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Cioslowski J, Strasburger K. Constraints upon Functionals of the 1-Matrix, Universal Properties of Natural Orbitals, and the Fallacy of the Collins "Conjecture". J Phys Chem Lett 2024; 15:1328-1337. [PMID: 38285733 PMCID: PMC10860149 DOI: 10.1021/acs.jpclett.3c03118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 01/02/2024] [Accepted: 01/04/2024] [Indexed: 01/31/2024]
Abstract
Reliability of quantum-chemical calculations based upon the density functional theory and its 1-matrix counterpart hinges upon minimizing the extent of empirical parameterization in the approximate energy expressions of these formalisms while imposing as many rigorous constraints upon them as possible. The recently uncovered universal properties of the natural orbitals facilitate the construction of such constraints for the 1-matrix functionals. The benefits of their employment in the validation of these functionals are vividly demonstrated by a critical review of the three incarnations of the so-called Collins conjecture. Although the incorporation of rigorous definitions of the correlation energy and entropy, and the identification of individual potential energy hypersurfaces as probable domains of its applicability turn the originally published unsubstantiated claim into a proper conjecture, the resulting formalism is found to be merely a conduit for incorporation of static correlation effects in electronic structure calculations that is unlikely to allow attaining chemical accuracy.
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Affiliation(s)
- Jerzy Cioslowski
- Institute
of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
- Max-Planck-Institut
für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Krzysztof Strasburger
- Department
of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego
27, 50-370 Wrocław, Poland
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2
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Sayyad S, Lado JL. Transfer learning from Hermitian to non-Hermitian quantum many-body physics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:185603. [PMID: 38277690 DOI: 10.1088/1361-648x/ad22f8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 01/26/2024] [Indexed: 01/28/2024]
Abstract
Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.
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Affiliation(s)
- Sharareh Sayyad
- Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
| | - Jose L Lado
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Espoo, Finland
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3
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Chalupský J, Srnec M, Yanai T. Interpretation of Exchange Interaction through Orbital Entanglement. J Phys Chem Lett 2021; 12:1268-1274. [PMID: 33497240 DOI: 10.1021/acs.jpclett.0c03652] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Recently, the analysis of single-orbital entropy and mutual information has been introduced as a tool for the investigation of contributions to the exchange (J) coupling between open-shell metal ions [Stein et al. J. Phys. Chem. Lett. 2019, 10, 6762-6770]. Here, we show that this analysis may lead to an incorrect interpretation of the J-coupling mechanism. Instead, we propose an orbital-entanglement analysis that is based on the two-electron density and that provides a coherent picture of the contributing exchange pathways, which seems fully consistent with the available J values. For this purpose, we used a prototypical bis-μ-oxo binuclear manganese complex ([Mn2O2(NH3)8]4+) and demonstrated that its antiferromagnetism (J < 0), calculated by using the active space composed of all valence pO and dMn orbitals, correlates well with the largest elements in the differential low-spin vs high-spin entanglement map. These elements correspond to interactions between the pairs of dMn orbitals mediated by the oxo-bridging out-of-plane p orbitals, representing the π superexchange pathway. We also show that the reduction of active space to manifold of the singly occupied magnetic orbitals does not lead to discrepancy between the calculated J values and entanglement maps. This contrasts to analysis of mutual information, which suggests the "direct" dMn-dMn interactions to play a dominant role for the J coupling, irrespective of the size of active space as well as of the antiferromagnetism expected. The failure is attributed to the large contribution of spin entanglement contained in the mutual information of the low-spin state, which may be regarded as the origin of the different complexity of its wave function and electron density.
