Combinatorial Information-Theoretic Model of Spin-Crossover Dynamics: An Algebraic Isomorphism for LIESST Kinetics and Mössbauer Spectroscopy

Overview We propose a parameter-free combinatorial information-theoretic model for the spin-crossover (SCO) dynamics in Iron(II) complexes. The active t2g subshell is treated as a discrete 6-state system whose informational limits are derived from Shannon entropy. Key Universal Invariants Two universal invariants emerge from this framework: Fundamental Impedance: Rfund = ln 2/6 ln 3 LIESST Activation Barrier: κinfo = ln 2/4 ln 3 Validation: The calculated barrier coincides with the experimental barrier of [Fe(ptz)₆](BF₄)₂ (Hauser, 1991) to within 1.8%. Spectroscopic Predictions & Cross-Validation A combinatorial asymmetry tensor (ηTSM) – based solely on the binary occupancy vector – yields the following Mössbauer quadrupole splitting plateaus: Low-Spin (LS): 0.34 mm s⁻¹ High-Spin (HS): 2.65 mm s⁻¹ Cross-validation with three archetypal SCO compounds shows excellent agreement. Thermodynamic Coupling & Extensions Temperature Dependence: When coupled to the Slichter-Drickamer thermodynamic fraction γHS(T), the model predicts the full temperature dependence of Δ EQ(T) with a mean squared error of 0.0060 (mm s⁻¹)² for [Fe(ptz)₆](BF₄)₂. Algebraic Isomorphism: The model contains no adjustable parameters, establishing a direct algebraic isomorphism between discrete information geometry and macroscopic SCO observables. Predictive Extensions: Extensions to d⁴ and d⁵ metal ions provide falsifiable predictions for future experimental validation. Status: Submitted to The Journal of Physical Chemistry Letters (ACS) id: jz-2026-018604