1
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Kumar K, Prasad V. Few generalized entropic relations related to Rydberg atoms. Sci Rep 2022; 12:7496. [PMID: 35523799 PMCID: PMC9076694 DOI: 10.1038/s41598-022-10854-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2021] [Accepted: 04/12/2022] [Indexed: 11/08/2022] Open
Abstract
We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, [Formula: see text], [Formula: see text], and [Formula: see text], respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom's wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms.
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Affiliation(s)
- Kirtee Kumar
- Department of Physics and Astrophysics, University of Delhi, Delhi, 110007, India
- Department of Physics, Motilal Nehru College, University of Delhi, Delhi, 110021, India
| | - Vinod Prasad
- Department of Physics, Swami Shraddhanand College, University of Delhi, Delhi, 110036, India.
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2
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Wan JJ, Gu J, Li J, Guo N. Shannon Entropy in LS-Coupled Configuration Space for Ni-like Isoelectronic Sequence. ENTROPY 2022; 24:e24020267. [PMID: 35205561 PMCID: PMC8870868 DOI: 10.3390/e24020267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Revised: 02/01/2022] [Accepted: 02/03/2022] [Indexed: 12/04/2022]
Abstract
The Shannon entropy in an LS-coupled configuration space has been calculated through a transformation from that in a jj-coupled configuration space for a Ni-like isoelectronic sequence. The sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction have been presented for adjacent levels. It is shown that eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, and both of them are a sufficient condition for information exchange, which is the same as the case of the jj-coupled configuration space. It is found that the structure of sudden change from jj-coupled into LS-coupled configuration spaces through the LS-jj transformation is invariant for Shannon entropy along the isoelectronic sequence. What is more, in an LS-coupled configuration space, there are a large number of information exchanges between energy levels whether with or without strong configuration interaction, and most of the ground and single excited states of Ni-like ions are more suitable to be described by a jj-coupled or other configuration basis set instead of an LS-coupled configuration basis set according to the configuration mixing coefficients and their Shannon entropy. In this sense, Shannon entropy can also be used to measure the applicability of a configuration basis set or the purity of atomic state functions in different coupling schemes.
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3
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Martínez-Sánchez MA, Martínez-Flores C, Vargas R, Garza J, Cabrera-Trujillo R, Sen KD. Ionization of many-electron atoms by the action of two plasma models. Phys Rev E 2021; 103:043202. [PMID: 34005965 DOI: 10.1103/physreve.103.043202] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2020] [Accepted: 03/22/2021] [Indexed: 11/07/2022]
Abstract
The Hartree-Fock equations for many-electron atoms embedded in a plasma medium are solved using two different plasma models: (a) Debye-Hückel screening (DHS) potential and (b) exponential cosine screened Coulomb (ECSC) potential. Roothaan's approach is implemented for these models after solving the inherent difficulties to evaluate integrals where screening appears explicitly. A corresponding computer code was developed using the method of global basis sets (GBS). The reliability of this approach was verified by solving the Hartree-Fock equations through implementation of the finite-differences and finite-element grid methods and applied to two-electron atoms, yielding excellent agreement with the Roothaan-GBS (RGBS) method. The RGBS method was used to study the energy evolution and ionization threshold of several closed- and open-shell many-electron atoms embedded either in weak or strong DHS or ECSC plasma conditions. In all cases, a critical value of the screening length is obtained for which ionization is achieved, being systematically larger for DHS conditions, indicating the effect of a more repulsive ECSC potential. For He-like atoms in the ground state, we report a comprehensive set of accurate total energy data as a function of the screening constant using the Lagrange mesh method, which includes the electron correlation effects. The electron correlation energy is estimated using this data with reference to the RGBS estimates of energy as the Hartree-Fock energy. The variation of correlation energy as a function of screening constant under the different plasma potentials is rationalized in terms of a conjectured comparison theorem. Finally, a discussion on the effect of plasma strength on localization or delocalization of the electronic density derived from the RGBS method is presented in terms of changes in the Shannon entropy, yielding consistent results for delocalization close to the ionization threshold.
