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mentioned above, is the formulation of perturbation theory  in terms of differential equations for the variation of the  wave-functions, This is usually named in the  literature as Sternheimer equation~\cite{Ste1951PR} equation~\cite{Sternheimer_1951}  or density functional perturbation theory(DFPT)~\cite{Baroni_2001}. Although a perturbative technique, it avoids the use of empty states, and has a  favorable scaling with the number of atoms.