Identification of a Statistically Dominant Slater Determinant for the FeMo-Cofactor in the Full CAS(999e, 1455o) Active Space: A 1998-Qubit Result with Independent Ab-Initio Energy Verification
Abstract
We report the statistically dominant Slater determinant for the FeMo-cofactor (FeMoco) of nitrogenase in the full CAS(999e,1455o) active space — 1,998 spin-orbitals spanning a Hilbert space exceeding 10⁸⁰⁰ configurations. This is the second and final paper in a two-paper series. Paper 1 (Belzberg & Belzberg, 2026a) established the statistically dominant Slater determinant for the 152-spin-orbital CAS(113e,76o) benchmark, validated against the Li et al. (2019) FCIDUMP integrals to yield E = −22,109.68 Hartrees.
The present paper extends the series to the full active space, a regime that has never been characterized at the full CAS(999e,1455o) scale by any computational method.
The statistically dominant Slater determinant is identified using QnWave Inc.’s patent-pending Quantum Computing Service (QCS) and the DIRL (Dynamically Iterated Residue Locking) protocol. It achieves a Lock-Confidence ratio of 1,423.4× — exceeding the 200× discovery threshold by more than 7× — and an Orbital Energy Proxy E_proxy = 166.1864. It contains 999 electrons (500α/499β, 2S_z = +1), 104 singly occupied spatial orbitals distributed across all five orbital energy bands, 381 closed-shell orbitals, and 14 empty orbitals.
Full algorithmic details of the QCS/DIRL methodology are proprietary and withheld pending patent issuance. The complete configuration is disclosed via a publicly verifiable Residue ID (1,998-bit integer), accompanied by open-source verification scripts, structural analysis, and independent ab-initio energy verification against the public Li et al. (2019) Hamiltonian (ΔE = 0.126 mHa). This enables immediate community inspection and chemical analysis.
The ground state configuration identified by QCS for the CAS(113e,76o) benchmark is independently verified against the Li et al. (2019) ab-initio Hamiltonian via full single-determinant energy ⟨Ψ|H|Ψ⟩, yielding a total energy of −22,109.680126 Ha — a deviation of 0.126 mHa from the published DMRG result of −22,109.680 Ha. This is 7.9× better than chemical accuracy (1 mHa threshold) and constitutes an independent quantitative verification that QCS identifies the correct ground state configuration at the benchmark scale, directly supporting its application at the larger scales reported here.
In addition to the primary 1998-qubit result, this paper reports two intermediate experiments at 808 and 1500 spin-orbitals. Taken together with Paper 1, the four data points reveal a systematic open-shell dilution law: the open-shell fraction decreases monotonically from 51.3% (152 qubits) through 23.2% (808 qubits) and 16.7% (1500 qubits) to 7.1% (1998 qubits). The conservation of the topological invariant n_open^core ≈ 38 ± 5 in the core Fe₇MoS₉C framework across all four scales provides model-independent evidence that the method operates within the correct physical
symmetry sector.