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Theory of Electron-Pair Density Functions and Its Quantum Chemical Applications

Research Project

Project/Area Number 13640495
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Physical chemistry
Research InstitutionMURORAN INSTITUTE OF TECHNOLOGY

Principal Investigator

KOGA Toshikatsu  Muroran Institute of Technology, Department of Applied Chemistry, Professor, 工学部, 教授 (90113688)

Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥2,600,000 (Direct Cost: ¥2,600,000)
KeywordsElectron-Pair Densities / Intracules / Extracules / interelectronic angles / Electron correlations / Atoms / 原子 / 相対運動 / 質量中心運動 / 総和則
Research Abstract

The motions of electron-pairs in atoms and molecules are described by the electron-pair intracule (relative motion) and extracule (center-of-mass motion) density functions. For atomic systems, these electron-pair densities are characterized by their spherical averages. The electron-pair densities are important probability density functions to understand the electron-electron interactions in atoms and molecules, but up to now we have neither sufficient knowledge about their theoretical structures nor practical applications to quantum chemical problems.
The purpose of this research project has been to clarify the theoretical structure of the electron-pair density functions and to apply new results to various chemical and physical problems. The results of this research project during the two years are summarized as follows:
(1) We introduced a generalized electron-pair density function. The intracule and extracule densities have been shown to be two particular cases of the density function. … More We have also shown that the second moments of the electron-pair densities satisfy a rigorous sum rule, which connects one- and two-electron properties of atoms and molecules.
(2) We found that the electron-pair density values at the origin is specified by the electron-electron coalescence and counterbalance functions, and clarified the mathematical structures of these functions. Numerical results were reported for 102 atoms in their ground states.
(3) We reported that the second moments of the intracule and extracule densities are rigorously connected to various physical properties, which were hitherto studies independently. The properties include electronic and nuclear kinetic energies, oscillator strength sums, nuclear mass correction energies, diamagnetic susceptibilities, and dipole polarizabilities.
(4) The second moments of the intracule and extracule densities also clarify the statistical correlation of electrons in atoms and molecules. In the Hartree-Fock approximation, electrons in atoms are either negatively correlated or uncorrelated.
(5) We have newly introduced the interelectronic angle density function which characterizes the spatial angular distribution of electrons and reported numerical results for atoms.
(6) For the He, Li, and Be atoms in their ground states, the electron correlation effect on the electron-pair properties were examined. The results point out and correct the inconsistency in the literature values. Less

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (39 results)

All Other

All Publications (39 results)