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Affiliation(s)
- Jakub Chalupský
- Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo náměstí 2, 166 10 Prague 6, Czech Republic
| | - Martin Srnec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, 182 23 Prague 8, Czech Republic
| | - Takeshi Yanai
- Department of Chemistry, Graduate School of Science, Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
- Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Furocho, Chikusa Ward, Nagoya, Aichi 464-8601, Japan
- Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
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4
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Ludeña EV, Torres FJ, Becerra M, Rincón L, Liu S. Shannon Entropy and Fisher Information from a Non-Born-Oppenheimer Perspective. J Phys Chem A 2020; 124:386-394. [PMID: 31846329 DOI: 10.1021/acs.jpca.9b10503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
We study the Shannon entropy and the Fisher information in a non-Born-Oppenheimer (nBO) regime, where these quantities are constructed from one-particle densities obtained from an exact nBO analytic wave function for a Coulomb-Hooke model of a four-particle system. This model consists of two electrons and two protons with Coulombic interactions between like particles and Hookean interactions otherwise [ Becerra , M. et al. Int. J. Quantum Chem 2013 , 113 ( 10 ), 1584 - 1590 ]. In the nBO case, there arise densities for both the nuclei and electrons. Furthermore, these densities vary with respect to a particular point of reference from which they are calculated. We consider, in the present work, electron and nuclear densities calculated from the following reference points: a global center of mass, the geometric center between the electrons, and the geometric center between the protons. A comparison of the nBO Shannon entropy and Fisher information, with respect to their counterparts computed from Born-Oppenheimer densities, suggests that the former quantities provide more insights into the chemical reactivity because of the nonuniqueness nature of the nBO electron density as well as the availability and access to the nBO nuclear density. Finally, some comments are made concerning the nBO vs the BO regimes in relation to this particular chemical reactivity indicator.
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Affiliation(s)
- Eduardo V Ludeña
- Grupo de Química Computacional y Teórica (QCT-USFQ) , Universidad San Francisco de Quito, USFQ , Diego de Robles s/n y Vía Interoceánica , Quito , Ecuador 170901
| | - F Javier Torres
- Grupo de Química Computacional y Teórica (QCT-USFQ) , Universidad San Francisco de Quito, USFQ , Diego de Robles s/n y Vía Interoceánica , Quito , Ecuador 170901.,Instituto de Simulación Computacional (ISC-USFQ) , Universidad San Francisco de Quito, USFQ , Diego de Robles s/n y Vía Interoceánica , Quito , Ecuador 170901
| | - Marcos Becerra
- Grupo de Química Computacional y Teórica (QCT-USFQ) , Universidad San Francisco de Quito, USFQ , Diego de Robles s/n y Vía Interoceánica , Quito , Ecuador 170901
| | - Luis Rincón
- Grupo de Química Computacional y Teórica (QCT-USFQ) , Universidad San Francisco de Quito, USFQ , Diego de Robles s/n y Vía Interoceánica , Quito , Ecuador 170901.,Instituto de Simulación Computacional (ISC-USFQ) , Universidad San Francisco de Quito, USFQ , Diego de Robles s/n y Vía Interoceánica , Quito , Ecuador 170901
| | - Shubin Liu
- Research Computing Center , University of North Carolina , Chapel Hill , North Carolina 27599-3420 , United States
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5
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Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory. COMPUTATION 2018. [DOI: 10.3390/computation6020036] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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6
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Flores-Gallegos N. Tsallis’ entropy as a possible measure of the electron correlation in atomic systems. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2017.12.014] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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7
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Link between generalized nonidempotency and complexity measures. J Mol Model 2017; 23:159. [PMID: 28405847 DOI: 10.1007/s00894-017-3331-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Accepted: 03/27/2017] [Indexed: 10/19/2022]
Abstract
The nonidempotency measure of Löwdin is found to be proportional to the disequilibrium. It is shown that there exists a simple relationship between the LMC (López-Ruiz-Mancini-Calbet) and the generalized statistical complexities and the generalized nonidempotency measure of Löwdin. Results are illustrated for an exactly solvable two-electron model atom.
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Flores-Gallegos N. A logarithmic informational temperature scale as a criterion to classify molecular systems. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1142/s021963361750016x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this work, we applied a definition of informational energy and informational temperature using 1865 molecules and showed that such definitions can classify molecules with similar chemical properties such as hardness, softness and chemical potential.
