Transcription of VASP: Basics (DFT, PW, PAW, … )
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VASP: Basics (DFT, PW, PAW, … )
VASP: Basics (DFT, PW, PAW, .. )University of Vienna,Faculty of Physics and Center for Computational Materials Science,Vienna, AustriaOutline Density functional theory Translational invariance and periodic boundary conditions Plane wave basis set The Projector-Augmented-Wave method Electronic minimizationThe Many-Body Schr dinger equation H (r1,..,rN)=E (r1,..,rN)0@ 12Xi i+XiV(ri)+Xi6=j1|ri rj|1A (r1,..,rN)=E (r1,..,rN) (r1,..,rN)!{ 1(r), 2(r),.., N(r)}For instance, many-body WF storage demands are prohibitive:A solution: map onto one-electron theory:5 electrons on a 10 10 10 grid ~ 10 PetaBytes! (r1,..,rN)(#grid points)NHohenberg-Kohn-Sham DFTE[ ]=Ts[{ i[ ]}]+EH[ ]+Exc[ ]+EZ[ ]+U[Z] (r1,..,rN)=NYi i(ri) (r)=NXi| i(r)|2 12 +VZ(r)+VH[ ](r)+Vxc[ ](r) i(r)= i i(r) (r1.)
The PAW orbitals (cont.) ⇣ 1 2 + ev e↵ + X ij |pe iiD ijhpe j| ⌘ |e ki = k ⇣ 1+ X ij |pe iiQ ijhpe j| ⌘ |e ki • The pseudo partial waves obey: D ij = h i| 1 2 + v e↵ | jihe i| 1 2 + ev e↵ |e ji Q ij = h i| jihe i|e ji • with the so-called PAW strength parameters and augmentation charges: The all-electron and pseudo eigenvalue ...
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