deletions | additions       diff --git a/forces2.tex b/forces2.tex  index 2d6dbf8..71b9eeb 100644  --- a/forces2.tex  +++ b/forces2.tex 
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%  Using this expression, the terms of the dynamical matrix, eq.~(\ref{eq:dynmatrix}), are evaluated as  %  \begin{equation} \begin{multline}  \left< \varphi_n \left| \frac{\partial v_{\alpha}}{\partial R_{i\alpha}} \right| \frac{\partial \varphi_n}{\partial R_{j \beta}} \right> = \left[  \left< \varphi_n \left| v_{\alpha} \right| \frac{\partial^2 \varphi_n}{\partial R_{j \beta} \partial r_i} \right> \right.\\  + \left.  \left< \frac{\partial \varphi_n}{\partial r_i}\left| v_{\alpha} \right| \frac{\partial \varphi_n}{\partial R_{j \beta}} \right>\right] + {\rm cc.}\ , \end{equation} \end{multline}  and  \begin{multline}   \left< \varphi_n \left| \frac{\partial^2 \hat{v}_{\alpha}}{\partial R_{i\alpha} \partial R_{j\alpha}} \right| \varphi_n \right> =