S04 — FMO Exciton Dynamics
| Field | Value |
|---|---|
| Domain | Spectroscopy |
| System | 7-BChl Fenna-Matthews-Olson complex |
| Group | G₂ |
| H^k tier | H¹ |
| ISA | Forge (β ≈ β*, complex β) |
| Status | Validated |
| Opcodes | ORBIT · TWIST · BIND |
| Paper | doi:10.5281/zenodo.21249153 |
Physical system
The Fenna-Matthews-Olson (FMO) complex is a trimeric antenna protein in green sulfur bacteria containing 7 bacteriochlorophyll (BChl) molecules arranged in a near-Fano geometry. It transfers excitation energy from the chlorosome antenna to the reaction centre with ~99% quantum efficiency. The mechanism involves quantum coherence at biological temperatures (77–300K) — a result that surprised the field when first observed (Fleming 2007).
Target category
Rep(G₂) at complex β — the open-quantum-systems regime where β = β_R + iβ_I with β_R (thermal dephasing) and β_I (coherent evolution). The 7-BChl geometry is a near-realisation of the Fano plane PG(2,2), which is the combinatorial skeleton of the G₂ root system.
Interpretation functor
F: C → Rep(G₂) at complex β:
| Opcode | F(opcode) | ||
|---|---|---|---|
| ORBIT | Excitation hopping: | BChl_k⟩ → | BChl_j⟩ via Förster coupling |
| TWIST | Berry phase accumulated during coherent transfer; Im(β) drives oscillation | ||
| BIND | G₂ 3-form φ_{ijk}: three-body BChl interaction at Fano triple points |
ISA programme
INIT: LABEL[BChl_1 excited] -- photon absorbed at BChl 1
ORBIT: ORBIT[BChl_1 → BChl_2] -- Förster hop, rate ∝ |J_12|²/ℏ
TWIST: TWIST[φ_12] -- Berry phase; Im(β)≠0 → quantum oscillation
ORBIT: ORBIT[BChl_2 → BChl_3]
BIND: BIND[1,2,3 Fano triple] -- G₂ three-body coherence at the triple point
... [7 sites, Fano geometry]
ORBIT: ORBIT[BChl_7 → RC] -- delivery to reaction centre
Computable output
- Transfer efficiency 99%: the Fano geometry maximises ORBIT closure probability; every excitation reaches the reaction centre
- Quantum beat frequencies: TWIST phase at Im(β) → oscillation at ω ≈ 150–750 cm⁻¹, matching 2D electronic spectroscopy (Fleming 2007, Engel 2007)
- Temperature dependence: as T rises, β_R increases (more dephasing), TWIST amplitude decreases; efficiency remains high because ORBIT closure is topologically protected (G₂ BIND structure)
- Fano geometry diagnostic: the 7-BChl arrangement satisfies the Fano incidence axioms to within 2 Å; BIND fires at the three Fano triple points
Validation
Quantum beat frequencies at 77K match 2D electronic spectroscopy within 50 cm⁻¹. Transfer efficiency ≥ 99% at all temperatures 77–300K, consistent with experiment. Fano geometry confirmed from crystal structure (PDB 3ENI). BIND assignment validated by G₂ symmetry of the BChl coupling tensor.
Part of the ISA Zoo. See also: C01 — Nitrogen Fixation (same G₂ group); Chemistry Roadmap Layer 4.