The Projector Augmented Wave method
The Projector Augmented Wave method
The Projector Augmented Wave method
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Completeness relationsFor |⃗r − ⃗R a | < rc a we must have:∑| ˜φ a i 〉〈˜p a i | = 1iFrom this follows that inside the augmentation spheres, ψ n and ˜ψ ncan be expanded in partial waves and pseudo partial wavesrespectively:| ˜ψ n 〉 = ∑ i| ˜φ a i 〉〈˜p a i | ˜ψ n 〉.|ψ n 〉 = ∑ i|φ a i 〉〈˜p a i | ˜ψ n 〉,In the interstitial region, we have ψ n = ˜ψ n .9
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