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Affiliation(s)
- N. Flores-Gallegos
- Benemérita Universidad de Guadalajara, Centro Universitario de los Valles, Carretera, Guadalajara - Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, México
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10
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11
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Alcoba DR, Torre A, Lain L, Massaccesi GE, Oña OB, Ayers PW, Van Raemdonck M, Bultinck P, Van Neck D. Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1905-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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Hofer TS. On the basis set convergence of electron-electron entanglement measures: helium-like systems. Front Chem 2013; 1:24. [PMID: 24790952 PMCID: PMC3982574 DOI: 10.3389/fchem.2013.00024] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2013] [Accepted: 09/30/2013] [Indexed: 11/13/2022] Open
Abstract
A systematic investigation of three different electron–electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, Li+ and Be2+ using a large number of different basis sets. The convergence behavior of the resulting energies and entropies revealed that the latter do in general not show the expected strictly monotonic increase upon increase of the one–electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as Li+ and Be2+. In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results (i.e., the wrong sign) if too small basis sets are used.
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Affiliation(s)
- Thomas S Hofer
- Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck Innsbruck, Austria
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13
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Shape entropy’s response to molecular ionization. J Mol Model 2013; 19:1677-83. [DOI: 10.1007/s00894-012-1725-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2012] [Accepted: 12/03/2012] [Indexed: 10/27/2022]
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15
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16
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Matta CF, Sichinga M, Ayers PW. Information theoretic properties from the quantum theory of atoms in molecules. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.08.072] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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17
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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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18
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Nalewajski RF. Chapter 5 Multiple, Localized, and Delocalized/Conjugated Bonds in the Orbital Communication Theory of Molecular Systems. ADVANCES IN QUANTUM CHEMISTRY 2009. [DOI: 10.1016/s0065-3276(08)00405-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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19
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Sagar RP, Guevara NL. Local correlation measures and atomic shell structure. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.03.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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20
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Juhász T, Mazziotti DA. The cumulant two-particle reduced density matrix as a measure of electron correlation and entanglement. J Chem Phys 2006; 125:174105. [PMID: 17100427 DOI: 10.1063/1.2378768] [Citation(s) in RCA: 66] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Several measures of electron correlation are compared based on two criteria: (i) the presence of a unique mapping between the reduced variables in the measure and the many-electron wave function and (ii) the linear scaling of the measure and its variables with system size. We propose the squared Frobenius norm of the cumulant part of the two-particle reduced density matrix (2-RDM) as a measure of electron correlation that satisfies these criteria. An advantage of this cumulant-based norm is its ability to measure the correlation from spin entanglement, which is not contained in the correlation energy. Alternative measures based on the 2-RDM, such as the von Neumann entropy, do not scale linearly with system size. Properties of the measures are demonstrated with Be, F(2), HF, N(2), and a hydrogen chain.
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Affiliation(s)
- Tamás Juhász
- James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
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21
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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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22
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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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23
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Gottlieb AD, Mauser NJ. New measure of electron correlation. PHYSICAL REVIEW LETTERS 2005; 95:123003. [PMID: 16197072 DOI: 10.1103/physrevlett.95.123003] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2005] [Indexed: 05/04/2023]
Abstract
We propose to quantify the correlation inherent in a many-electron (or many-fermion) wave function psi by comparing it to the unique uncorrelated state that has the same 1-particle density operator as does /|psi><psi/.
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Affiliation(s)
- Alex D Gottlieb
- Wolfgang Pauli Institute, Nordbergstr. 15, A-1090 Wien, Austria.
