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<B><FONT face="Gill Sans"><FONT color="#000000"><FONT size="+1">DFT in a Plane Wave Basis</B></FONT></FONT></FONT></TD>
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<LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Construct the real space representation of the density, n(r) :<BR>
</FONT></FONT></FONT><UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Use 3D-FFTs to convert g-space representation of each state to its r-space representation on a discrete grid of points.<BR>
<LI>Modulus square each state in real space and sum to obtain n(r).<BR>
</FONT></FONT></FONT></UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Construct the g-space representation of the density, n(g):<BR>
</FONT></FONT></FONT><UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Use a 3D-FFT of n(r) to compute n(g). This procedure is </FONT></FONT></FONT><B><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">exact</B></FONT></FONT></FONT><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2"> for a finite plane wave basis.<BR>
</FONT></FONT></FONT></UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Using n(r) :<BR>
</FONT></FONT></FONT><UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Compute the exchange correlation energy using trapezoidal rule integration (not exact).<BR>
<LI>Compute the exchange correlation potential to the r-space representation of the KS potential.<BR>
</FONT></FONT></FONT></UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Using n(g) :<BR>
</FONT></FONT></FONT><UL><LI><FONT face="Gill Sans"><FONT color="#000000"><FONT size="-2">Compute the local electron-ion interaction (exact).<BR>
<LI>Compute the Hartree energy (exact).<BR>
<LI>Add the e-atom and Hartree contributions to the g-space representation of the exchange correlation potential.<BR>
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