Ceiling and Cliff: Tsirelson-Limited Correlations as a Structural Constraint on Molecular Bonding

Overview We propose a quantum information-theoretic framework for characterizing covalent bond formation based on the Tsirelson bound β = 2√2. Using full configuration interaction calculations on H₂, we demonstrate that the CHSH maximum is universally achieved in the covalent sector, acting as a geometric ceiling rather than a bond diagnostic. The physically meaningful cliff emerges from a composite index κ_phys that combines bond character, quantum excess, and binding energy gain. This index peaks in the bonding region and vanishes at both short range and dissociation, providing a testable structural criterion for covalent bond formation. Key Finding The Tsirelson bound β = 2√2 acts as a formal ceiling on admissible quantum correlations, while molecular bonding emerges only when this ceiling is weighted by both chemical connectivity and energetic benefit. Contents Manuscript ceiling_cliff_preprint.pdf - Main manuscript (4 pages, with Figure 1) ceiling_cliff_preprint.tex - LaTeX source Figures h2_tstt_publication_final.png - Figure 1: Complete H₂ CHSH analysis (4-panel) si_figure_s1_basis.png - Figure S1: Basis set dependence verification Data h2_tstt_publication_data.csv - Numerical data for H₂ analysis si_table_s1_basis.csv - Basis set comparison table Code h2_publication_final.py - Main analysis code (PySCF/FCI) si_basis_comparison.py - Basis set dependence verification Reproducibility All calculations can be reproduced using Python 3.x with PySCF, NumPy, and Matplotlib. Future Perspective The present work establishes a geometric ceiling governing quantum correlations in the simplest molecular system. While demonstrated here for covalent bonding, the same formal constraint is expected to play a role in other regimes characterized by extreme correlation density, including thermodynamic limits and nuclear binding processes. These extensions are left for future investigation.