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Affiliation(s)
- Michael-Adán Martínez-Sánchez
- División de Ciencias Básicas e Ingeniería, Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, 09340 Iztapalapa, México City, México
| | - César Martínez-Flores
- División de Ciencias Básicas e Ingeniería, Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, 09340 Iztapalapa, México City, México
| | - Rubicelia Vargas
- División de Ciencias Básicas e Ingeniería, Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, 09340 Iztapalapa, México City, México
| | - Jorge Garza
- División de Ciencias Básicas e Ingeniería, Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, 09340 Iztapalapa, México City, México
| | - Remigio Cabrera-Trujillo
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad S/N, Cuernavaca, Morelos 62210, México
| | - K D Sen
- School of Chemistry, University of Hyderabad, Hyderabad 500 046, India
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4
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Hazra S. A comparative study on information theoretic approach for atomic and molecular systems. COMPUT THEOR CHEM 2020. [DOI: 10.1016/j.comptc.2020.112801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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5
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Rong C, Wang B, Zhao D, Liu S. Information‐theoretic approach in density functional theory and its recent applications to chemical problems. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1461] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Chunying Rong
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China) Hunan Normal University Changsha P.R. China
- Department of Chemistry, College of Chemistry and Chemical Engineering Hunan Normal University Changsha P.R. China
| | - Bin Wang
- Department of Chemistry, College of Chemistry and Chemical Engineering Hunan Normal University Changsha P.R. China
| | - Dongbo Zhao
- Department of Chemistry, School of Chemistry and Chemical Engineering Nanjing University Nanjing P.R. China
| | - Shubin Liu
- Research Computing Centre University of North Carolina Chapel Hill North Carolina
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6
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Shannon Entropy in Configuration Space for Ni-Like Isoelectronic Sequence. ENTROPY 2019; 22:e22010033. [PMID: 33285808 PMCID: PMC7516455 DOI: 10.3390/e22010033] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 12/20/2019] [Accepted: 12/21/2019] [Indexed: 12/03/2022]
Abstract
Discrete Shannon entropy was introduced in view of the mathematical properties of multiconfiguration methods and then used to interpret the information in atomic states expressed by the multiconfiguration Dirac–Hartree–Fock wavefunction for Ni-like isoelectronic sequence. Moreover, the relationship between the concepts, including sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction, was clarified by induction on the basis of the present calculation of the energy structure for Ni-like isoelectronic sequence. It was found that there is an interesting connection between the change of Shannon entropies and eigenlevel anticrossings, along with the nuclear charge Z, which is helpful to conveniently locate the position of eigenlevel anticrossings and information exchanging and understand them from the point of view of information, besides the traditional physical concepts. Especially, it is concluded that in a given configuration space eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, which is also a sufficient condition for information exchange.
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Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium. ATOMS 2019. [DOI: 10.3390/atoms7030070] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
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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Nasser I, Zeama M, Abdel-Hady A. The nonadditive entropy for the ground state of helium-like ions using Hellmann potential. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1612105] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- I. Nasser
- Department of Basic Science, Faculty of Engineering, Egyptian Chinese University, Cairo, Egypt
| | - Mostafa Zeama
- Department of Physics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
| | - Afaf Abdel-Hady
- Department of Basic Science, Faculty of Engineering, Egyptian Chinese University, Cairo, Egypt
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Cammi R. Linear chains of hydrogen molecules under pressure: An extreme-pressure continuum model study. J Chem Phys 2019; 150:164122. [PMID: 31042923 DOI: 10.1063/1.5075511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
New analytical gradients of the electronic energy of a confined molecular system within the extreme-pressure continuum model are presented and applied to the study of the equilibrium geometries of linear chains of hydrogen molecules nH2 under pressures. The decrease in inter- and intramolecular H-H distances with the increase in the pressure has been studied up to 80 GPa. We have also shown that the compression of the bond-lengths can be interpreted in terms of the effect of the confining potential of the electron density of the molecular systems.
