# ⚛  L1 Principle — Implicit Solvation Models (PCM, COSMO, SMD)

**ID:** `L1-305` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Chemistry — *Continuum dielectric solvent models*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** solvation free energy
> **📡 Carrier:** electron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554114

---

## 🧠 1. Introduction

**Implicit Solvation Models (PCM, COSMO, SMD)** is a **linear inverse problem** whose unknown lives in **solvation free energy** space, within the **Continuum dielectric solvent models** sub-domain of **Computational Chemistry**.

Measurements consist of electrons collected by an electron detector via a **solvation free energy** sensing mechanism.

The forward operator applies, in order: E · cavity tessellate operator; E · reaction field operator; a fixed-point or gradient iteration on the unknown; O · DG solv operator.

Observations are corrupted by additive Gaussian noise. Well-posed; model error dominates over numerical error.

## ⚙ 2. Forward Model

Physical chain: **x** → E · cavity tessellate → E · reaction field → O · DG solv → **y** (detector).

```
y = `O.DG_solv` `E.reaction_field` `E.cavity_tessellate` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.cavity_tessellate` | E · cavity tessellate operator |
| `E.reaction_field` | E · reaction field operator |
| `O.DG_solv` | O · dg solv operator |

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

| Primitive | What it does |
|---|---|
| `O.iter` | A fixed-point or gradient iteration on the unknown |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Chemistry |
| Sub domain | Continuum dielectric solvent models |
| Carrier | electron |
| Problem class | linear_inverse |
| Solution space | solvation_free_energy |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 3.2 |

## 📡 4. Measurement Model

Well-posed; model error dominates over numerical error.

| Metric | Value |
|---|---|
| Metric | DG_solv_error_kcal_mol |
| Secondary | pKa_shift_error |

## 📏 5. Operating Range (Ω)

**Center problem class:** `implicit_solvation` · **Forward operator:** `implicit_solvation_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Method | — | SMD/B3LYP |
| N atoms | — | 20 |
| Solvent | — | water |
| Cavity type | — | UFF |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Method | — | PCM, CPCM, COSMO, SMD |
| N atoms | — | 2 – 1000 |
| Solvent | — | water, ethanol, DMSO, toluene, hexane |

## 🎯 6. Tolerance (ε)

**Center tolerance:** DG_solv <= 0.5 kcal/mol

| Metric | Range |
|---|---|
| Dg solv error kcal mol | 0.2 – 10 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **DG_solv_error_kcal_mol**, with κ = `150` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x697c934e49e8a10fc2afe375fff87a3b64934aca165412190beffe17ba6f6296`
- **Chain tx hash:** `0x68fcc5c4295f37d808c51df313df43a339cdc1ce4eac20ba5c0884721f6a5c62`
- **Chain block:** `41554114`

---

## File Mapping

This bundle consists of: `L1-305.md`, `L1-305.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-305.md` | Source of truth — edit this | Human or LLM |
| `L1-305.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.
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> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-305`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._