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This cost can be greatly reduced using a special grid with only two additional points placed at $\pm \alpha L$   as shown in Fig.~\ref{fig:pes_nfft}~(c).  Since the new grid has non uniform spacing a non-equispaced FFT (NFFT) is used~\cite{Kunis:2006wg,Potts:2009kn}. used~\cite{Kunis_2006,Keiner_2009}.  With this strategy a price is paid in momentum space where the maximum momentum $k_{\rm max}$ is reduced by a factor $\alpha$ compared to ordinary FFT.  In Octopus we implemented all the three strategies: bare FFT, zero padding with FFT and zero padding with NFFT.