# ⚛  L1 Principle — Post-Hartree-Fock Correlated Methods (MP2, CCSD, CI)

**ID:** `L1-296` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Electron correlation beyond mean-field*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** correlated wavefunction
> **📡 Carrier:** electron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554113

---

## 🧠 1. Introduction

**Post-Hartree-Fock Correlated Methods (MP2, CCSD, CI)** is a **nonlinear inverse problem** whose unknown lives in **correlated wavefunction** space, within the **Electron correlation beyond mean-field** sub-domain of **Computational Chemistry**.

Measurements consist of electrons collected by an electron detector via a **high accuracy quantum chem** sensing mechanism.

The forward operator applies, in order: E · hf reference operator; E · correlation expand operator; computes eigen-pairs of a linear operator; O · correlated energy operator.

Observations are corrupted by additive Gaussian noise. Formally well-defined; convergence with basis slow (1/N^3 for CCSD); scaling N^6-N^7 limits size.

## ⚙ 2. Forward Model

Physical chain: **x** → E · hf reference → E · correlation expand → O · correlated energy → **y** (detector).

```
y = `O.correlated_energy` `E.correlation_expand` `E.hf_reference` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.hf_reference` | E · hf reference operator |
| `E.correlation_expand` | E · correlation expand operator |
| `O.correlated_energy` | O · correlated energy operator |

**🛠 Solver components** _(used inside the solver, not in the forward equation)_:

| Primitive | What it does |
|---|---|
| `E.eigensolve` | Computes eigen-pairs of a linear operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Electron correlation beyond mean-field |
| Carrier | electron |
| Problem class | nonlinear_inverse |
| Solution space | correlated_wavefunction |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 10 |
| L dag | 4 |

## 📡 4. Measurement Model

Formally well-defined; convergence with basis slow (1/N^3 for CCSD); scaling N^6-N^7 limits size.

| Metric | Value |
|---|---|
| Metric | reaction_energy_error_kcal_mol |
| Secondary | barrier_height_error_kcal_mol |

## 📏 5. Operating Range (Ω)

**Center problem class:** `post_hartree_fock` · **Forward operator:** `ccsd_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Basis | — | cc-pVTZ |
| Method | — | CCSD(T) |
| N basis | — | 200 |
| N electrons | — | 10 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Basis | — | cc-pVDZ, cc-pVTZ, cc-pVQZ, aug-cc-pV5Z |
| Method | — | MP2, CCSD, CCSD(T), CCSDT |
| N basis | — | 20 – 5000 |
| N electrons | — | 2 – 300 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** reaction E <= 1 kcal/mol

| Metric | Range |
|---|---|
| Reaction energy error kcal mol | 0.1 – 10 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **reaction_energy_error_kcal_mol**, with κ = `2000` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x01658dc151f6d139d29d971bca48fa8fa669fe9c80eace9009eaa01a54eba56f`
- **Chain tx hash:** `0x17f0891fa6bab85ce815135bd16199b6002d65983ecea9973d5cbfebc22d940a`
- **Chain block:** `41554113`

---

## File Mapping

This bundle consists of: `L1-296.md`, `L1-296.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-296.md` | Source of truth — edit this | Human or LLM |
| `L1-296.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 `L1-296`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._