Approximating a wavefunction as an unconstrained sum of Slater determinants
Abstract
The wavefunction for the multiparticle Schroedinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.
- Authors:
-
- Department of Applied Mathematics, University of Colorado at Boulder, 256 UCB, Boulder, Colorado 80309-0526 (United States)
- Department of Mathematics, Ohio University, 321 Morton Hall, Athens, Ohio 45701 (United States)
- Publication Date:
- OSTI Identifier:
- 21100228
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 49; Journal Issue: 3; Other Information: DOI: 10.1063/1.2873123; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; APPROXIMATIONS; GREEN FUNCTION; INTEGRAL EQUATIONS; INTEGRALS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; MATRICES; POTENTIALS; SCHROEDINGER EQUATION; SLATER METHOD; WAVE FUNCTIONS
Citation Formats
Beylkin, Gregory, Perez, Fernando, and Mohlenkamp, Martin J. Approximating a wavefunction as an unconstrained sum of Slater determinants. United States: N. p., 2008.
Web. doi:10.1063/1.2873123.
Beylkin, Gregory, Perez, Fernando, & Mohlenkamp, Martin J. Approximating a wavefunction as an unconstrained sum of Slater determinants. United States. https://doi.org/10.1063/1.2873123
Beylkin, Gregory, Perez, Fernando, and Mohlenkamp, Martin J. 2008.
"Approximating a wavefunction as an unconstrained sum of Slater determinants". United States. https://doi.org/10.1063/1.2873123.
@article{osti_21100228,
title = {Approximating a wavefunction as an unconstrained sum of Slater determinants},
author = {Beylkin, Gregory and Perez, Fernando and Mohlenkamp, Martin J},
abstractNote = {The wavefunction for the multiparticle Schroedinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.},
doi = {10.1063/1.2873123},
url = {https://www.osti.gov/biblio/21100228},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 3,
volume = 49,
place = {United States},
year = {Sat Mar 15 00:00:00 EDT 2008},
month = {Sat Mar 15 00:00:00 EDT 2008}
}