Copula methods for modeling pair densities in density functional theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912266533732352 |
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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 |