Fertilizer from water, air and sunlight. Anywhere.

Haber-Bosch: a 117-year-old process the world can't quit

Half the people alive today are fed by fertilizer made from atmospheric nitrogen through a single chemical process: Haber-Bosch. Because breaking nitrogen's triple bond requires 450°C and 200 atmospheres of pressure, the industrial chemical process consumes 2% of all energy produced on Earth, and the fundamental chemistry behind it hasn't changed since 1909.

Nature already broke nitrogen's triple bond 3 billion years ago.

Every nitrogen-fixing bacterium on Earth converts nitrogen from the air into ammonia, but at room temperature, in water, at atmospheric pressure. No fossil fuels. No extreme heat or pressure. Every one of these bacteria relies on the same enzyme family to do it: nitrogenase. Its primary catalytic core is an iron-molybdenum cluster called FeMoco. No other enzyme in nature can break the nitrogen triple bond under ambient conditions.

We determined how FeMoco works. Then we identified the catalyst candidate.

Replicating what FeMoco does synthetically requires first understanding its electronic structure. FeMoco is strongly correlated: its 76 orbitals and 113 electrons occupy entangled configurations at once, none dominant.

The field has long assumed that solving FeMoco at this scale would require a quantum computer. We did it on a classical one.

The solution let us screen for a synthetic catalyst that replicates FeMoco's mechanism. One compound survived. We designated it BE-1.

Laboratory confirmation is next.

A century of experimental catalyst discovery has not produced a working ambient-condition alternative to Haber-Bosch. The search has faced two problems: knowing what to test, and knowing what worked. Researchers have used frameworks like DFT-based screening and bioinspired catalyst design. However, FeMoco's electron correlation is too strong for either to resolve precisely enough to specify the catalyst target. The second problem is measurement. Of 127 nitrogen-reduction studies reviewed in 2020 (Choi et al.), none could confirm a genuine result. Every reported result could be explained by contamination.

We've built a computational platform that resolves FeMoco's electronic structure on a classical computer. That capability turns catalyst discovery from a search into a specification. The specification hinges on one number: the ground-state energy of FeMoco's active space. It sets the reference against which every downstream property (spin states, orbital occupations, magnetic moments) is calculated. Get the energy wrong, and every property derived from it is wrong too.

In January 2026, Zhai et al. published the prior best estimate of FeMoco's ground-state energy, a calculation that required approximately 2.77 million CPU core-hours on the Flatiron Institute and Caltech high-performance computing clusters. We computed a value 556 mHa more accurate. That precision brought the electronic fingerprint of nitrogen fixation into focus, giving us the criteria a working catalyst must meet. We screened candidates against those criteria. One matched: BE-1.

Certification and zero-knowledge proofs

We computed the ground-state energy of FeMoco, accompanied by a formal proof of its logical correctness. This verification was conducted using Lean, a theorem-prover that validates mathematical arguments against the rules of formal logic.

To ensure the results are accessible and verifiable, the computation is sealed by a Succinct Non-interactive Argument of Knowledge (SNARK), a cryptographic certificate that any researcher can verify on a standard laptop in seconds, without re-executing the original large-scale computation.

The certification process is structured in two stages:

• Paper 1 establishes a certified reference electron configuration.
• Paper 2 utilizes that foundation to certify the full ground-state energy.

Both are certified against the LLDUC Hamiltonian, the standard 113-electron, 76-orbital benchmark model of FeMoco introduced by Li et al. (2019), defined by 33 million two-electron integrals.

Paper 1: FeMoco's Certified Reference Slater Determinant

Simulating FeMoco accurately starts with specifying where each of its 113 electrons sits among its 76 orbitals. That configuration is called a Slater determinant. Finding the one closest to the true ground state is the first computational challenge.

There are 3.6×10³⁵ possible Slater determinants for FeMoco's active space, each with an associated energy. Finding the right one is equivalent to finding a specific grain of sand among fifty quadrillion Earths.

We identified a single Slater determinant for the LLDUC Hamiltonian and encoded it as a 152-bit string: 76 bits for spin-up occupations, 76 for spin-down. Its certified energy is −22,053.165 Ha.

Paper 2: FeMoco's Certified Ground-State Energy

Starting from the reference determinant of Paper 1, our platform computed the additional correlation energy needed to reach the Full Configuration Interaction (FCI) ground-state energy of the LLDUC Hamiltonian and certified that value at −22,140.967 Ha.

Results: BE-1, electronic fingerprint identified from a 556 mHa precision advantage

We achieved a certified ground-state energy for FeMoco of −22,140.967 Ha, surpassing the prior best estimate of −22,140.411 Ha by 556 mHa (Zhai et al., 2026). At that precision, the electronic fingerprint of nitrogen fixation comes into focus, revealing the specific features any synthetic catalyst would need to reproduce.

FeMoco's diagnostic properties include per-site isomer shifts, effective magnetic moment, total spin, and inter-center mutual information. We then screened candidate catalysts against the full fingerprint.

One matched our diagnostics criteria. We designated it BE-1, an electronic twin to nitrogenase's active site predicted to catalyze ammonia from nitrogen and water at room temperature. A standard electrochemistry lab can test the prediction by measuring H₂:NH₃ ratio and Faradaic efficiency.