnetostructural coupling between the structural and the magnetic transition has a crucial role in magnetoresponsive effects in a martensitic-transition system. A combination of various magnetoresponsive effects based on this coupling may facilitate the multifunctional applications of a host material. Here we demonstrate the feasibility of obtaining a stable magnetostructural coupling over a broad temperature window from 350 to 70 K, in combination with tunable magnetoresponsive effects, in mnniGe:Fe alloys. The alloy exhibits a magneticfield-induced martensitic transition from paramagnetic austenite to ferromagnetic martensite. The results indicate that stable magnetostructural coupling is accessible in hexagonal phasetransition systems to attain the magnetoresponsive effects with broad tunability.

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Section: Magnetic Measurementsmentioning

confidence: 99%

Stable magnetostructural coupling with tunable magnetoresponsive effects in hexagonal ferromagnets

et al. 2012

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“…[17][18][19] These positions can be found more exactly by a suitable analysis of the electron density such as that provided by the electron localization function (ELF). [28][29][30] This function exhibits maxima at the most probable positions of localized electron pairs and each maximum is surrounded by a basin in which there is an increased probability of finding an electron pair. These basins correspond to the qualitative electron pair domains of the VSEPR model and have the same geometry as the VSEPR domains.…”

Section: The Classical Electron Pair and The Electron Pair Todaymentioning

confidence: 99%

Gilbert N. Lewis and the chemical bond: The electron pair and the octet rule from 1916 to the present day

Gillespie

Robinson

2006

J Comput Chem

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We describe the development of Lewis's ideas concerning the chemical bond and in particular the concept of the electron pair bond and the octet rule. We show that the concept of the electron pair bond has endured to the present day and is now understood to be a consequence of the Pauli principle. In contrast the octet rule is now regarded as much less important than was originally generally believed, although Lewis himself knew several exceptions and regarded it as less important than what he called the rule of two (the electron pair). The octet rule was more strongly promoted by Langmuir who is also responsible for the term covalent bond. However, many more exceptions to the octet rules than were known to Lewis are now known and the terms hypervalent and hypovalent used to describe such molecules are no longer particularly useful. Today it is realized that bonding electron pairs in many molecules are not as well localized as Lewis believed, nevertheless resonance structures, i.e., plausible alternative Lewis structures, are still often used to describe such molecules. Moreover electrons are not always found in pairs, as for example in linear molecules, which can, however, be satisfactorily described by Linnett's double quartet theory. The electron density distribution in a molecule can now be analyzed using the ELF and other functions of the electron density to show where electron pairs are most probably to be found in a molecule.

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“…In many cases, the space is divided using the topology induced by the gradient field of an orbital invariant scalar, like the electron density (which gives rise to the atomic partioning of the quantum theory of atoms in molecules (QTAIM) developed by Bader and coworkers, 10 , or the electron localization function (that isolates core, bond and lone pair regions). 11,12 When this topological tools are used we say that we are under the Quantum Chemical Topology umbrella. 13 In the context of the QTAIM/QCT, we proposed a number of years ago an exact, general decomposition of the total molecular energy E into atomic and inter-atomic terms that we called the interacting quantum atoms (IQA) approach.…”

Section: Introductionmentioning

confidence: 99%

A multipolar approach to the interatomic covalent interaction energy

et al. 2017

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Interatomic exchange-correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp) expansion is customary used in biomolecular modelling to approximate the classical Coulomb interaction between two charge densities ρ A (r) and ρ B (r), we examine in this work the mp approach to approximate the interatomic exchange-correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1−2 pairs) albeit it works reasonably well most times for 1−n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to l 1 + l 2 = 2 usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole-monopole xc mp term and the inter-atomic bond order, as measured by the delocalization index of the Quantum Theory of Atoms in Molecules, is also established. Interatomic or interfragment covalent energies in real space, as measured by the interacting quantum atoms (IQA) exchange-correlation energies (V AB xc ) are shown to be well-approximated by a multipolar approximation if terms up to the chargequadrupole interaction are retained (cdq). The cdq approximation improves considerably the performance of the zeroth-order approximation, in which V xc is equal to the bond order (delocalization index, δ AB ) over the interatomic distance.2

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A simple measure of electron localization in atomic and molecular systems

Cited by 6,107 publications

References 22 publications

Stable magnetostructural coupling with tunable magnetoresponsive effects in hexagonal ferromagnets

Stable magnetostructural coupling with tunable magnetoresponsive effects in hexagonal ferromagnets

Gilbert N. Lewis and the chemical bond: The electron pair and the octet rule from 1916 to the present day

A multipolar approach to the interatomic covalent interaction energy

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