# The Unbound Mean Field model of Catalysis

> A research tool that computes apparent kinetic descriptors — apparent
> reaction order (gamma_m), Tafel slope (b), and apparent activation energy
> (E_app) — for arbitrary heterogeneous and electrocatalytic reaction
> networks, from a single domain-independent kinetic matrix K. All three
> descriptors are realisations of the same mathematical object,
> gamma_xi = d ln r_net / d xi, evaluated for the perturbation variable xi
> of each domain (concentration, electrode potential, temperature). Free
> to use; developed at Aalborg University and the CAPeX Pioneer Center.

This file follows the [llms.txt](https://llmstxt.org/) convention so that
language-model agents can discover both the human-facing app and a
machine-callable API for it.

## What this app does

Given an elementary reaction network (e.g. `H2 <=> 2 *H`), a few
phenomenological parameters per step (reversibility chi, symmetry beta,
optional electron transfer count z, optional activation energy E_A), and
a lateral-interaction matrix Psi between adsorbed species, the app
returns:

- The apparent reaction order gamma_m for every external species
- The Tafel slope b in mV/decade (when any step transfers electrons)
- The apparent activation energy E_app in kJ/mol (when any E_A > 0)
- The full topology / kinetic matrix K
- All limiting "stationary regimes" (every combination of chi in {0, 1}
  and Psi-row in {0, infinity}) as a downloadable spreadsheet
- A best-match search: given a measured gamma vector, which microscopic
  regimes are even compatible with it

Typical users: catalysis and electrochemistry students, researchers
interpreting experimental Tafel / order data, and anyone teaching
Sabatier / volcano / microkinetic concepts.

## Key terms (for vocabulary disambiguation)

- **UMF** = Unbound Mean Field. A coverage-response framework that drops
  the global site-balance constraint of classical Langmuir-Hinshelwood
  kinetics and replaces it with pair-dependent lateral interactions Psi.
- **Generalised apparent reaction order** = a single mathematical
  observable gamma_xi that unifies reaction order, Tafel slope, and
  apparent activation energy into one determinant ratio.
- **Reference species `*`** = a pure book-keeping gauge (not a free-site
  count) used to make V_R / V_P square. The boundary condition annihilates
  its column; predicted gamma_xi is invariant to the gauge.
- **Stationary regime** = a corner of the (chi, Psi) parameter cube where
  every step is either irreversible or quasi-equilibrated and every
  Psi-row is either zero or infinite.

## API (machine-callable)

A JSON HTTP API exposes everything the in-browser app does. It is
unauthenticated and CORS-open.

- [OpenAPI 3 schema (canonical, machine-readable)](https://reactionorders.energy.aau.dk/openapi.json)
- [Swagger UI (human-readable, try-it-live)](https://reactionorders.energy.aau.dk/docs)
- [ReDoc (alternative human-readable view)](https://reactionorders.energy.aau.dk/redoc)

### Recommended entry points

- `POST /api/analyze` — combined parse + compute in a single call. The
  electron-transfer vector z is inferred automatically from the
  equations. Recommended for programmatic use.
- `POST /api/parse` — parse a reaction network into stoichiometric
  matrices, species lists, the net reaction, and z.
- `POST /api/compute` — compute reaction orders given pre-parsed matrices
  and parameters.
- `POST /api/regimes-match` — given a target gamma vector, rank all
  limiting regimes by how closely they reproduce it.
- `GET  /api/example` — return a Haber-Bosch starter network.

### Minimal example (curl)

```
curl -X POST https://reactionorders.energy.aau.dk/api/analyze \
  -H 'Content-Type: application/json' \
  -d '{
    "equations": "H+ + e- <=> *H\n2 *H <=> H2",
    "chi":   [1.0, 0.0],
    "beta":  [0.5, 0.5],
    "Psi":   [[0.0]],
    "T_ref": 298.15
  }'
```

## MCP server (for agentic clients)

For Claude.ai, Claude Desktop, Claude Code, and Cursor users, the same
compute endpoints are exposed as a Model Context Protocol server at:

- MCP endpoint: <https://reactionorders.energy.aau.dk/mcp>

To use it, paste this URL as a custom remote MCP connector in the host
client's settings (e.g. Claude.ai → Settings → Connectors → Add custom
connector). The exposed tools cover network parsing, descriptor
computation, regime enumeration, and best-regime matching.

## Scientific background

- [How does it work? (full theory, plain-text mirror with raw LaTeX)](https://reactionorders.energy.aau.dk/how-it-works.md)
  — a self-contained walkthrough of the UMF framework: the elementary
  rate law, the universal balance equation, the construction of the
  kinetic matrix K, the three driving-force vectors, and the closed-form
  determinant ratio for the apparent reaction order gamma_xi. Mirrors
  the in-app "How does it work?" section for non-JS-executing crawlers,
  with inline `[KO]` / `[TC]` references at every claim that comes from
  one of the two underlying manuscripts.
- **[KO]** Brandes, B. A. & Vegge, T., *On the Universal Algebraic
  Structure of Kinetic Observables in Catalysis*, 2026 (in preparation;
  DOI to be added).
- **[TC]** Brandes, B. A., Hansen, H. A., Vegge, T. & Chatzichristodoulou, C., *Correcting the Foundations of
  Tafel Analysis in Electrocatalysis*, 2026 (in submission; DOI to be
  added).

## Licensing & attribution

The intellectual property for the underlying model and this web
implementation rests with Aalborg University. The geolocation lookup uses
DB-IP Lite under CC BY 4.0 and stores only aggregated city counts (no IP
addresses are persisted). Contact: see the *Legal Notice* link in the app.