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PreprintCC BY 4.0arXiv

Pair density Shannon information measures and their N-dependent behaviour in diatomic molecular systems

  • Saul J. C. Salazar
  • J. Antonio Zarate
  • J. M. Solano-Altamirano
  • Humberto G. Laguna
  • Julio M. Hernandez-Perez
  • Robin P. Sagar
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Abstract

Pair density Shannon entropies and mutual information in position and in momentum space are calculated for two series of homonuclear and heteronuclear diatomic molecules using Hartree-Fock wave functions. The pair density entropy sum increases with the quality of the basis set. Mutual information, a measure of statistical correlation, is seen to be smaller in momentum space as compared to position space. The interpretation is that the momentum pair density is closer than the position pair density to a Hartree-like reference. The N-dependent behaviours of the entropy and mutual information sums are examined by fitting the data to three different model behaviours. Results show that these models are capable of representing the molecular data in differing degrees. The parameters obtained from a particular model are relatively constant across different chemical series. This adds evidence to the argument of a universal N-dependent behaviour of the entropy sums.

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Cite

BibTeXRIS
BibTeX
@misc{salazar2026pair,
  title = {{Pair density Shannon information measures and their $N$-dependent behaviour in diatomic molecular systems}},
  author = {Saul J. C. Salazar and J. Antonio Zarate and J. M. Solano-Altamirano and Humberto G. Laguna and Julio M. Hernandez-Perez and Robin P. Sagar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21260},
  eprint = {2609.21260},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21260},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Pair density Shannon information measures and their N-dependent behaviour in diatomic molecular systems
AU  - Saul J. C. Salazar
AU  - J. Antonio Zarate
AU  - J. M. Solano-Altamirano
AU  - Humberto G. Laguna
AU  - Julio M. Hernandez-Perez
AU  - Robin P. Sagar
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21260
UR  - https://arxiv.org/abs/2609.21260
AB  - Pair density Shannon entropies and mutual information in position and in momentum space are calculated for two series of homonuclear and heteronuclear diatomic molecules using Hartree-Fock wave functions. The pair density entropy sum increases with the quality of the basis set. Mutual information, a measure of statistical correlation, is seen to be smaller in momentum space as compared to position space. The interpretation is that the momentum pair density is closer than the position pair density to a Hartree-like reference. The N-dependent behaviours of the entropy and mutual information sums are examined by fitting the data to three different model behaviours. Results show that these models are capable of representing the molecular data in differing degrees. The parameters obtained from a particular model are relatively constant across different chemical series. This adds evidence to the argument of a universal N-dependent behaviour of the entropy sums.
ER  -