deletions | additions       diff --git a/Sternheimer2.tex b/Sternheimer2.tex  index 0b7a5ca..43f000c 100644  --- a/Sternheimer2.tex  +++ b/Sternheimer2.tex 
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%  \begin{multline}  D_{i \alpha, j \beta} = \frac{\partial^2 E}{\partial R_{i \alpha} \partial R_{j \beta}} = D_{i \alpha, j \beta}^{\rm ion-ion} \\  + -  \sum_n^{\rm occ} \left[ \left< \varphi_n \left| \frac{\partial \hat{v}_{\alpha}}{\partial R_{i \alpha}} \right| \frac{\partial \varphi_n}{\partial R_{j \beta}} \right> + {\rm cc.} + \delta_{\alpha \beta} \left< \varphi_n \left| \frac{\partial^2 \hat{v}_{\alpha}}{\partial R_{i \alpha} \partial R_{\alpha j}} \right| \varphi_n \right> \right] \label{eq:dynmatrix}  \end{multline}  %