The electronic ground state and low-lying spectrum of the nitrogenase FeMo-cofactor in its protein environment

• Model Hamiltonian. Reiher et al. (2017) used a CAS of about 54 electrons in 54 orbitals as the target for fault-tolerant quantum phase estimation. Li et al. (arXiv:1809.10307, J. Chem. Phys. 2019) argued that the FeMoco ground-state problem is characterised by many spin-state candidates close in energy.
• Classical estimate to chemical accuracy (preprint). Zhai, Li, Zhang, Li, Lee and Chan (arXiv:2601.04621, January 2026, preprint) report a ground-state energy for a FeMoco model to chemical accuracy using high-order coupled cluster (UCCSDTQ) plus extrapolated DMRG, identify several spin-isomer candidates degenerate to chemical accuracy, and examine the impact of extra excitations and geometry on the low-lying landscape. They report a wall-clock cost for their largest DMRG sweeps that is of the same order as published fault-tolerant quantum estimates for the same model at 1 kcal/mol (both figures are the authors' own accounting, on their own hardware and under assumptions such as order-one initial-state overlap; neither has been independently reproduced, so the comparison should be read as indicative rather than settled). This weakens the case that the standard model Hamiltonian needs a quantum computer; the work has not yet been through peer review as far as this entry knows.
• Alternative classical studies. A March 2026 conference abstract using selected CI reports that FeMoco and Fe–S clusters lie near the edge of classical feasibility while P450 and Ru clusters are tractable, and that baselines differ because problem definitions differ (APS March Meeting 2026; abstract only). Legeza et al. (arXiv:2603.28648, preprint) report a high-accuracy classical ground-state energy for an Fe$_4$S CAS(54,36) model space and CAS-SCF orbital optimisation for active spaces up to 89 electrons in 102 orbitals.

Understanding how nitrogenase breaks the N≡N bond at ambient conditions informs catalysts for ammonia synthesis (a process consuming around 1–2% of world energy via Haber–Bosch) and clarifies the electronic structure of metal–sulfur clusters generally. As a benchmark, the model problem defines whether a quantum computer offers an edge for this class of molecule.

Model problem: an energy of the agreed active-space Hamiltonian (published coefficients) with a rigorous bound or independent agreement of two methods within 1 kcal/mol. Real system: a first-principles ground-state and low-lying-state assignment of the E$_0$ and E$_4$ states that reproduces measured spectroscopic parameters (Mössbauer isomer shifts, hyperfine and zero-field splittings) within experimental error, with the environment included.