deletions | additions       diff --git a/Forces and geometry optimization.tex b/Forces and geometry optimization.tex  index 5ea9e8a..f734c1d 100644  --- a/Forces and geometry optimization.tex  +++ b/Forces and geometry optimization.tex 
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\begin{equation}  \label{eq:forcespot}  \vec{F}_{\alpha} = \vec{F}_{\alpha}^{\mathrm{ion-ion}}  -\sum_{n} \left< \varphi_{n} \left| \frac{\partial \hat{v}_{\alpha}{\partial \hat{v}_{\alpha}}{\partial  \vec{R}_{\alpha}} \right| \varphi_{n} \right>\ . %\int \mathrm{d}\vec{r}  %\varphi^*_{n}(\vec{r})\frac{\partial v_{\alpha}(\vec{r}-  %\vec{R}_\alpha)}{\partial \vec{R}_{\alpha}}\varphi_{n}(\vec{r})\ . 
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%  \begin{equation}  \label{eq:forcesgrad}  \vec{F}_\alpha = \vec{F}_\alpha^{\mathrm{ion-ion}}+\sum_{n} \left[ \left< \frac{\partial \varphi_{n}}{\partial r_{\vec{r}} r_{\vec{r}}}  \left|\partial  \hat{v}_{\alpha} \right| \varphi_{n} \right> + \mathrm{cc.} \right]\,. %\int \mathrm{d}\vec{r}  %\frac{\partial \varphi^*_{n}(\vec{r})}{\partial \vec{r}}v_{\alpha}(\vec{r}-  %\vec{R}_\alpha)\varphi_{n}(\vec{r}) + \mathrm{cc.}\,.