diff --git a/doc/Eqs/angle_cosine_periodic.jpg b/doc/Eqs/angle_cosine_periodic.jpg
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diff --git a/doc/Eqs/angle_cosine_periodic.tex b/doc/Eqs/angle_cosine_periodic.tex
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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=C\left[ 1-B(-1)^ncos\left( n\theta\right) \right]  
+$$
+
+\end{document}
diff --git a/doc/Eqs/dreiding_hbond.jpg b/doc/Eqs/dreiding_hbond.jpg
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diff --git a/doc/Eqs/improper_umbrella.jpg b/doc/Eqs/improper_umbrella.jpg
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diff --git a/doc/Eqs/improper_umbrella.tex b/doc/Eqs/improper_umbrella.tex
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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=\frac{1}{2}K\left( \frac{1+cos\omega_0}{sin\omega_0}\right) ^2 \left( cos\omega - cos\omega_0\right) \qquad \omega_0 \neq 0^o
+$$
+
+$$
+E=K\left( 1-cos\omega\right)  \qquad \omega_0 = 0^o
+$$
+
+\end{document}
diff --git a/doc/Eqs/pair_hbond_dreiding.jpg b/doc/Eqs/pair_hbond_dreiding.jpg
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diff --git a/doc/Eqs/pair_hbond_dreiding.tex b/doc/Eqs/pair_hbond_dreiding.tex
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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E^{hb}_{LJ}(r)=AR^{-12}-BR^{-10}cos^n\theta=4\epsilon\left\lbrace 5\left[ \frac{\sigma}{r}\right]^{12}-6\left[ \frac{\sigma}{r}\right]^{10}  \right\rbrace cos^n\theta
+$$
+
+$$
+E^{hb}_{MORSE}(r)=D_0\left\lbrace \chi^2 - 2\chi\right\rbrace cos^n\theta=D_{0}\left\lbrace e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right\rbrace cos^n\theta
+$$
+
+$$
+where \qquad r < r_c, \qquad cos^2\left( \theta\right) >  cos^2\left( \theta_c\right)
+$$
+\end{document}
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