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

Harry Yserentant

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 5, page 803-824
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Yserentant, Harry. "The mixed regularity of electronic wave functions multiplied by explicit correlation factors***." ESAIM: Mathematical Modelling and Numerical Analysis 45.5 (2011): 803-824. <http://eudml.org/doc/197501>.

@article{Yserentant2011,
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. },
author = {Yserentant, Harry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Schrödinger equation; regularity; mixed derivatives; correlation factor; complexity; correlation factor},
language = {eng},
month = {2},
number = {5},
pages = {803-824},
publisher = {EDP Sciences},
title = {The mixed regularity of electronic wave functions multiplied by explicit correlation factors***},
url = {http://eudml.org/doc/197501},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Yserentant, Harry
TI - The mixed regularity of electronic wave functions multiplied by explicit correlation factors***
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/2//
PB - EDP Sciences
VL - 45
IS - 5
SP - 803
EP - 824
AB - 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.
LA - eng
KW - Schrödinger equation; regularity; mixed derivatives; correlation factor; complexity; correlation factor
UR - http://eudml.org/doc/197501
ER -

References

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Citations in EuDML Documents

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  1. Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
  2. Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
  3. Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
  4. Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

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