{"id":"doi:10.26434/chemrxiv.15000134/v8","kind":"article","title":"Natural Orbital Correlation Analysis of Cluster Bonding: From Aromatic Clusters to Metallic Superatoms with Quantum Topology Probes","authors":["Celal Arda"],"author_count":1,"year":2026,"published":"2026-06-15","venue":"ChemRxiv","cited_by":0,"doi":"10.26434/chemrxiv.15000134/v8","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.26434/chemrxiv.15000134/v8","archive_url":"https://space-kitty.com/papers/doi:10.26434/chemrxiv.15000134/v8","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W7164801810","pdf_url":null,"abstract":"We present a systematic study of electron correlation across 11 molecular and cluster systems using the number of effectively unpaired electrons ND = P i ni(2 − ni), the Takatsuka–Head-Gordon index, computed from coupled-cluster natural orbital occupations over the complete correlated orbital space. Computed at the CCSD/def2-SVP level, all systems studied exhibit substantial total electron correlation when the full natural orbital space is retained: aromatic Al4 2 – (ND = 3.84), antiaromatic Al4 4 – (4.03), planar and icosahedral B12 clusters (4.42 and 4.99), heteroatomic B6N6 (5.11), and cesium–aluminum superatoms Cs3Al8 – and Cs3Al12 – (5.58 and 7.10, respectively), and the B12N12 cage (7.18, the largest in the set). We show that ND is an extensive quantity dominated by the dynamic correlation tail over many weakly occupied virtual orbitals, and introduce the per-electron correlation density fe = ND/Ncorr as a complementary intensive measure. This intensive measure reveals a correlation-density trend: small clusters (Al4, B12, B6N6) exhibit fe ≈ 0.08–0.14 at CCSD/def2-SVP, while metallic superatoms show fe ≈ 0.03–0.05. The separation is clearest between the regime extremes and in matched-element comparisons (Al4 vs. Cs3Aln – family means differ by ∼2× at comparable orbital density); at the larger def2-TZVP basis the boundary-adjacent Al4 2 – /Cs3Al8 – pair narrows to ∼1.1×, so we frame this as a trend in per-electron correlation density rather than a sharp two-regime boundary. We demonstrate that truncation of the natural orbital space to a small active window dramatically underestimates ND, and that complete occupation data are essential for physically meaningful correlation diagnostics. In a separate, exploratory study we map atomic coordinates of ten molecular systems onto Rydberg atom registers and measure entanglement on an analog neutral-atom emulator (Pasqal). We observe topology-dependent entanglement, but within this ten-system set no graph-theoretic metric reaches statistical significance; we therefore present this component as preliminary and hypothesisgenerating, not as a demonstrated structure–property relationship.","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Advanced Chemical Physics Studies"],"details":null,"provenance":"openalex","attribution":"Abstract of \"Natural Orbital Correlation Analysis of Cluster Bonding: From Aromatic Clusters to Metallic Superatoms with Quantum Topology Probes\" by Celal Arda, https://doi.org/10.26434/chemrxiv.15000134/v8, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"atoms-and-ions","name":"Neutral-Atom & Trapped-Ion Quantum Computing","domain_slug":"quantum-computing"}],"cited_in_dossiers":[]}