FeMoco Labs Reports Exact Solution to One of Chemistry's Hardest Problems, and a Candidate Catalyst for Fertilizer from Air, Water, and Sunlight

A century-old process

Half the people alive today are fed by fertilizer made through a single chemical process: Haber-Bosch, invented in 1909. Because it breaks nitrogen's triple bond at roughly 450°C and 200 atmospheres of pressure, it consumes about 2% of all energy produced on Earth and accounts for 1 to 3% of global CO₂ emissions. Its fundamental chemistry has not changed in more than a century.

FeMoco Labs, the first company launched by Beloved Ecosystem, is working on an alternative.

Learning from nature

Nitrogen-fixing bacteria have performed the same reaction for billions of years, at room temperature, in water, at ordinary pressure. They rely on an enzyme called nitrogenase, whose catalytic core is an iron-molybdenum cluster known as FeMoco. Scientists have long hoped to replicate what FeMoco does, but its electronic structure is so complex that it has been regarded as one of the hardest problems in computational chemistry, and a benchmark target for future quantum computers.

An exact answer

FeMoco Labs reports that it has solved FeMoco's standard benchmark model, the 76-orbital, 113-electron LLDUC Hamiltonian, exactly. The company certifies the model's ground-state energy at −22,140.967 hartree, pinned from above and below within two millionths of a hartree.

Until now, the field has relied on extrapolated estimates. The best of these, published in January 2026 by Zhai et al. of Caltech's Chan group, required about 2.77 million CPU core-hours on Caltech and Flatiron Institute computing clusters and placed the energy at −22,140.411 hartree. FeMoco Labs' certified value lies 556 millihartree lower, indicating that the true ground state holds substantially more correlation energy than the most advanced existing methods captured.

How the result is certified

The energy is certified from both directions: a lower bound established by a positive-definiteness (LDLᵀ) certificate, and an upper bound established by a Rayleigh-quotient certificate, both checked in exact rational arithmetic. The mathematical framework is formalized in the Lean 4 theorem prover against the mathlib library, and the computation is sealed with a Groth16 zero-knowledge proof, cryptographically bound to the public LLDUC Hamiltonian file.

The work is published in two preprints:

A Zero-Knowledge Proof for a 152-Bit Slater Determinant of FeMoco (doi.org/10.5281/zenodo.19683391)

A Zero-Knowledge Formal Proof of FeMoco's Active-Space Ground-State Energy (doi.org/10.5281/zenodo.19986746)

The preprints have not yet been peer reviewed.

From solution to catalyst

With FeMoco's electronic structure resolved, the team defined the electronic fingerprint a synthetic catalyst would need to reproduce, including spin state, magnetic moment, and how strongly its metal centers are correlated. Screening candidate compounds against that fingerprint, one matched: BE-1, predicted to produce ammonia from nitrogen and water at room temperature.

BE-1 now moves to laboratory testing. FeMoco Labs is at Technology Readiness Level 3, experimental proof of concept, and the next milestone is confirming in controlled experiments that BE-1 produces ammonia, using established safeguards such as ¹⁵N₂ isotope labeling.

Why it matters

If BE-1 performs as predicted, it could power the N1, a solar-driven unit the size of a shipping container that makes nitrogen fertilizer from air and water with no grid, no natural gas, and zero operating emissions. Fertilizer could be made where crops grow, including in regions today's supply chains serve poorly or not at all.

That is what Beloved Ecosystem was built to do: use human and artificial intelligence to solve hard problems, and build new engines of wealth in the communities that need them most. FeMoco Labs is the first of those engines.

Learn more at femocolabs.com.