Marcus Electron Transfer theory is a cornerstone of modern chemistry and electrochemistry. It explains how electron-transfer rates depend on thermodynamic driving force (ΔG°), reorganization energy (λ), and electronic coupling, including the characteristic transitions through normal, barrierless, and inverted regimes.
Within the Unified Conceptual Framework / Grand Unified Tensor Theory (UCF/GUTT), the core structure of Marcus theory has been reconstructed from first principles using discrete relational tensors (NRTs), clock hierarchy coherence (CHC), and resonance separation machinery (PSB).
The critical advance is not merely formalization, but derivation: the parabolic reactant and product energy surfaces — classically taken as postulates — are here proved to be the unique Q-quadratics satisfying three explicit CHC-grounded boundary conditions. That inversion, from assumption to theorem, defines the UCF/GUTT approach.
The 15-file development establishes:
- Parabolic energy surfaces as the unique Q-quadratics derived from relational boundary conditions — not assumed.
- The classical activation barrier ΔG‡ = (λ + ΔG°)²/(4λ) as a proven theorem.
- A novel robust certificate for the inverted regime that holds under simultaneous bounded drift in both ΔG° and λ.
- A complete layered derivation chain: NRT structural mismatch → CHC-grounded reorganization energy → PSB resonance separation → full three-regime Marcus theory.
- Constructive rate expressions using Taylor partial sums and Babylonian square-root approximations, each with explicit error bounds — results are certifiable, not merely computable.
- NRT mismatch equipped with pseudometric structure, yielding a clean relational lower bound on reorganization energy.
All results are proved with zero new axioms and zero admits, enforced library-wide by mechanical audit across 118 theorems. This architectural guarantee ensures that no theorem in the Marcus stack can introduce an axiom without breaking the entire build.
This work demonstrates that a foundational relational framework can generate a coherent, formally verified descendant of an established physical theory by deriving — rather than importing — its foundational commitments. It indicates that UCF/GUTT possesses genuine generative capacity for physical science, with natural extension paths into electrochemistry, energy conversion, materials modeling, and other charge-transfer domains.
Technical details, the full Coq development, and supporting formal materials are available on a limited basis for qualified research, licensing, evaluation, or partnership discussions.
Intellectual Property Notice The Unified Conceptual Framework / Grand Unified Tensor Theory (UCF/GUTT), related chemistry applications, formal artifacts, source code, algorithms, documentation, and associated materials are proprietary works owned by Michael Fillippini. All rights are reserved, including copyrights, trade secrets, patent rights, and trademarks where applicable. No unauthorized use, reproduction, distribution, modification, adaptation, or commercial exploitation is permitted without express written permission.
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