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The mixed regularity of electronic wave functions multiplied by explicit correlation factors***

Published online by Cambridge University Press:  23 February 2011

Harry Yserentant
Harry Yserentant*
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany. yserentant@math.tu-berlin.de
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Abstract

The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of two electrons. The present paper complements this work. It is shown that one can reach almost the same complexity as in the one-electron case adding a simple regularizing factor that depends explicitly on the interelectronic distances.

Keywords

Schrödinger equationregularitymixed derivativescorrelation factorcomplexity
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 5 , September 2011 , pp. 803 - 824
Copyright
© EDP Sciences, SMAI, 2011

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