Abstract.
For 357 subshells of the 53 neutral atoms He through Xe in their ground states, the two-electron intracule (relative motion) <u k> nl and extracule (center-of-mass motion) <R k> nl subshell moments in position space are examined as well as their counterparts <v k> nl and <P k> nl in momentum space, where n and l are the principal and azimuthal quantum numbers of the atomic subshell, respectively. It is clarified that between the intracule and extracule moments the “2k-rule” is strictly valid, which means <u k> nl = 2k<R k> nl and <v k> nl = 2k<P k> nl for any nl subshell. Theoretical analysis also proves that for a particular case of k = +2, two relations <u 2> nl = (N nl −1)<r 2> nl and <v 2> nl = (N nl −1)<p 2> nl hold exactly, where N nl (≥2) is the number of electrons in the subshell nl, and <r k> nl and <p k> nl are the familiar one-electron subshell moments in position and momentum spaces, respectively. The latter equality establishes a new and rigorous relation between the second electron-pair moments in momentum space and the total energy of an atom through the virial theorem. For k=+1, −1, and −2, the numerical Hartree-Fock results for the 357 subshells show that there are approximate but accurate linear relations between <u k> nl and <r k> nl and between <v k> nl and <p k> nl , in which the proportionality constant in each space depends on n,l, and k.
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Received: 27 April 1998 / Accepted: 29 May 1998 / Published online: 28 August 1998
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Koga, T., Matsuyama, H. Atomic one- and two-electron subshell moments in position and momentum spaces. Theor Chem Acc 99, 320–328 (1998). https://doi.org/10.1007/s002140050342
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DOI: https://doi.org/10.1007/s002140050342