The Projector Augmented Wave method
The Projector Augmented Wave method
The Projector Augmented Wave method
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Finally ...... we have E C = ẼC + ∑ a (Ea C − Ẽa C ), where ẼC has contributionsfrom all of space:(∫ ñ(⃗r) + ∑ ˜ZẼ C = d⃗rd⃗r ′ a a (⃗r − R ⃗ ) (a ) ñ(⃗r ′ ) + ∑ ˜Z a a (⃗r ′ − R ⃗ )a )|⃗r − ⃗r ′ ,|and EC a − Ẽa C is a correction from each augmentation sphere:()∫EC a = d⃗rd⃗r ′ (na (⃗r) + Z a (⃗r)) n a (⃗r ′ ) + Z a (⃗r ′ )|⃗r − ⃗r ′ ,|(∫ ñ a (⃗r) + ˜Z) ()a (⃗r) ñ a (⃗r ′ ) + Z a (⃗r ′ )ẼC a = d⃗rd⃗r ′ |⃗r − ⃗r ′ |16
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