Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

Ou, Jen-Hao; Ho, Yew Kam

doi:10.3390/atoms5020015

Cited by 26 publications

(26 citation statements)

References 46 publications

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“…In confined two-electron isoelectronic series (H − , He, Li + , Be 2+ ), S has been reported for only ground states [64] by means of BLYP calculations. Some reports [52,[68][69][70][71][72][73] are available on S in penetrable confinement in atoms. For example, it was observed [68] that, in CHA, up to a certain value of r c , S r decreases with r c .…”

Section: Introductionmentioning

confidence: 99%

“…It was also proposed [72] as an indicator to measure the delocalization of electron density. Ground-state atomic S's, as a function of the width of confining potential, was calculated by employing the correlated Hylleraas-type wave function in both repulsive and attractive finite potentials [70]. Confinement by an inert geometric planar boundary with finite barrier height has been studied [69] within a Thomas-Fermi-Dirac-Weizsäcker-type DFT framework.…”

Section: Introductionmentioning

confidence: 99%

“…Some limited works exist on excited states as well, viz. low-lying singly [70] and doubly [71] excited states. It is worth noting that S values in He are available [74] in selected excited states, such as 1,3 S e , 1,3 P o and 1,3 D e .…”

Section: Introductionmentioning

confidence: 99%

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Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Majumdar

Roy

2020

Quantum Reports

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Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius r c . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) 3S, 1snp (n = 2–3) 3P, 1s3d 3D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to r c in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower r c regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Majumdar

Roy

2020

Quantum Reports

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“…The key to accuracy of our result is the explicit treatment of electron correlation via highly correlated Hylleraas wave functions. Previously, we successfully used Shannon entropy to quantify electron delocalization in a quantum dot modeled by He under a finite confinement potential . In addition, Ho and his coworkers have reported accurate entanglement entropies such as linear entropy and von Neumann entropy for ground and excited states of helium‐like systems and for plasma‐embedded helium .…”

Section: Introductionmentioning

confidence: 99%

Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

2019

Int J of Quantum Chemistry

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Accurate values of physical quantities serve as the stepping stone for further researches. Consequently, we provide benchmark values of Shannon, Rényi, Tsallis entropies, and Onicescu information energy for ground state helium. With the highly correlated Hylleraas wave functions, our calculations fully considered the effect of electron correlation. Presented numerical results converge with increasing size of basis set, fulfill analytic relations between the quantities, and satisfactorily agree with those in the literature. In particular, we present these information‐theoretic quantities with high accuracy, and it is believed that the reported data would be a valuable reference for further research on information‐theoretic quantities of atomic and molecular systems.

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“…Originated from the information theory and later extended to the position space, the information-theoretic (IT) quantities provide a possible quantitative account of the extent of electron localization. For instance, the more delocalized is the electron distribution, the larger is the Shannon entropy (S) [3][4][5][6][7][8][9][10][11][12][13][14]. Moreover, Rényi entropy of order α (R α ) [15][16][17] and Tsallis entropy of order α (T α ) [18][19][20][21] are the one-parameter generalizations of Shannon entropy and offer extended descriptions.…”

Section: Introductionmentioning

confidence: 99%

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

2019

Atoms

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Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α .

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Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

Cited by 26 publications

References 46 publications

Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism

Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

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