The Rényi entropy, a comparative study for He-like atoms using the exponential-cosine screened Coulomb potential

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.

Section: Theoretical Methodsmentioning

confidence: 99%

“…Shannon entropy for two‐electron density, S [ ρ 2 ], and for one‐normalized two‐electron density, S [ σ 2 ( r 1 , r 2 )], are defined by

S ([], ρ_{2} ((),, {boldr}_{1}, {boldr}_{2})) \equiv - \int ρ_{2} ((),, {boldr}_{1}, {boldr}_{2}) \ln ρ_{2} ((),, {boldr}_{1}, {boldr}_{2}) d r_{1} d r_{2},

S ([], σ_{2} ((),, {boldr}_{1}, {boldr}_{2})) \equiv - \int σ_{2} ((),, {boldr}_{1}, {boldr}_{2}) \ln σ_{2} ((),, {boldr}_{1}, {boldr}_{2}) d r_{1} d r_{2},

respectively, and are connected by the relation

S ([], σ_{2} ((),, {boldr}_{1}, {boldr}_{2})) = S ([], ρ_{2} ((),, {boldr}_{1}, {boldr}_{2})) \frac{2}{N ((), N - 1)} + \ln \frac{N ((), N - 1)}{2} .

…”

Section: Theoretical Methodsmentioning

confidence: 99%

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

2019

“…In recent years, there has been an increasing interest in the information‐theoretical analysis of interelectronic correlation in atomic systems. Different works have been performed within this field, nevertheless, all of them deal with two‐electron systems, usually restricted to the analysis in terms of entropic functionals in position space.…”

Section: Resultsmentioning

confidence: 99%

“…Preceding studies on this subject are relatively recent, as a consequence of dealing with a subject considered some years ago, but not efficiently developed until very recently. In fact, all those publications only deal with two‐electron systems, usually restricted to the analysis in terms of entropic functionals in position space.…”

Section: Introductionmentioning

confidence: 99%

“…More recent studies afford: (1) the analysis of the four helium‐like systems H ‐ , He, Li + , and Ps − (positronium negative ion), attending to the dependence of the position‐space Shannon entropy on the continuous variable Z (nuclear charge), particularly around the critical value for which the system becomes unstable, and posing as future work determining the momentum space entropy and checking the uncertainty relation for the total entropy S r + S p ≥ 3(1 + ln π ); (2) the analysis of three Rydberg series of He doubly excited states, by means of Shannon entropy and Fisher information (for the reduced one‐particle spatial density) and von Neumann and linear entropies (as measures of entanglement, from the reduced one‐particle density matrix); and (3) a comparative study of the atomic Rényi entropies for the exponential‐cosine screened Coulomb potential, by using different wave functions for the 1s 2 ‐state of the helium isoelectronic series.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electron‐pair entropic and complexity measures in atomic systems

López-Rosa

Martín

Antolín

et al. 2018

The two-electron atomic densities are analyzed in both position and momentum spaces in terms of different information-theoretic measures, such as disequilibrium, Shannon entropy, shape complexity, and its corresponding information plane. This study is conveyed throughout the Periodic Table and the obtained results are discussed in terms of varied atomic properties such as (1) atomic charge, (2) shell filling patterns, and (3) electronic correlation. A detailed discussion on how these properties modify in a particular manner the electron density structure when considering a one-electron or a two-electron density description is conducted.

Calculation of information entropies for the 1s² state of helium‐like ions

Nasser

Zeama

Abdel-Hady

2020

Self Cite

This work presents analytical and numerical results for the position‐ and momentum‐space information entropies of the 1s2 state of helium‐like ions using different interaction potentials. The potentials that we used are the Yukawa potential and the exponential‐cosine‐screened Coulomb potential. The investigated studies allow us to relate the position‐space information with the momentum‐space information of Shannon and Fisher, as well as Shannon entropy power and the Fisher‐Shannon information product, through different famous relations. The calculation is performed using the one‐electron charge density of entangled two‐parameter wavefunction. On one hand, the results that are presented for 10 members in the helium isoelectronic sequence demonstrate with precision the effect of correlation on bare charge distributions. On the other hand, it leads to some very important results for both the correlated and uncorrelated values of the informatic entropies. Analytical formulas for the momentum‐space information entropies are given. The effect of the nuclear charge and the screening parameter on the information expressions has been studied for both potentials. Detailed computational and numerical values and characteristics of these information quantities, as a function of the screening parameter, are reported here for the first time. New inequality has been proposed with Fisher's total value to measure the correlation of two electrons.