Theoretical Chemistry Accounts

, Volume 105, Issue 1, pp 96–99 | Cite as

Isomorphism in electron-pair densities of atoms

  • Toshikatsu Koga


The spherically averaged electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities are a couple of densities which characterize the motion of electron pairs in atomic systems. We study a generalized electron-pair density \(\)(q; a, b) that represents the probability density function for the magnitude of two-electron vector ar j +br k of any pair of electrons j and k to be q, where a and b are nonzero real numbers. In particular, h(u)=g(u;1, −1) and d(R) = \(\). It is shown that the scaling property of the Dirac delta function and the inversion symmetry of orbitals in atoms due to the central force field generate several isomorphic relations in the electron-pair density \(\)(q; a, b) with respect to the two parameters a and b. The approximate isomorphism d(R)≅8h(2R) known in the literature between the intracule and extracule densities is a special case of the present results.

Key words: Isomorphism – Electron-pair density – Intracule density – Extracule density – Atoms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Toshikatsu Koga
    • 1
  1. 1.Department of Applied Chemistry, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, JapanJP

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