Related papers: Shannon and Rényi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation

Shannon and Rényi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation

URL: http://arxiv.org/abs/2604.18081v1
Date: Mon, 20 Apr 2026 10:53:35 GMT
Title: Shannon and Rényi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation
Abstract summary: We investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and Rényi entropies, as descriptors of electronic correlation.<n>By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, we analyze the behavior of the entropies at the infinite-internuclear-distance limit.
Score: 0.0
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and Rényi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis reveals several flaws in the use of these density-based descriptors. We demonstrate that for minimal-basis and different theoretical levels, the Shannon and Rényi entropies fail to encode the amount of static correlation conveyed by the underlying wavefunction. Conversely, shape-function Shannon entropies and Rényi entropies (for $α\neq 1$) violate extensivity. In larger basis sets, uncorrelated Hartree-Fock densities consistently overestimate entropy compared to sufficiently correlated (e.g., full-valence-CAS) densities. Moreover, the entropies for insufficiently correlated methods violate extensivity. These findings indicate that electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.

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