Relativistic Bond Reconstruction in Chemical Bonding: An Information Dynamics Perspective on the CBi− Molecular Ion
Abstract
In July 2026, the team of Lai-Sheng Wang at Brown University reported a landmark experimental observation in Science: the first direct spectroscopic evidence for the relativistic breakdown of the classical triple-bond picture in the CBi− molecular ion. Here we reinterpret this discovery through the lens of information dynamics—a framework that distinguishes between “real space” (wavefunctions and electron densities, where traditional quantum chemistry operates) and “virtual space” (defined here as the symmetry-rule manifold that organizes how real-space observables behave). We formalize virtual space as the set of irreducible representations of the Hamiltonian’s symmetry group, and show that relativistic effects drive a restructuring of this virtual space from the nonrelativistic C∞v to the relativistic C∗ ∞v double group. Four-component Dirac–Coulomb CCSD(T) calculations on CBi− provide the ab initio anchor: projecting the resulting spinors onto the symmetry-rule basis defines the coupling matrix Sij = ⟨ϕω i |ϕNR j ⟩ that connects real-space states to virtualspace rules. From this coupling matrix we extract a single input, the σ weight σ1 = 58.3% of the upper |ω| = 1/2 Kramers pair, and characterize the restructuring with the mixing parameter η, the label ambiguity A = ⟨H(σ/π|ω)⟩, and the mutual information I—the calculations supply the wavefunctions, while η, A, and I are outputs of the symmetry-constrained S-matrix model built on this one extracted input. A single-parameter constraint structure emerges: given the extracted σ fraction, unitarity enforces the complementary fraction and angular-momentum projection orthogonality enforces zero σ character in the |ω| = 3/2 orbital. We obtain η = 0.722, A = 0.453 nats, and I = 0.646 nats. The restructuring is a smooth crossover driven by the spin–orbit coupling strength λ, with η decreasing from 1.00 and I decreasing from ln 3 ≈ 1.099 nats in the nonrelativistic limit, the steepest change in A and I occurring near λ ≈ 0.4. All reported values are produced by a self-consistent, reproducible analysis pipeline, and are stress-tested by five numerical validation experiments (pairing-algorithm robustness, noise injection, subspace closure, the CN− null test, and a basis-set incompleteness model), which rule out numerical noise as the origin of the mixing signatures. Our findings demonstrate that the “anomalies” in heavy-element chemistry are not exceptions to existing rules but rather the manifestation of rule reorganization when the system crosses from the nonrelativistic to the relativistic regime.
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BibTeX
@misc{huang2026relativistic,
title = {{Relativistic Bond Reconstruction in Chemical Bonding: An Information Dynamics Perspective on the CBi− Molecular Ion}},
author = {Kai Huang and Hongkui Liu and Ziwei Huang},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010457/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010457/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Relativistic Bond Reconstruction in Chemical Bonding: An Information Dynamics Perspective on the CBi− Molecular Ion
AU - Kai Huang
AU - Hongkui Liu
AU - Ziwei Huang
PY - 2026
DA - 2026/10/14
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010457/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010457/v1
AB - In July 2026, the team of Lai-Sheng Wang at Brown University reported a landmark experimental observation in Science: the first direct spectroscopic evidence for the relativistic breakdown of the classical triple-bond picture in the CBi− molecular ion. Here we reinterpret this discovery through the lens of information dynamics—a framework that distinguishes between “real space” (wavefunctions and electron densities, where traditional quantum chemistry operates) and “virtual space” (defined here as the symmetry-rule manifold that organizes how real-space observables behave). We formalize virtual space as the set of irreducible representations of the Hamiltonian’s symmetry group, and show that relativistic effects drive a restructuring of this virtual space from the nonrelativistic C∞v to the relativistic C∗ ∞v double group. Four-component Dirac–Coulomb CCSD(T) calculations on CBi− provide the ab initio anchor: projecting the resulting spinors onto the symmetry-rule basis defines the coupling matrix Sij = ⟨ϕω i |ϕNR j ⟩ that connects real-space states to virtualspace rules. From this coupling matrix we extract a single input, the σ weight σ1 = 58.3% of the upper |ω| = 1/2 Kramers pair, and characterize the restructuring with the mixing parameter η, the label ambiguity A = ⟨H(σ/π|ω)⟩, and the mutual information I—the calculations supply the wavefunctions, while η, A, and I are outputs of the symmetry-constrained S-matrix model built on this one extracted input. A single-parameter constraint structure emerges: given the extracted σ fraction, unitarity enforces the complementary fraction and angular-momentum projection orthogonality enforces zero σ character in the |ω| = 3/2 orbital. We obtain η = 0.722, A = 0.453 nats, and I = 0.646 nats. The restructuring is a smooth crossover driven by the spin–orbit coupling strength λ, with η decreasing from 1.00 and I decreasing from ln 3 ≈ 1.099 nats in the nonrelativistic limit, the steepest change in A and I occurring near λ ≈ 0.4. All reported values are produced by a self-consistent, reproducible analysis pipeline, and are stress-tested by five numerical validation experiments (pairing-algorithm robustness, noise injection, subspace closure, the CN− null test, and a basis-set incompleteness model), which rule out numerical noise as the origin of the mixing signatures. Our findings demonstrate that the “anomalies” in heavy-element chemistry are not exceptions to existing rules but rather the manifestation of rule reorganization when the system crosses from the nonrelativistic to the relativistic regime.
ER -