F bond as a Unified Measure of Electron Correlation: From Aromatic Clusters to Metallic Superatoms

We present a unified study of electron correlation across molecular and cluster systems using the F bond descriptor derived from coupled-cluster natural orbital occupations. We define F bond through a direct occupation-number summation over all correlated natural orbitals, F bond = i n i (2 − n i), which captures the total deviation from idempotency in the one-particle density matrix. Computed at the CCSD/def2-SVP level, all systems studied exhibit substantial multiconfigurational character when the complete natural orbital space is included: aromatic Al 4 2-(F bond = 3.84), antiaromatic Al 4 4-(4.03), planar and icosahedral B 12 clusters (4.42 and 4.99), heteroatomic B 6 N 6 (5.11), and cesium-aluminum superatoms Cs 3 Al 8 and Cs 3 Al 12-(5.58 and 7.10, respectively). We show that F bond is an extensive quantity that scales with the number of correlated orbitals, and introduce the perelectron correlation density f e = F bond /N e as a complementary intensive measure. This intensive measure reveals a clear separation: small clusters (Al 4 , B 12 , B 6 N 6) exhibit f e ≈ 0.07, while metallic superatoms show f e ≈ 0.04, reflecting the diluted nature of correlation in large delocalized systems. We demonstrate that previous reports of "weakly correlated" behavior (F bond < 0.001) in aluminum clusters were artifacts of natural orbital space truncation, and that complete occupation data are essential for physically meaningful correlation diagnostics. This work establishes F bond and f e as complementary extensive and intensive measures bridging quantum information theory and electron correlation across fundamentally different bonding regimes. We further validate the framework using analog quantum simulation on a neutral-atom quantum processor, confirming that the topological entanglement signatures of aromaticity and superatomicity are reproducible on near-term quantum hardware.