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

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

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

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topYserentant, 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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- J. Pople, Nobel lecture: Quantum chemical models. Rev. Mod. Phys.71 (1999) 1267–1274.
- J. Rychlewski Ed., Explicitly Correlated Wave Functions in Chemistry and Physics, Progress in Theoretical Chemistry and Physics13. Kluwer (2003).
- H. Yserentant, On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. Numer. Math.98 (2004) 731–759. Zbl1062.35100
- H. Yserentant, The hyperbolic cross space approximation of electronic wavefunctions. Numer. Math.105 (2007) 659–690. Zbl1116.78007
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## Citations in EuDML Documents

top- Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
- Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
- Markus Bachmayr, Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

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