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Affiliation(s)
- Roberto Cammi
- Department of Chemistry, Life Science and Environmental Sustainability, University of Parma, I-43100 Parma, Italy
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Cammi R, Chen B, Rahm M. Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme-Pressure Polarizable Continuum Model. J Comput Chem 2018; 39:2243-2250. [PMID: 30242867 DOI: 10.1002/jcc.25544] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Revised: 07/02/2018] [Accepted: 07/04/2018] [Indexed: 11/06/2022]
Abstract
We show that the pressure acting on atoms and molecular systems within the compression cavity of the eXtreme-Pressure Polarizable Continuum method can be expressed in terms of the electron density of the systems and of the Pauli-repulsion confining potential. The analytical expression holds for spherical cavities as well as for cavities constructed from van der Waals spheres of the constituting atoms of the molecular systems. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Roberto Cammi
- Department of Chemical Science, Life Science and Environmental Sustainability, University of Parma, Parma, Italy
| | - Bo Chen
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York
| | - Martin Rahm
- Department of Chemistry and Chemical Engineering, Division of Chemistry and Biochemistry, Chalmers University of Technology, Gothenburg, Sweden
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11
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Wang Y, Shang P. Analysis of Shannon-Fisher information plane in time series based on information entropy. CHAOS (WOODBURY, N.Y.) 2018; 28:103107. [PMID: 30384635 DOI: 10.1063/1.5023031] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2018] [Accepted: 09/26/2018] [Indexed: 06/08/2023]
Abstract
In this paper, we propose a Shannon-Fisher information plane based on the information entropy to analyze financial stock markets. In order to evaluate the effectiveness of this method, we apply this method to two types of artificial time series: Autoregressive Fractionally Integrated Moving Average models and Chebyshev map model. The results show that with the embedding dimension m and the number of possible states of the system M increasing, the normalized Shannon entropy increases, and the Fisher information measure (FIM) decreases. When the parameter M is not so big, the embedding dimension m plays a leading role in determining the FIM. In addition, compared with the classical Shannon-Fisher information through permutation entropy, we conclude that the proposed approach can give us more accurate information on the classification of financial stock markets.
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Affiliation(s)
- Yuanyuan Wang
- Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China
| | - Pengjian Shang
- Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, People's Republic of China
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12
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13
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Ou JH, Ho YK. Shannon information entropy in position space for doubly excited states of helium with finite confinements. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.10.007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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14
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Martínez-Sánchez MA, Aquino N, Vargas R, Garza J. Exact solution for the hydrogen atom confined by a dielectric continuum and the correct basis set to study many-electron atoms under similar confinements. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.10.035] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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15
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Sriraman T, Chakrabarti B, Trombettoni A, Muruganandam P. Characteristic features of the Shannon information entropy of dipolar Bose-Einstein condensates. J Chem Phys 2017; 147:044304. [PMID: 28764376 DOI: 10.1063/1.4994922] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Calculation of the Shannon information entropy (S) and its connection with the order-disorder transition and with inter-particle interaction provide a challenging research area in the field of quantum information. Experimental progress with cold trapped atoms has corroborated this interest. In the present work, S is calculated for the Bose-Einstein condensate (BEC) with dominant dipolar interaction for different dipole strengths, trap aspect ratios, and number of particles (N). Trapped dipolar bosons in an anisotropic trap provide an example of a system where the effective interaction is strongly determined by the trap geometry. The main conclusion of the present calculation is that the anisotropic trap reduces the number of degrees of freedom, resulting in more ordered configurations. Landsberg's order parameter exhibits quick saturation with the increase in scattering length in both prolate and oblate traps. We also define the threshold scattering length which makes the system completely disordered. Unlike non-dipolar BEC in a spherical trap, we do not find a universal linear relation between S and lnN, and we, therefore, introduce a general quintic polynomial fit rather well working for a wide range of particle numbers.
