deletions | additions       diff --git a/Forces and geometry optimization.tex b/Forces and geometry optimization.tex  index 1a3c664..4ecc3d6 100644  --- a/Forces and geometry optimization.tex  +++ b/Forces and geometry optimization.tex 
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\left< \varphi_n \left| \frac{\partial^2 \hat{v}_{\alpha}}{\partial R_{i\alpha} \partial R_{j\alpha}} \right| \varphi_n \right> =  \left[ \left< \frac{\partial^2 \varphi_n}{\partial r_i \partial r_j} \left| \hat{v}_{\alpha} \right| \varphi_n \right> +   \left< \frac{\partial \varphi_n}{\partial r_i} \left| \hat{v}_{\alpha}\right| \frac{\partial \varphi_n}{\partial r_j} \right>\right] + {\rm cc.}\ .  \end{align} \end{equation}