Copula methods for modeling pair densities in density functional theory

Fuente: arXiv
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Main Authors: Dusson, Geneviève, Klüppelberg, Claudia, Friesecke, Gero
Format: Preprint
Published: 2025
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author Dusson, Geneviève
Klüppelberg, Claudia
Friesecke, Gero
author_facet Dusson, Geneviève
Klüppelberg, Claudia
Friesecke, Gero
contents We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate) pair density by the single-particle density and a copula. We present analytical formulas for the exact copula in scaling limits, numerically compute the copula for dissociating systems with two to four particles in one dimension, and propose accurate approximations of the copula between equilibrium and dissociation for two-particle systems.
format Preprint
id arxiv_https___arxiv_org_abs_2501_17515
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Copula methods for modeling pair densities in density functional theory
Dusson, Geneviève
Klüppelberg, Claudia
Friesecke, Gero
Computational Physics
Statistics Theory
We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate) pair density by the single-particle density and a copula. We present analytical formulas for the exact copula in scaling limits, numerically compute the copula for dissociating systems with two to four particles in one dimension, and propose accurate approximations of the copula between equilibrium and dissociation for two-particle systems.
title Copula methods for modeling pair densities in density functional theory
topic Computational Physics
Statistics Theory
url https://arxiv.org/abs/2501.17515