Kohn-Sham Density Functional Theory L1-294

Computational ChemistryGround-state electronic structureδ=5 · challengingL_DAG = 3.3📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

(- (hba r^{2} /2 m) \cdot L a pl a c ian + V_{e} x t (r) + V_{H} a r t r ee (r) + V_{x} c (r)) p h i_{i} (r) = E_{i} p h i_{i} (r); r h o (r) = i \sum ∣ p h i_{i} ∣^{2}

Kohn-Sham DFT: map N-electron interacting problem to non-interacting auxiliary system with same density; self-consistent via V_Hartree + V_xc[rho].

L-DAG

E.potential_ext -> E.hartree_xc -> E.eigensolve -> O.density_energy

E.potential_extE.hartree_xcE.eigensolveO.density_energy

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 600

Well-posed (Hohenberg-Kohn theorem); XC functional approximation is dominant error source.

Solvability C

Solver class:: VASP, Quantum ESPRESSO, Gaussian, ORCA, NWChem; Pulay DIIS / Broyden mixing
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.