git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@4650 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/eff_KE.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+E_{KE}  = \frac{\hbar^2 }{{m_{e} }}\sum\limits_i {\frac{3}{{2s_i^2 }}}
+$$
+
+\end{document}

doc/Eqs/eff_NN.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+E_{NN}  = \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{{Z_i Z_j }}{{R_{ij} }}}
+$$
+
+\end{document}

doc/Eqs/eff_Ne.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+E_{Ne}  =  - \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i,j} {\frac{{Z_i }}{{R_{ij} }}Erf\left( {\frac{{\sqrt 2 R_{ij} }}{{s_j }}} \right)}
+$$
+
+\end{document}

doc/Eqs/eff_Pauli.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+E_{Pauli}  = \sum\limits_{\sigma _i  = \sigma _j } {E\left( { \uparrow  \uparrow } \right)_{ij}}  + \sum\limits_{\sigma _i  \ne \sigma _j } {E\left( { \uparrow  \downarrow } \right)_{ij}}
+$$
+
+\end{document}

doc/Eqs/eff_ee.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+E_{ee}  = \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{1}{{r_{ij} }}Erf\left( {\frac{{\sqrt 2 r_{ij} }}{{\sqrt {s_i^2  + s_j^2 } }}} \right)} 
+$$
+
+\end{document}

doc/Eqs/eff_energy_expression.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+U\left(R,r,s\right) =  E_{NN} \left( R \right) + E_{Ne} \left( {R,r,s} \right) + E_{ee} \left( {r,s} \right) + E_{KE} \left( {r,s} \right) + E_{PR} \left( { \uparrow  \downarrow ,S} \right)
+$$
+
+\end{document}