1. Ewald summation equations
2. Some interesting links
3. MD code written in C++
Below are the equations that I used for the Ewald summation open source code in github.
Ewald summation
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1. Short range Potential
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\[\color{black} {U_{SR}=\frac{1}{2}\sum_{i=1}^N\sum_{j=1}^N\sum_{n}q_iq_j\frac{erfc(\alpha|r_{ij}+n|)}{|r_{ij}+n|}}\]
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2. Short range Force
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\[\color{black} {F_{SR}=q_i\sum_{j=1}^N\sum_n\left\{\frac{2\alpha}{\sqrt\pi}exp[-\alpha^{2}\left(r_{ij}+n\right)^{2}]+\frac{erfc(\alpha\mid r_{ij}+n\mid)}{\mid r_{ij}+n\mid)}\right\}\frac{r_{ij}+n}{\mid r_{ij}+n\mid^{2}}}\]
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3. Short range Virial
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\[\color{black} {P_{SR\space(\beta\gamma)}=\frac{1}{2V}\sum_n\sum_{i,j=1}^Nq_iq_j(\frac{erfc(\alpha|r_{ij}+n|)}{|r_{ij}+n|^3}+\frac{2\alpha exp(-\alpha^2|r_{ij}+n|^2)}{\sqrt\pi\space|r_{ij}+n|^2})(r_{ij}+n)_\beta(r_{ij}+n)_\gamma}\]
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4. Long range potential
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\[\color{blue} {U_{LR}=\frac{2\pi}{V}\sum_{i=1}^N\sum_{j=1}^N\sum_{k\neq0}\frac{q_iq_j}{k^2}exp[\frac{-k^2}{4\alpha^2}]exp[-i\overrightarrow{k}.\overrightarrow{r_{ij}}]}\]
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5. Long range Force
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\[\color{blue} {F_{LR}=4\pi q_i\sum_{k\neq0}\frac{\overrightarrow{k}}{k^2V}exp(-\frac{k^2}{4\alpha^2})\sum_{j=1}^Nq_j sin(\overrightarrow{k}.\overrightarrow{r_{ij}})}\]
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6. Long range Virial
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\[\color{blue} {P_{LR\space(\beta\gamma)}=\frac{2\pi}{V}\sum_{i=1}^N\sum_{j=1}^N\sum_{k\neq0}\frac{q_iq_j}{k^2}exp[\frac{-k^2}{4\alpha^2}]exp[-i\overrightarrow{k}.\overrightarrow{r_{ij}}\space] (1-(\frac{2}{k^2}+\frac{1}{2\alpha^2})k_\beta k_\gamma)}\]
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7. Self Energy
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\[\color{green} {U_{SELF}=\frac{-\alpha}{\sqrt\pi}\sum_{i=1}^Nq_i^2}\]
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8. Intra molecular correction (Energy)
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\[\color{navy} {E_{INTRA}=-\frac{1}{2}\sum_{(i,j) \epsilon M}\frac{q_iq_j erf(\alpha \space r_{ij})}{r_{ij}} }\]
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9. Intra molecular correction (Force)
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\[\color{navy} {F_{INTRA}=\frac{1}{2}\sum_{(i,j) \epsilon M} q_iq_j\left\{\frac{2\alpha}{\sqrt\pi}exp[-\alpha^{2}r_{ij}^{2}]-\frac{erf(\alpha\mid r_{ij}\mid)}{\mid r_{ij}\mid)}\right\}\frac{r_{ij}}{\mid r_{ij}\mid^{2}}}\]
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10. Intra molecular correction (Virial)
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\[\color{navy} {P_{INTRA\space(\beta\gamma)}=\frac{1} {2V}\sum_{(i,j)\epsilon M}q_iq_j\left\{\frac{2\alpha}{\sqrt\pi}exp[-\alpha^{2}|r_{ij}|^{2}]-\frac{erf(\alpha|r_{ij}|}{|r_{ij}|}\right\}\frac{r_{ij\beta}r_{ij\gamma}}{|r_{ij}|^{2}}}\]
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References
[1]. Lipkowitz, Kenny B., Thomas R. Cundari, and Donald B. Boyd. Reviews in Computational Chemistry. Chichester: John Wiley, 2007. Print.
[2]. Essmann, Ulrich, Lalith Perera, Max L. Berkowitz, Tom Darden, Hsing Lee, and Lee G. Pedersen. "A Smooth Particle Mesh Ewald Method." J. Chem. Phys. The Journal of Chemical Physics 103.19 (1995): 8577. Web.
[1]. Lipkowitz, Kenny B., Thomas R. Cundari, and Donald B. Boyd. Reviews in Computational Chemistry. Chichester: John Wiley, 2007. Print.
[2]. Essmann, Ulrich, Lalith Perera, Max L. Berkowitz, Tom Darden, Hsing Lee, and Lee G. Pedersen. "A Smooth Particle Mesh Ewald Method." J. Chem. Phys. The Journal of Chemical Physics 103.19 (1995): 8577. Web.