Ab Initio Molecular Dynamics (Car-Parrinello / BOMD) L1-298

Computational ChemistryOn-the-fly DFT forces in MDδ=10 · hardL_DAG = 3.7📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

m_{I} \cdot d^{2} R_{I} / d t^{2} = - g r a d_{I} E_{D} F T [R]; C a r - P a r r in e l l o : m u \cdot d^{2} p h i_{i} / d t^{2} = - d E / d p h i_{i} \cdot + co n s t r ain t s

AIMD: forces from DFT at each step; Car-Parrinello integrates electronic DOFs as fictitious dynamics; Born-Oppenheimer MD solves SCF each step.

L-DAG

E.dft_forces -> D.time.symplectic -> O.trajectory

E.dft_forcesD.time.symplecticO.trajectory

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 1500

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

Solvability C

Solver class:: CPMD, CP2K, VASP-MD; Nose-Hoover / Parrinello-Rahman
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.