Prime-Driven Quantum Criticality in Ternary Alloys for CO₂ Catalysis: A Theoretical and Computational Framework

The document presents a theoretical framework proposing that prime-indexed stoichiometries in FCC ternary alloys (e.g., Au_3Fe_2Ni) induce quantum critical states through symmetry-constrained phonon modes. These prime harmonics (\omega_p = 5 \log p meV) are predicted to resonantly couple to CO_2 bending vibrations, reducing activation energy to E_a = 0.42 eV. The Coherence Evolution Model (CEM) unifies group theory and quantum critical phenomena, with open-source protocols for future experimental validation. Key Concepts and Findings: * Prime-Enforced Symmetry Breaking: Ternary alloys with prime stoichiometric ratios enforce irreducible FCC lattice symmetries, generating phonon modes resonant with CO_2 bending vibrations. * Group theory analysis shows that prime stoichiometries eliminate reducible representations in the dynamical matrix. * Prime-indexed lattice vectors preserve 7-fold rotational symmetry, quantizing force constants and yielding irreducible phonon modes. * ζ-Zero Electron Density Criticality: At critical electron density, the grand potential diverges near ζ-function zeros, predicting activation energy quantization. * The document establishes a mechanistic link between ζ-zeros and density singularities through Green's function analysis. * Computational Validation: * DFT and phonon dispersion calculations using VASP confirm the existence of an isolated 667 cm^{-1} mode in Au_3Fe_2Ni. * Nudged Elastic Band (NEB) calculations show a lower activation energy (E_a = 0.43 \pm 0.02 eV) for CO_2 dissociation in Au_3Fe_2Ni compared to a control alloy. * Ab initio molecular dynamics (AIMD) simulations predict a rate constant of k = 2.3 \times 10^3 s^{-1}. * Predicted Experimental Signatures: * The document outlines protocols for synthesizing and characterizing prime-driven catalysts, including RF sputtering and LEED/XRD for symmetry verification. * It predicts specific FTIR and Raman spectroscopic data, as well as performance metrics like activation energy and TOF. * Addressing Skepticism: The document addresses potential critiques regarding the physical basis of primes in catalysis, the link to ζ-zeros, and reproducibility concerns, providing detailed responses and open-source resources for replication.