  • [Publications] T.Koga: "A Generalized Electron-Pair Density Function for Atoms"Journal of Chemical Physics. 114・1. 72-75 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Koga: "Electron-Electron Coalescence and Counterbalance Functions for Atoms"Journal of Chemical Physics. 114・1. 102-107 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Koga: "Sum Rules for Generalized Electron-Pair Moments"Journal of Chemical Physics. 114・5. 2511-2512 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Koga: "Correlated Electron-Pair Properties of the Li Atom in Momentum Space"Theoretical Chemistry Accounts. 107・4. 246-249 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Koga: "Correlated Electron-Pair Properties of the Be Atom in Position and Momentum Space"Journal of Chemical Physics. 116・15. 6614-6617 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Koga: "Interelectronic Angle Densities of Atoms"Journal of Chemical Physics. 117・23. 10493-10498 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "A Generalized Electron-Pair Density Function for Atoms"J. Chem. Phys.. 114 (1). 72-75 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "A Generalized Electron-Pair Density Function for Atoms"J. Chem. Phys.. 114 (20), Erratum. 9194 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Electron-Electron Coalescence and Counterbalance Functions for Atoms"J. Chem. Phys.. 114 (1). 102-107 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Sum Rules for Generalized Electron-Pair Moments"J. Chem. Phys.. 114 (5). 2511-2512 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Electron-Electron Coalescence and Counterbalance Functions in Momentum Space"J. Phys.. B, 34 (8). 1383-1393 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Sum Rules for Generalized Electron-Pair Moments of Hartree-Fock Orbitals"J. Chem. Phys.. 114 (19). 8382-8385 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga, Y. Kato, H. Matsuyama: "Radial Electron-Pair Densities in Momentum Space and Shell Structure of Atoms"Theor. Chem. Acc.. 106 (4). 237-240 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "On the Extremum Property of Electron Density Functions in Position and Momentum Spaces"Chem. Phys. Lett.. 340 (5-6). 547-551 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "On the Electron-Electron Coalescence Function in Hartree-Fock Theory"Chem. Phys. Lett.. 344 (1-2). 120-124 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga, H. Matsuyama: "Physical Significance of Second Electron-Pair Moments in Position and Momentum Spaces"J. Chem. Phys.. 115 (9). 3984-3991 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Statistical Angular Correlation Coefficients and Second Electron-Pair Moments for Atoms"J. Chem. Phys.. 115 (15). 6847-6852 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Correlated Electron-Pair Properties of the He Atom in Position and Momentum Spaces"Chem. Phys. Lett.. 350 (1-2). 135-140 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Correlated Electron-Pair Properties of the Li Atom in Momentum Space"Theor. Chem. Acc.. 107 (4). 246-249 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Correlated Electron-Pair Properties of the Be Atom in Position and Momentum Spaces"J. Chem. Phys.. 116 (15). 6614-6617 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Comment on 'Correlated One-Body Momentum Density for Helium to Neon Atoms'"J. Phys.. B, 35 (5). 1407-1408 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga, H. Matsuyama: "On the Oscillator Strength Sums S(±1) of Atoms and Ions"J. Chem. Phys.. 117 (1). 55-58 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Interelectronic Angles of Atoms in Position and Momentum Spaces"Chem. Phys. Lett.. 363 (5-6). 598-603 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga, Y. Kawata: "Statistical Angular Correlation Coefficients of Atomic Hartree-Fock Orbitals"J. Chem. Phys.. 117 (20). 9133-9137 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Matsuyama, T. Koga: "Average Inner Product Sums of Electron Linear Momenta for Atoms and Ions"Theor. Chem. Acc.. 108 (6). 347-351 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga: "Interelectronic Angle Densities of Atoms"J. Chem. Phys.. 117 (23). 10493-10498 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T. Koga, H. Matsuyama: "Nuclear Mass Corrections for Atoms and Ions"Chem. Phys. Lett.. 366 (5-6). 601-605 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] T.Koga: "Correlated Electron-Pair Properties of the Li Atom in Momentum Space"Theoretical Chemistry Accounts. 107・4. 246-249 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Koga: "Correlated Electron-Pair Properties of the Be Atom in Position and Momentum Space"Journal of Chemical Physics. 116・15. 6614-6617 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Koga, H.Matsuyama: "On the Oscillator Strength Sums of Atoms and Ions"Journal of Chemical Physics. 117・1. 55-58 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Koga: "Interelectronic Angles of Atoms in Position and Momentum Spaces"Chemical Physics Letters. 363・5-6. 598-603 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Koga, Y.Kawata: "Statistical Angular Correlation Coefficients of Atomic Hartree-Fock Orbitals"Journal of Chemical Physics. 117・20. 9133-9137 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Koga: "Interelectronic Angle Densities of Atoms"Journal of Chemical Physics. 117・23. 10493-10498 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Koga: "A Generalized Electron-Pair Density Function for Atoms"Journal of Chemical Physics. 114・1. 72-75 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Koga: "Electron-Electron Coalescence and Counterbalance Functions for Atoms"Journal of Chemical Physics. 114・1. 102-107 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Koga: "Sum Rules for Generalized Electron-Pair Moments"Journal of Chemical Physics. 114・5. 2511-2512 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Koga: "Electron-Electron Coalescence and Counterbalance Functions in Momentum Space"Journal of Physics B. 34・8. 1383-1393 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Koga: "Sum Rules for Generalized Electron-Pair Moments of Hartree-Fock Orbitals"Journal of Chemical Physics. 114・19. 8382-8385 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Koga: "On the Electron-Electron Coalescence Function in Hartree-Fock Theory"Chemical Physics Letters. 344・1-2. 120-124 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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