L1 ⚛ L1-297 ⊙ Testnet

Time-Dependent Density Functional Theory (TDDFT)

Computational Chemistry · Excitation spectra and dynamics

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⬇ L1-297.md

# ⚛ L1 Principle — Time-Dependent Density Functional Theory (TDDFT) **ID:** `L1-297` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Chemistry — *Excitation spectra and dynamics* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** excitation spectrum > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554113 --- ## 🧠 1. Introduction **Time-Dependent Density Functional Theory (TDDFT)** is a **linear inverse problem** whose unknown lives in **excitation spectrum** space, within the **Excitation spectra and dynamics** sub-domain of **Computational Chemistry**. Measurements consist of photons collected by an optical detector via a **uv vis spectroscopy** sensing mechanism. The forward operator applies, in order: E · tddft kernel operator; computes eigen-pairs of a linear operator; O · excitations operator. Observations are corrupted by additive Gaussian noise. Adiabatic approximation breaks down for double excitations and charge-transfer states. ## ⚙ 2. Forward Model Physical chain: **x** → E · tddft kernel → O · excitations → **y** (detector). ``` y = `O.excitations` `E.tddft_kernel` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.tddft_kernel` | E · tddft kernel operator | | `O.excitations` | O · excitations 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 | Excitation spectra and dynamics | | Carrier | photon | | Problem class | linear_inverse | | Solution space | excitation_spectrum | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 5 | | L dag | 3.6 | ## 📡 4. Measurement Model Adiabatic approximation breaks down for double excitations and charge-transfer states. | Metric | Value | |---|---| | Metric | excitation_energy_error_eV | | Secondary | oscillator_strength_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `time_dependent_dft` · **Forward operator:** `tddft_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Xc | — | B3LYP | | N atoms | — | 20 | | N basis | — | 500 | | N states | — | 20 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Xc | — | B3LYP, CAM-B3LYP, wB97X-D | | N atoms | — | 2 – 500 | | N basis | — | 50 – 10000 | | N states | — | 5 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** excitation E <= 0.15 eV | Metric | Range | |---|---| | Excitation energy error ev | 0.03 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **excitation_energy_error_eV**, with κ = `700` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc0380521533593c72ac2e3d09ca5a4ba111ba0237253bd2f65f470905a6e9f76` - **Chain tx hash:** `0x8e7aecefa556914651be64a50ce5363c5666627f563d6869d7c3a4a0a092921a` - **Chain block:** `41554113` --- ## File Mapping This bundle consists of: `L1-297.md`, `L1-297.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-297.md` | Source of truth — edit this | Human or LLM | | `L1-297.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 `L1-297`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-297.md).
Regenerate L1-297.json so every field matches the Markdown.
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L2-297-001 Time-Dependent Density Functional Theory (TDDFT) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554113,
  "chain_hash": "0xc0380521533593c72ac2e3d09ca5a4ba111ba0237253bd2f65f470905a6e9f76",
  "chain_tx_hash": "0x8e7aecefa556914651be64a50ce5363c5666627f563d6869d7c3a4a0a092921a",
  "domain": "Computational Chemistry",
  "hardness_fn": {
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    "metric": "excitation_energy_error_eV",
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    "regime": "Adiabatic approximation breaks down for double excitations and charge-transfer states.",
    "secondary": "oscillator_strength_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.6,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Computational Chemistry",
    "integration_axis": "energy",
    "noise_model": "gaussian",
    "primitives": [
      "E.tddft_kernel",
      "E.eigensolve",
      "O.excitations"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "uv_vis_spectroscopy",
    "solution_space": "excitation_spectrum",
    "sub_domain": "Excitation spectra and dynamics",
    "title": "Time-Dependent Density Functional Theory (TDDFT)"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "N_basis",
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    "center_spec": {
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      "forward_operator": "tddft_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_basis": 500,
        "N_states": 20,
        "xc": "B3LYP"
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    "epsilon_bounds": {
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        0.03,
        1.0
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    },
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        500
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      "N_states": [
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      "xc": [
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        "CAM-B3LYP",
        "wB97X-D"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Excitation spectra and dynamics",
  "title": "Time-Dependent Density Functional Theory (TDDFT)"
}

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