Density Functional Calculations:Plane Wave - Pseudopotential

Methods•Plane waves: Basis set and super cell geometry•Pseudopotential: Effective valence-ion core interaction•Optimization: Wavefunction, geometry, (super cell)

“Electronic Structure: Basic Theory and Practical Methods”, R. M. MartinM.C. Payne et al., Rev. Mod. Phys. 64, 1045 (1992)G. Kresse and J. Furthmuller, Phys. Rev. B54, 11169 (1996) (VASP)

Codes: VASP, DACAPO, CASTEP, CPMD, PWSCF, ABINIT, ...

Plane Wave Basis Set

K-point sampling of SBZSemi-conductors and insulators: band-gapMetals: no band-gap handled by Fermi surface smearing

Number of k-points in sampling ?

Less k-points for larger super cells(semi-conductors, insulators)

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*Iterative diagonalization: occupied states form a (very) smallSubset of the total set !

Conjugate gradients method:Restrict the search direction to paths that are orthogonal to all previous searches

DIIS: (Direct Inversion in Iterative Subspace method)Solve exactly by direct inversion an optimality condition withinthe subspace of states generatedby the iterations

Hellmann-Feynman force:

• Conjugate Gradient• DIIS• Quasi-Newton• ...