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PreprintCC BY-NC-NDChemRxiv

Sequential Adaptive Natural Density Partitioning (AdNDP) Systematically Produces Non-N-Representable Densities

  • Cristian Guerra
  • Jose Burgos
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Abstract

Adaptive natural density partitioning (Ad-NDP) sequentially extracts fragment natural orbitals from the one-electron density matrix. Herein, we show, with an exact and basisindependent argument, that the residual density left behind after two non-orthogonal bonding elements are extracted is not guaranteed to be N-representable. The breakdown has a precise, traceable origin: whenever two sequentially depleted orbitals carry a nonzero overlap, S12 ̸= 0, the second extraction re-subtracts density along a direction the first depletion step has already emptied, driving a diagonal element of the compressed 2 × 2 residual block negative independently of basis set, correlation treatment, or system size. At CCSD/cc-pVTZ, five benchmark multicenter systems (diborane, B−

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Cite

BibTeXRIS
BibTeX
@misc{guerra2026sequential,
  title = {{Sequential Adaptive Natural Density Partitioning (AdNDP) Systematically Produces Non-N-Representable Densities}},
  author = {Cristian Guerra and Jose Burgos},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15010528/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010528/v1},
  note = {CC BY-NC-ND},
}
RIS
TY  - UNPB
TI  - Sequential Adaptive Natural Density Partitioning (AdNDP) Systematically Produces Non-N-Representable Densities
AU  - Cristian Guerra
AU  - Jose Burgos
PY  - 2026
DA  - 2026/10/15
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15010528/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010528/v1
AB  - Adaptive natural density partitioning (Ad-NDP) sequentially extracts fragment natural orbitals from the one-electron density matrix. Herein, we show, with an exact and basisindependent argument, that the residual density left behind after two non-orthogonal bonding elements are extracted is not guaranteed to be N-representable. The breakdown has a precise, traceable origin: whenever two sequentially depleted orbitals carry a nonzero overlap, S12 ̸= 0, the second extraction re-subtracts density along a direction the first depletion step has already emptied, driving a diagonal element of the compressed 2 × 2 residual block negative independently of basis set, correlation treatment, or system size. At CCSD/cc-pVTZ, five benchmark multicenter systems (diborane, B−
ER  -