Natural Orbital Correlation Analysis of Cluster Bonding: From Aromatic Clusters to Metallic Superatoms with Quantum Topology Probes

We present a systematic study of electron correlation across 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). 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 clear separation: small clusters (Al4, B12, B6N6) exhibit fe ≈ 0.07–0.14, while metallic superatoms show fe ≈ 0.04, reflecting the diluted nature of correlation in large delocalized systems. 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 study, we explore whether molecular bonding topology generates characteristic entanglement signatures on a neutral-atom quantum processor (Pasqal). Mapping atomic coordinates of nine molecular systems onto Rydberg atom registers, we find that different chemical topology classes—aromatic, antiaromatic, cage, and metallic—produce systematically distinct entanglement patterns, suggesting that molecular graphs encode topological information accessible to analog quantum hardware.