The Projector Augmented Wave method

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PBE atomization energy of anitrogen moleculefrom ASE import Atom , ListOfAtomsfrom gridpaw import Calculatora = 8.0 # size of unit cellh = 0.18 # grid spacingN = ListOfAtoms ([ Atom (’N’ , (0 , 0 , 0) , magmom =3)],cell =(a , a , a) , periodic =1)calc = Calculator ( nbands =4 , xc=’PBE ’ , h=h)N. SetCalculator ( calc )e1 = N. GetPotentialEnergy()d = 1.1 # bond lengthN2 = ListOfAtoms ([ Atom (’N’ , [0 , 0 , 0]) ,Atom (’N’ , [0 , 0 , 1.1]) ],cell =(a , a , a) , periodic =1)calc = Calculator ( nbands =5 , xc=’PBE ’ , h=h)N2. SetCalculator ( calc )e2 = N2 . GetPotentialEnergy()print 2 * e1 - e2 , ’eV ’22
Convergencespd 11 22 221 222 321 231∆E (eV) 10.016 10.141 10.520 10.519 10.519 10.514l max 0 1 2∆E (eV) 10.520 10.574 10.560Dacapo Blaha et al. Experiment∆E (eV) 9.611 10.546 9.90923
Page 1 and 2: The Projector AugmentedWave method
Page 3 and 4: LiteratureThe PAW method was invent
Page 5 and 6: Platinum atom43211s2s3s4s5s6s2p3p4p
Page 7 and 8: Electron densityn= ñ plane waves/c
Page 9 and 10: Completeness relationsFor |⃗r −
Page 11 and 12: Electron density (continued)n = ∑
Page 13 and 14: Compensation chargesLet Z a (⃗r)
Page 15 and 16: Compensation charges (continued)Usi
Page 17 and 18: • Frozen core states.Approximatio
Page 19 and 20: Exchange-correlation energyE xc =
Page 21: OrthogonalityKeep the wave function

The Projector Augmented Wave method

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