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Affiliation(s)
- Thangarasu Sriraman
- Department of Physics, Bharathidasan University, Tiruchirapalli 620024, India
| | - Barnali Chakrabarti
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - Andrea Trombettoni
- CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy
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16
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Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements. ATOMS 2017. [DOI: 10.3390/atoms5020015] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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17
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Abdelmonem MS, Abdel-Hady A, Nasser I. Scaling behaviour of Fisher and Shannon entropies for the exponential-cosine screened coulomb potential. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1299887] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- M. S. Abdelmonem
- Department of Physics, College of Science and Supporting, University of Hafr AL−Batin, Hafr AL−Batin, Saudi Arabia
| | - Afaf Abdel-Hady
- Department of Basic Science, Faculty of Engineering, Egyptian Chinese University, Cairo, Egypt
| | - I. Nasser
- Physics Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
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18
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Quantum Entanglement and Shannon Information Entropy for the Doubly Excited Resonance State in Positronium Negative Ion. ATOMS 2015. [DOI: 10.3390/atoms3030422] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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19
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Lin CH, Ho YK. Shannon information entropy in position space for two-electron atomic systems. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.05.029] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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21
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Rong C, Lu T, Liu S. Dissecting molecular descriptors into atomic contributions in density functional reactivity theory. J Chem Phys 2014; 140:024109. [DOI: 10.1063/1.4860969] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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22
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Concurrent Phenomena at the Reaction Path of the SN2 Reaction CH3Cl + F−. Information Planes and Statistical Complexity Analysis. ENTROPY 2013. [DOI: 10.3390/e15104084] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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23
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24
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Alipour M, Mohajeri A. Onicescu information energy in terms of Shannon entropy and Fisher information densities. Mol Phys 2012. [DOI: 10.1080/00268976.2011.649795] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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25
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On the relationship between one-electron potential and densities of Fisher information and Shannon entropy. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.10.027] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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26
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Insight into the stability of molecular clusters from the information theory computations. COMPUT THEOR CHEM 2011. [DOI: 10.1016/j.comptc.2011.07.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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27
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Esquivel RO, Liu S, Angulo JC, Dehesa JS, Antolín J, Molina-Espíritu M. Fisher Information and Steric Effect: Study of the Internal Rotation Barrier of Ethane. J Phys Chem A 2011; 115:4406-15. [DOI: 10.1021/jp1095272] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Rodolfo O. Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana, 09340 México D.F., México
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States
| | | | | | - Juan Antolín
- Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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29
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Esquivel RO, Flores-Gallegos N, Dehesa JS, Angulo JC, Antolín J, López-Rosa S, Sen KD. Phenomenological Description of a Three-Center Insertion Reaction: An Information-Theoretic Study. J Phys Chem A 2010; 114:1906-16. [DOI: 10.1021/jp908898w] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Rodolfo O. Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Nelson Flores-Gallegos
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Jesús S. Dehesa
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Juan Carlos Angulo
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Juan Antolín
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - Sheila López-Rosa
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
| | - K. D. Sen
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México D.F., Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, and School of Chemistry, University of Hyderabad, Hyderabad 500046, India
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30
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Noorizadeh S, Shakerzadeh E. Shannon entropy as a new measure of aromaticity, Shannon aromaticity. Phys Chem Chem Phys 2010; 12:4742-9. [DOI: 10.1039/b916509f] [Citation(s) in RCA: 125] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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31
