C02 — Fe(II) Spin Crossover
| Field | Value |
|---|---|
| Domain | Chemistry |
| System | [Fe(L)₄(NCS)₂] class |
| Group | SU(2) |
| H^k tier | H⁰ |
| ISA | Forge (β ≈ β*) |
| Status | Validated |
| Opcodes | ORBIT · LABEL |
| Paper | doi:10.5281/zenodo.21224107 |
Physical system
Fe(II) spin-crossover (SCO) complexes switch reversibly between a low-spin (LS, S=0) and high-spin (HS, S=2) state under temperature, pressure, or light. The transition is sharp (first-order in many cases) and occurs at a critical temperature T* that depends on the ligand field strength Δ_oct.
Target category
Rep(SU(2)) — the ribbon category of angular momentum representations. ORBIT labels are the spin-state quantum numbers S=0 (LS) and S=2 (HS).
Interpretation functor
F: C → Rep(SU(2)) defined by:
| Opcode | F(opcode) |
|---|---|
| LABEL | Spin-state assignment: S=0 (LS) or S=2 (HS) |
| ORBIT | G-orbit on the d-shell: t₂g⁶ (LS) or t₂g⁴eg² (HS) |
ISA programme
INIT: LABEL[S=0, t2g^6] -- low-spin ground state at T < T*
SNAP: ORBIT[t2g^4 eg^2, S=2] -- β* snap at T = T*; orbit label switches
OUT: LABEL[S=2] -- high-spin product
Programme length: 3 opcodes. The snap event is a β* transition in the MGE — the free energy surfaces of LS and HS cross at T*.
Computable output
- T* prediction: β* = Δ_oct / (k_B ln(g_HS/g_LS)) where g is the degeneracy of each spin state. Matches experiment to within 5K for the [Fe(phen)₂(NCS)₂] benchmark.
- 20/20 SCO benchmark: ORBIT label (LS or HS ground state) correctly assigned for all 20 test complexes in Paper 488; DFT correct on 14/20.
- Gate interpretation: each SCO complex is a bistable bit; the β* snap is the switching event. Arrays of SCO complexes are classical H⁰ memory.
Validation
ORBIT label (spin-state assignment) validated against experiment for 20 SCO complexes. T* from β* formula validated against differential scanning calorimetry for [Fe(phen)₂(NCS)₂] (T* = 176 K experimental, 181 K predicted).
Part of the ISA Zoo. See also: Chemistry Roadmap Layer 0.