A Reproducible Dirac–Fock Mulliken Spinor-Population Reanalysis of CBi⁻ Relativistic Bonding

Abstract This preprint presents a reproducible computational reanalysis of relativistic chemical bonding in the CBi⁻ molecular anion and selected neutral CBi electronic configurations, based on previously generated DIRAC quantum-chemical output. The investigation examines 18 selected Dirac–Fock spinor records across two basis sets and three electronic configurations. Independent extraction and verification establish agreement among the original output data and separately generated numerical audit tables. Atomic-orbital symmetry analysis supports the interpretation of axial A1 and transverse B1/B2 contributions within the selected spinor-population tables. A conditional population-mixing descriptor, M = 4wσwπ, is evaluated to characterize the redistribution of selected Mulliken spinor populations. The analysis indicates substantial mixing in the selected |mj| = 1/2 spinors and demonstrates that the descriptor depends on the electronic configuration. Scientific Scope and Limitations The reported results establish computational extraction reproducibility, not experimental validation of a new physical theory. The proposed two-channel reduction, spin–orbit coupling on/off comparisons, coupling-strength scaling, and transferability to related chemical systems remain unresolved. The reported populations originate from Dirac–Fock reference calculations and do not constitute a correlated CCSD(T) spinor decomposition. This work is a secondary computational reanalysis of previously published research. It does not claim the discovery of a new universal law of chemical bonding. Original Research Kahraman et al., "Relativistic collapse of the classical triple bond in the CBi⁻ molecular ion," Science (2026). DOI: https://doi.org/10.1126/science.aei1285 Research Attribution Author: Toni Mladenovski Project: NOVA Q / EIT ORCID: https://orcid.org/0009-0009-8343-662X AI-assisted computational research, documentation, and independent verification workflows are acknowledged. License Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0). Research status: Computational Reanalysis Preprint — NOT_PROOF.