deletions | additions       diff --git a/Forces and geometry optimization.tex b/Forces and geometry optimization.tex  index e04af72..d9a24bc 100644  --- a/Forces and geometry optimization.tex  +++ b/Forces and geometry optimization.tex 
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%  \begin{equation}  \label{eq:forcesgrad}  \vec{F}_\alpha = \vec{F}_\alpha^{\mathrm{ion-ion}}-\sum_{n}\int \mathrm{d}\vec{r}\left[ \mathrm{d}\vec{r}  \frac{\partial \varphi^*_{n}(\vec{r})}{\partial \vec{r}}v_{\alpha}(\vec{r}-  \vec{R}_\alpha)\varphi_{n}(\vec{r}) + c.c.  \right]\ .  \end{equation}  %  The first advantage of this formulation is that it is easier to implement than eq.~\ref{eq:forcespot}, as it does not require the derivatives of the potential, that can be quite complex and difficult to code, especially when relativistic corrections are included.