md2011-06-note_Part_13

md2011-06-note_Part_13 - DFT I One starts from an initial...

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I Requirements for a “good” pseudopotential are I All-electron and pseudo valence eigenvalues agree. I Wavefunctions agree beyound a chosen R c . I Logarithmic derivatives agree at R c . I The integrated charge inside R c for each wavefunction agrees ( norm-conservation ). I First energy derivative of the logarithmic derivatives of the wavefunctions agree at all r > R c . I The PAW pseudopotentials use combinations of smooth functions extending through space and localized contributions evaluated for “muffin-tin spheres” (intra-atomic regions). I Hence, the resulting total wavefunction is similar to the all-electron wavefunction. Notes
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DFT Algorithm I Solving the Kohn-Sham equations is in the heart of
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Unformatted text preview: DFT. I One starts from an initial guess for the density, and uses it to calculate the potential. I Using the potential, the KS equation is solved for the wavefunctions (matrix diagonalization). I Then new density is calculated, and the self-consistency is checked (i.e., did the n converge?). Initial guess n ( r ), n ( r ) Calculate potential V eff ( r ) = V ext ( r )+ V Hart [ n ]+ V xc [ n , n ] Solve KS equation [-½ ∇ 2 + V eff( r )] ψ i ( r ) = ε i ψ i ( r ) Calculate electron density n ( r ) = Σ i fi | ψ i( r )|2 Self-consistent? No Yes Output quantities ( E , f , ε ,...) Notes S±²²³´µ I A. Notes...
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