deletions | additions       diff --git a/Forces and geometry optimization.tex b/Forces and geometry optimization.tex  index 8711bb8..b8d2a14 100644  --- a/Forces and geometry optimization.tex  +++ b/Forces and geometry optimization.tex 
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\begin{equation}  \label{eq:ionicpertmod}  \frac{\partial V_\alpha(\vec{r}-\vec{R}_\alpha)}{\partial \hat{v}_\alpha}{\partial  R_{i\alpha}} = V_{\alpha}(\vec{r}-\vec{R}_\alpha)\frac{\partial}{\partial \hat{v}_{\alpha}\frac{\partial}{\partial  r_i} -\frac{\partial}{\partial  r_i}V_{\alpha}(\vec{r}-\vec{R}_\alpha)\ r_i}\hat{v}_\alpha\  . \end{equation}