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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board Member: Fetecau, Corina / Kiefer, Claus / Röpke, Gerd / Steeb, Willi-Hans

12 Issues per year


IMPACT FACTOR 2016: 1.432

Cite Score 2016: 1.35

SCImago Journal Rank (SJR) 2016: 0.368
Source Normalized Impact per Paper (SNIP) 2016: 0.594

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ISSN
1865-7109
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Volume 15, Issue 10 (Oct 1960)

Issues

Über die Berechnung der Korrelationsenergie der Atomelektronen

Levente Szász
Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-1960-1007

To calculate the correlation energy of an atom with N electrons we suggest the wave function

where à is the antisymmetrizer operator, φ1, φ2, ..., φN are one electron wave functions, and Wjk are correlation functions of the following form:

where the constants c j km, n, l are variational parameters. The function (a) is a generalization of the

wave function of Hylleraas for He. After a discussion of the properties of our function, an energy expression is derived. Numerical calculation is made for the ground state of the Be atom with the function

where φ1 and φ2 are ls wave functions, φ3 and φ4 are 2s wave functions, r1, r2, r3 and r4 are the radial coordinates of the four electrons, r12 and r34 are the distances between the corresponding electrons, and C1 and c2 are variational parameters. Using the one electron wave functions calculated by Roothaan and coll. with the Roothaan procedure, we got the energy value E= -14.624 a. u. while the Hartree-Fock and experimental values are EH,F= -14.570 a. u. and Eexp= -14.668 a. u. respectively. Thus the function (c) gives about one-half of the correlation energy of the Be atom.

About the article

Received: 1960-05-28

Published Online: 2014-06-02

Published in Print: 1960-10-01


Citation Information: Zeitschrift für Naturforschung A, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-1960-1007.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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