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physics_chemistry:coulomb_repulsion_jh_and_slater_integrals [2017/12/11 16:33] – Maurits W. Haverkort | physics_chemistry:coulomb_repulsion_jh_and_slater_integrals [2018/05/03 22:02] (current) – Maurits W. Haverkort | ||
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The expansion of $e^2/ | The expansion of $e^2/ | ||
\begin{equation} | \begin{equation} | ||
- | \sum_{i\neq j} \frac{1}{2} \frac{e^2}{|r_i-r_j|} = \sum_{i\neq j} \frac{1}{2}\sum_{k=0}^{\infty} \sum_{m=-k}^{m=k} \frac{4 \pi}{2k+1} \frac{\mathrm{Min}[r_i, | + | \sum_{i\neq j} \frac{1}{2} \frac{e^2}{|r_i-r_j|} = \sum_{i\neq j} \frac{1}{2}\sum_{k=0}^{\infty} \sum_{m=-k}^{m=k} \frac{4 \pi e^2}{2k+1} \frac{\mathrm{Min}[r_i, |
\end{equation} | \end{equation} | ||