deletions | additions       diff --git a/Forces and geometry optimization.tex b/Forces and geometry optimization.tex  index 13ded61..a9580d3 100644  --- a/Forces and geometry optimization.tex  +++ b/Forces and geometry optimization.tex 
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-\frac{\partial}{\partial  r_i}V_{\alpha}(\vec{r}-\vec{R}_\alpha)\ .  \end{equation}  %The matrix elements of the perturbation are best calculated by differentiating the wavefunctions, as discussed for the forces in section \ref{sec:forces}. % FIXME  %\begin{align}  % \left< \varphi_n \left| \frac{\partial V_{\alpha}}{\partial x_i} %\right| \frac{\partial \varphi_n}{\partial R_{j \beta}} \right> =  % \left< \varphi_n \left| V_{\alpha} \right| \frac{\partial^2 %\varphi_n}{\partial R_{j \beta} \partial x_i} \right> \\  % \left< \varphi_n \left| \frac{\partial^2 V_{\alpha}}{\partial x_i %\partial x_j} \right| \varphi_n \right> =  % \left< \frac{\partial^2 \varphi_n}{\partial x_i \partial x_j} \left| V_{\alpha} \right| \varphi_n \right> + {\rm cc.} +  % \left< \frac{\partial \varphi_n}{\partial x_i} \left| V_{\alpha} \right| \frac{\partial \varphi_n}{\partial x_j} \right> + {\rm cc.}  %\end{align}