Coulomb correlation and information entropies in confined helium-like atoms

Nascimento, Wallas S.; Almeida, Marcos de; Prudente, Frederico V.

doi:10.1140/epjd/s10053-021-00177-6

Cited by 10 publications

(7 citation statements)

References 82 publications

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“…For the confined helium atom, different expressions [19,35,86] have been used to evaluate the integrals involved in the energy functional;…”

Section: Energy Calculationsmentioning

confidence: 99%

“…Gimarc [20] used the same method but employing 5 different trial wave functions, one of which produced results similar to the HF calculations, and two of them explicitly included electronic correlation. Subsequent to Gimarc, different methods have been developed, for example, Hartree-Fock [21], Roothaan-Hartree-Fock [22], Configuration Interaction [23], time independent perturbation theory [24], linear and non-linear variational method [24][25][26][27][28][29][30][31][32][33][34][35], Lagrange mesh method [36], B-splines [37], variational quantum Monte Carlo [38,39] and density functional theory [40][41][42]. Most of these studies have been devoted to the total energy calculations, correlation energy due to the radial and angular contribution of trial wave functions [31,32], polarizability, critical cage radius and so forth, as a function of the confining radius.…”

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confidence: 99%

“…Information theory has been used in the study of one-, two-, and three-dimensional (1D, 2D and 3D) systems [64][65][66][67][68][69][70], in free systems and in systems subject to spatial confinement. As examples, we mention the study of free and spatially confined hydrogen and helium atoms [35,41,[71][72][73][74][75][76].…”

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confidence: 99%

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The confined helium atom: An information–theoretic approach

Estañón,

Montgomery,

Angulo

et al. 2024

Int J of Quantum Chemistry

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In this article, we study the helium atom confined in a spherical impenetrable cavity by using informational measures. We use the Ritz variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius . As trial wave functions we use one uncorrelated function and five explicitly correlated basis sets in Hylleraas coordinates with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback–Leibler entropy, Tsallis entropy, disequilibrium and Fisher–Shannon complexity, as a function of . We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. As expected these entropic measures are less sensitive to electron correlation in the strong confinement regime ( a.u.).

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“…For the confined helium atom, different expressions [19,35,86] have been used to evaluate the integrals involved in the energy functional;…”

Section: Energy Calculationsmentioning

confidence: 99%

mentioning

confidence: 99%

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The confined helium atom: An information–theoretic approach

Estañón,

Montgomery,

Angulo

et al. 2024

Int J of Quantum Chemistry

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“…We have mentioned one example where the electronic structure of atoms is altered by hard confinement. Several examples of these systems exist [11][12][13][14][15]. Confinement imposed by soft walls is another important model potential for studying the electronic structure of confined atoms and molecules, although this confinement is not considered in this article [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Electron density analysis of two-electron systems confined by prolate spheroids with hard walls

Yanajara-Parra,

Corella-Madueño,

Adrián Duarte-Alcaraz

et al. 2024

J. Phys. Commun.

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The electron density of two-electron systems, He and H2, was analyzed when prolate spheroids with hard walls confine these systems. For this purpose, Hartree-Fock equations were solved using Roothaan's approach with a basis set defined in prolate spheroidal coordinates imposing Dirichlet boundary conditions. Total energy, its components, and orbital energies were analyzed for several confinements, and some of these results were compared with those reported by other authors to test the performance of the proposed approach. For both systems, the electron density exhibits a maximum value out of the nuclear region for extreme confinements. The chemical bond for H2 was analyzed through the concepts of the quantum theory of atoms in molecules, concluding that the chemical bond of this molecule disappears under extreme conditions. For this system, estimations of the correlation energy indicate that this is a small contribution to the total energy, and the Hartree-Fock method contains the necessary elements to describe the chemical bond for strong confinements.

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“…[32][33][34][35][36][37][38][39][40][41][42] For example, the 1D harmonic oscillator limited by impenetrable walls is called a 1D confined harmonic oscillator (CHO). [43,44] As has been shown in many studies, quantum confinement changes the system's wave functions, energies, and other parameters, [45][46][47][48][49][50][51][52][53] which may result in a modified correlation.…”

Section: Introductionmentioning

confidence: 99%

Control of Correlation Using Confinement in Case of Quantum System

Kumar,

Prasad

2023

Annalen der Physik

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This article investigates the behavior of a Moshinsky atom in a 1D harmonic trap. Focus is given on the theoretical foundations of confinement and its impact on the correlation between particles in the Moshinsky atom. The investigation begins by illustrating the (de)localization of the probability density function using Shannon entropy. The basics of correlation and interpretation of correlation using tools such as mutual information and statistical correlation coefficients and how these can be quantified are discussed. Then the concept of confinement is explored. The impact of interaction strength and confinement on Shannon entropy, statistical correlation coefficients, and mutual information is investigated. How interaction strength and confinement can be used to induce correlations between previously uncorrelated particles, as well as how they can be used to suppress correlations between previously correlated particles is discussed. Their implications for quantum information processing and quantum simulation are discussed. In conclusion, confinement is a powerful tool for controlling correlations in quantum systems, and its impact on correlation can be understood through theoretical models. The importance of experimental studies in this field, which provide insights into the behavior of quantum systems under confinement and pave the way for future applications in quantum technology is also emphasized.

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Coulomb correlation and information entropies in confined helium-like atoms

Cited by 10 publications

References 82 publications

The confined helium atom: An information–theoretic approach

The confined helium atom: An information–theoretic approach

Electron density analysis of two-electron systems confined by prolate spheroids with hard walls

Control of Correlation Using Confinement in Case of Quantum System

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