Finite‐Size Scaling for Atomic and Molecular Systems

Kais, Sabre; Serra, Pablo

doi:10.1002/0471428027.ch1

Cited by 57 publications

(80 citation statements)

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“…This notion is consistent with the finite-size-scaling philosophy of bonding and dissociation due to Kais, Herschbach, and others. 35,36 Here we observe that changes in bond order are associated with transitions in the strength, but also symmetry of the charge density wave. Discrete changes in bond order come about naturally in venerable theories of bonding, such as the molecular orbital theory or the early ideas of G. N. Lewis.…”

Section: Discussionmentioning

confidence: 69%

The chemical bond as an emergent phenomenon

Golden

Lubchenko

2017

The Journal of Chemical Physics

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We first argue that the covalent bond and the various closed-shell interactions can be thought of as symmetry broken versions of one and the same interaction, viz., the multi-center bond. We use specially chosen molecular units to show that the symmetry breaking is controlled by density and electronegativity variation. We show that the bond order changes with bond deformation but in a step-like fashion, regions of near constancy separated by electronic localization transitions. These will often cause displacive transitions as well so that the bond strength, order, and length are established self-consistently. We further argue on the inherent relation of the covalent, closed-shell, and multi-center interactions with ionic and metallic bonding. All of these interactions can be viewed as distinct sectors on a phase diagram with density and electronegativity variation as control variables; the ionic and covalent/secondary sectors are associated with on-site and bond-order charge density wave respectively, the metallic sector with an electronic fluid. While displaying a contiguity at low densities, the metallic and ionic interactions represent distinct phases separated by discontinuous transitions at sufficiently high densities. Multi-center interactions emerge as a hybrid of the metallic and ionic bond that results from spatial coexistence of delocalized and localized electrons. In the present description, the issue of the stability of a compound is that of mutual miscibility of electronic fluids with distinct degrees of electron localization, supra-atomic ordering in complex inorganic compounds comes about naturally. The notions of electronic localization advanced hereby suggest a high throughput, automated procedure for screening candidate compounds and structures with regard to stability, without the need for computationally costly geometric optimization. I. MOTIVATIONChemical bonding is traditionally discussed in terms of the covalent, ionic, and metallic bond 1 , and weaker, closed-shell interactions such as secondary, donoracceptor, hydrogen, and van der Waals.2,3 The distinction between these canonical bond types is not always clear-cut. For instance, a directional, multi-center 4 bond holding together identical atoms has an inherent ionic feature: In a three-center, linear ppσ bond, 5,6 the central atom contributes only a half orbital to each of the individual ppσ bonds.7 The terminal atoms, on the other hand, each contribute one full orbital, implying a non-uniform charge distribution over the bond. At the same time, the three-center ppσ bond can be thought of as a limiting case of the metallic bond, since the appropriate electron count for an infinite chain corresponds to a half-filled band.4 This identification is consistent with the metallic luster of compounds in which covalent and secondary bonds are comparable in length.3 . In solid-state contexts, interplay between ionic and covalent interactions is often discussed using the van Arkel-Ketelaar triangle for binary compounds;8-11 or revealed, for insta...

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Section: Discussionmentioning

confidence: 69%

The chemical bond as an emergent phenomenon

Golden

Lubchenko

2017

The Journal of Chemical Physics

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“…The method has a potential applicability in predicting stable and metastable atomic and molecular states. For future studies, we will investigate the bound and resonance state energies for two-electron systems (He-like atoms) and will be compared with the available experimental and theoretical data, for example, the finite-size scaling method [16,17]. It is also valuable to extend the present work to the cases of the two-dimensional problems [18].…”

Section: Resultsmentioning

confidence: 99%

Scaling behaviour of the Hellmann potential with different strength parameters

2014

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We are reporting the scaling behaviour of the bound state energies associated with the Hellmann potential, with different strength parameters, using the Laguerre basis. We show the existence of a crossover phenomenon for the energy spectrum; the scaling laws for bound states as we approach the continuum are calculated. Close to the bound-resonance phase transition region, state energies and wavefunctions for the Hellmann potential, with different strength parameters, have been studied.

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“…Using statistical mechanics terminology, we can associate "first order phase transitions" with the existence of a normalizable eigenfunction at the critical point. The absence of such a function could be related to "continuous phase transitions" [30].…”

Section: Finite Size Scaling For the Schrödinger Equationmentioning

confidence: 99%

Finite Size Scaling for Criticality of the Schrödinger Equation

Kais

2011

Solving the Schrödinger Equation

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By solving the Schrödinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a transition from bound to continuum states. The behavior of systems near the threshold, which separates bound-states from continuum states, is important in the study of such phenomenon as: ionization of atoms and molecules, molecule dissociation, scattering collisions and stability of matter. In general, the energy is non-analytic as a function of the Hamiltonian parameters or a bound-state does not exist at the threshold energy. The overall goal of this chapter is to show how one can predict, generate and identify new class of stable quantum systems using large-dimensional models and the finite size scaling approach. Within this approach, the finite size corresponds not to the spatial dimension but to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. This method is efficient and very accurate for estimating the critical parameters, {λi}, for stability of a given Hamiltonian, H(λi). We present two methods of obtaining critical parameters using finite size scaling for a given quantum Hamiltonian: The finite element method and the basis set expansion method. The long term goal of developing finite size scaling is treating criticality from first principles at quantum phase transitions. In the last decade considerable attention has concentrated on a new class of phase transitions, transitions which occur at the absolute zero of temperature. These are quantum phase transitions which are driven by quantum fluctuations as a consequence of Heisenberg's uncertainty principle. These new transitions are tuned by parameters in the Hamiltonian. Finite size scaling might be useful in predicting the quantum critical parameters for systems going through quantum phase transitions. a kais@purdue.edu arXiv:1009.4393v1 [quant-ph]

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Finite‐Size Scaling for Atomic and Molecular Systems

Cited by 57 publications

References 0 publications

The chemical bond as an emergent phenomenon

The chemical bond as an emergent phenomenon

Scaling behaviour of the Hellmann potential with different strength parameters

Finite Size Scaling for Criticality of the Schrödinger Equation

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