The mixed regularity of electronic wave functions multiplied by explicit correlation factors
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 5, p. 803-824

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 Mathematics 2000, 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.

DOI : https://doi.org/10.1051/m2an/2010103
Classification:  35J10,  35B65,  41A25,  41A63
Keywords: schrödinger equation, regularity, mixed derivatives, correlation factor, complexity
@article{M2AN_2011__45_5_803_0,
     author = {Yserentant, Harry},
     title = {The mixed regularity of electronic wave functions multiplied by explicit correlation factors},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {5},
     year = {2011},
     pages = {803-824},
     doi = {10.1051/m2an/2010103},
     mrnumber = {2817545},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_5_803_0}
}
Yserentant, Harry. The mixed regularity of electronic wave functions multiplied by explicit correlation factors. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 5, pp. 803-824. doi : 10.1051/m2an/2010103. http://www.numdam.org/item/M2AN_2011__45_5_803_0/

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