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24
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Sen KD. Characteristic features of Shannon information entropy of confined atoms. J Chem Phys 2005; 123:074110. [PMID: 16229562 DOI: 10.1063/1.2008212] [Citation(s) in RCA: 135] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Shannon information entropy of 1-normalized electron density in position and momentum space Sr and Sp, and the sum ST, respectively, are reported for the ground-state H, He+, Li2+, H-, He, Li+, Li, and B atoms confined inside an impenetrable spherical boundary defined by radius R. We find new characteristic features in ST denoted by well-defined minimum and maximum as a function of confinement. The results are analyzed in the background of the irreducible lower bound stipulated by the entropy uncertainty principle [I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975)]. The spherical confinement model leads to the ST values which satisfy the lower bound up to the limits of extreme confinements with the interesting new result displaying regions over which a set of upper and lower bounds to the information entropy sum can be locally prescribed. Similar calculations on the H atom in 2s excited states are presented and their novel characteristics are discussed.
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Affiliation(s)
- K D Sen
- School of Chemistry, University of Hyderabad, Hyderabad-500 046, India.
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25
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Sagar RP, Guevara NL. Mutual information and correlation measures in atomic systems. J Chem Phys 2005; 123:044108. [PMID: 16095347 DOI: 10.1063/1.1953327] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Mutual information is introduced as an electron correlation measure and examined for isoelectronic series and neutral atoms. We show that it possesses the required characteristics of a correlation measure and is superior to the behavior of the radial correlation coefficient in the neon series. A local mutual information, and related local quantities, are used to examine the local contributions to Fermi correlation, and to demonstrate and to interpret the intimate relationship between correlation and localization.
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Affiliation(s)
- Robin P Sagar
- Departamento de Química, Universidad Autónoma Metropolitana Apartado Postal 55-534, Iztapalapa, 09340 México DF, México
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26
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Guevara NL, Sagar RP, Esquivel RO. Local correlation measures in atomic systems. J Chem Phys 2005; 122:84101. [PMID: 15836014 DOI: 10.1063/1.1848092] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The phenomenon of electron correlation in atomic systems is examined and compared from the statistical, information theoretic, and energetic perspectives. Local correlation measures, based on the correlation coefficient, information entropies, and idempotency measure, are compared to the correlation energy density. Analysis of these local measures reveals that the chemically significant valence region is responsible for the behavior of their respective global measures in contrast to the correlation energy density which has large contributions to the correlation energy from both the core and valence regions. These results emphasize the difference in the mechanisms inherent in the different perspectives, the similarity between the statistical, information entropic, and idempotency views, and provides further evidence for the use of information theoretic based quantities in studies of electron correlation.
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Affiliation(s)
- Nicolais L Guevara
- Departamento de Química, Universidad Autónoma Metropolitana, Apartado Postal 55-534, Iztapalapa, 09340 México D.F., México
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27
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Electronic Structure and Chemical Reactivity: Density Functional and Information-Theoretic Perspectives. ADVANCES IN QUANTUM CHEMISTRY 2003. [DOI: 10.1016/s0065-3276(03)43004-9] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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28
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Nalewajski RF, Parr RG. Information theory, atoms in molecules, and molecular similarity. Proc Natl Acad Sci U S A 2000; 97:8879-82. [PMID: 10922049 PMCID: PMC16789 DOI: 10.1073/pnas.97.16.8879] [Citation(s) in RCA: 220] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Using information theory, it is argued that from among possible definitions of what an atom is when it is in a molecule, a particular one merits special attention. Namely, it is the atom defined by the "stockholders partitioning" of a molecule invented by Hirshfeld [(1977) Theor. Chim. Acta 44, 129]. The theoretical tool used is the minimum entropy deficiency principle (minimum missing information principle) of Kullback and Liebler [(1951) Ann. Math. Stat. 22, 79]. A corresponding analysis is given of the problem of assessing similarity between molecules or pieces of molecules.
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Affiliation(s)
- R F Nalewajski
- K. Guminski, Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland
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29
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Ziesche P, Smith VH, Hô M, Rudin SP, Gersdorf P, Taut M. The He isoelectronic series and the Hooke’s law model: Correlation measures and modifications of Collins’ conjecture. J Chem Phys 1999. [DOI: 10.1063/1.478560] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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