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$$
{\begin{matrix}\rho (r_{1})=\sum _{{G_{p}}}e^{{-iG_{p}.r_{1}}}{\tilde  \rho }[G_{p}]\\{\frac  {1}{r_{{12}}}}=\sum _{{G_{d}}}e^{{-iG_{d}.(r_{1}-r_{2})}}{\tilde  v}[G_{d}]\end{matrix}}
$$
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