The Projector Augmented Wave method

HamiltonianE = Ẽ + ∑ ∆E a (D a δEij),aδ ˜ψ= f n Ĥ ˜ψ nn∗Ĥ = − 1 2 ∇2 + ṽ + ∑ ∑|˜p a i 〉∆Hij〈˜p a a j |,aijwhere ṽ = δẼ/δñ = ṽ H + ṽ xc and∆H a ij = ∆Ea∂D a ij+ ∑ lm∂Q a lm∂D a ij∫d⃗rṽ H˜g a lmThe PAW method is a generalized Kleinman-Bylander nonlocalpseudopotential that adapts to the current environment!20