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López-Rosa S, Esquivel RO, Angulo JC, Antolín J, Dehesa JS, Flores-Gallegos N. Fisher Information Study in Position and Momentum Spaces for Elementary Chemical Reactions. J Chem Theory Comput 2009; 6:145-54. [DOI: 10.1021/ct900544m] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Sheila López-Rosa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Rodolfo O. Esquivel
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Juan Carlos Angulo
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Juan Antolín
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Jesús S. Dehesa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
| | - Nelson Flores-Gallegos
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071-Granada, Spain, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071-Granada, Spain, Departamento de Química, Universidad Autónoma Metropolitana, 09340-México D.F., México, and Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018-Zaragoza, Spain
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Sagar RP, Laguna HG, Guevara NL. Conditional entropies and position–momentum correlations in atomic systems. Mol Phys 2009. [DOI: 10.1080/00268970903153675] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Esquivel RO, Flores-Gallegos N, Iuga C, Carrera EM, Angulo JC, Antolín J. Phenomenological description of the transition state, and the bond breaking and bond forming processes of selected elementary chemical reactions: an information-theoretic study. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0641-x] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Affiliation(s)
- Vladimir G. Tsirelson
- Quantum Chemistry Department, Mendeleev University of Chemical Technology, Miusskaya Sq. 9, Moscow, 125047 Russia, and Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary
| | - Ágnes Nagy
- Quantum Chemistry Department, Mendeleev University of Chemical Technology, Miusskaya Sq. 9, Moscow, 125047 Russia, and Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary
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35
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Burrows B, Cohen M. Exact solutions for shell-confined hydrogen-like atoms: polarisabilities and Shannon entropies. Mol Phys 2008. [DOI: 10.1080/00268970701787864] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Liu S. On the relationship between densities of Shannon entropy and Fisher information for atoms and molecules. J Chem Phys 2007; 126:191107. [PMID: 17523787 DOI: 10.1063/1.2741244] [Citation(s) in RCA: 99] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
An analytical relationship between the densities of the Shannon entropy and Fisher information for atomic and molecular systems has been established in this work. Two equivalent forms of the Fisher information density are introduced as well. It is found that for electron densities of atoms and molecules the Shannon entropy density is intrinsically related to the electron density and the two forms of the Fisher information density. The formulas have been confirmed by the numerical results for the first two-row atoms.
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Affiliation(s)
- Shubin Liu
- Division of Research Computing, Information Technology Services, University of North Carolina, Chapel Hill, North Carolina 27599-3455, USA.
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38
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Sagar RP, Guevara NL. Shannon entropies of atomic structure factors, off-diagonal order and radial correlation. Mol Phys 2007. [DOI: 10.1080/00268970701335771] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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39
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Sen KD, Katriel J. Information entropies for eigendensities of homogeneous potentials. J Chem Phys 2006; 125:074117. [PMID: 16942332 DOI: 10.1063/1.2263710] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
For homogeneous potentials, the sum S(T), of position and momentum Shannon information entropies Sr and Sp is shown to be independent of the coupling strength scaling. The other commonly used uncertainty like products also follow similar behavior. The ramifications of this scaling property in the cases of hydrogenlike, harmonic oscillator, Morse, and Poeschl-Teller potentials are discussed with the example of S(T).
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Affiliation(s)
- K D Sen
- School of Chemistry, University of Hyderabad, Hyderabad 500 046, India.
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40
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Sagar RP, Guevara NL. Mutual information and electron correlation in momentum space. J Chem Phys 2006; 124:134101. [PMID: 16613443 DOI: 10.1063/1.2180777] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mutual information and information entropies in momentum space are proposed as measures of the nonlocal aspects of information. Singlet and triplet state members of the helium isoelectronic series are employed to examine Coulomb and Fermi correlations, and their manifestations, in both the position and momentum space mutual information measures. The triplet state measures exemplify that the magnitude of the spatial correlations relative to the momentum correlations depends on and may be controlled by the strength of the electronic correlation. The examination of one- and two-electron Shannon entropies in the triplet state series yields a crossover point, which is characterized by a localized momentum density. The mutual information density in momentum space illustrates that this localization is accompanied by strong correlation at small values of p.
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Affiliation(s)
- Robin P Sagar
- Departamento de Química, Universidad Autónoma Metropolitana Apartado Postal 55-534, Iztapalapa, 09340 México D.F., México
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