deletions | additions       diff --git a/forces2.tex b/forces2.tex  index 71b9eeb..aa160e5 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{multline}  \left< \varphi_n \left| \frac{\partial v_{\alpha}}{\partial \hat{v}_{\alpha}}{\partial  R_{i\alpha}} \right| \frac{\partial \varphi_n}{\partial R_{j \beta}} \right> = \left[ \left< \varphi_n \left| v_{\alpha} \hat{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} \hat{v}_{\alpha}  \right| \frac{\partial \varphi_n}{\partial R_{j \beta}} \right>\right] + {\rm cc.}\ , \end{multline}  and  \begin{multline}