# ⚛  L1 Principle — Ab Initio Molecular Dynamics (Car-Parrinello / BOMD)

**ID:** `L1-298` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *On-the-fly DFT forces in MD*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** atomic trajectory plus orbitals
> **📡 Carrier:** electron · **🌫 Noise:** thermal langevin
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554113

---

## 🧠 1. Introduction

**Ab Initio Molecular Dynamics (Car-Parrinello / BOMD)** is a **nonlinear inverse problem** whose unknown lives in **atomic trajectory plus orbitals** space, within the **On-the-fly DFT forces in MD** sub-domain of **Computational Chemistry**.

Measurements consist of electrons collected by an electron detector via a **trajectory observable** sensing mechanism.

The forward operator applies, in order: E · dft forces operator; D · time · symplectic operator; O · trajectory operator.

Observations are corrupted by Langevin-type thermal fluctuations. Well-posed locally; ergodic sampling requires long trajectories; DFT error propagates.

## ⚙ 2. Forward Model

Physical chain: **x** → E · dft forces → D · time · symplectic → O · trajectory → **y** (detector).

```
y = `O.trajectory` `D.time.symplectic` `E.dft_forces` x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.dft_forces` | E · dft forces operator |
| `D.time.symplectic` | D · time · symplectic operator |
| `O.trajectory` | O · trajectory operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | On-the-fly DFT forces in MD |
| Carrier | electron |
| Problem class | nonlinear_inverse |
| Solution space | atomic_trajectory_plus_orbitals |
| Noise model | thermal_langevin |
| Integration axis | time |
| Difficulty delta | 10 |
| L dag | 3.7 |

## 📡 4. Measurement Model

Well-posed locally; ergodic sampling requires long trajectories; DFT error propagates.

| Metric | Value |
|---|---|
| Metric | diffusion_coeff_relative_error |
| Secondary | rdf_L2 |

## 📏 5. Operating Range (Ω)

**Center problem class:** `ab_initio_md` · **Forward operator:** `aimd_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Xc | — | PBE |
| T k | — | 300 |
| Dt fs | — | 0.5 |
| N atoms | — | 64 |
| N steps | — | 10000 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Xc | — | LDA, PBE, B3LYP |
| T k | — | 4 – 5000 |
| Dt fs | — | 0.01 – 5 |
| N atoms | — | 8 – 10000 |
| N steps | — | 1000 – 10000000.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** D rel error <= 0.05

| Metric | Range |
|---|---|
| Diffusion coeff relative error | 0.02 – 0.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **diffusion_coeff_relative_error**, with κ = `1500` and δ = `10`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x098f7fc316e02a630384a7ffa9fa8d90623f88dc6586d2192161c9b6feb66ef1`
- **Chain tx hash:** `0xddbabc4b25ae2e56bc698b5abe8d705a56abbc12116c8a3f3bcf976f53e2be0d`
- **Chain block:** `41554113`

---

## File Mapping

This bundle consists of: `L1-298.md`, `L1-298.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-298.md` | Source of truth — edit this | Human or LLM |
| `L1-298.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-298`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._