Atomic Bonding via Coherence Geometry

This paper applies Coherence Geometry (CG) to the problem of chemical bonding, modeling atoms as continuous amplitude and phase fields evolving under a shared energy functional. Bond formation is treated as a real-time process of phase alignment, curvature minimization, field deformation, and coherent bridge formation. The paper extends the orbital morphogenesis work of "Atomic Orbitals via Coherence Geometry" into interacting atomic systems. Simulations of symmetric and asymmetric configurations, including H2 and HF, show visible amplitude bridges, field deformation, directional lobe capture, and bond localization behavior. A central result is lobe locking: in the HF simulation, the hydrogen field is drawn into a pre-formed fluorine lobe, producing deterministic bond localization through curvature capture. The paper also studies spin-dependent bonding behavior by modeling spin as a continuous torsional phase field. In the reported simulations, spin misalignment suppresses bonding through curvature tension and phase incompatibility, offering a real-space reinterpretation of Pauli-like exclusion as a geometric constraint. This document should be read as a geometric and simulation-driven CG study of bond formation. It focuses on phase alignment, amplitude bridging, lobe locking, spin-channel interaction, curvature tension, and bond-like field stabilization. Broader chemistry-scale modeling, quantitative energy calibration, spectral prediction, and molecular engineering applications are left to future work. This paper was originally written in September 2025 and updated in May 2026 for public release with current Zenodo references where available. Simulation code is not included in this release. Internal reference: CGI-RSR-000027.