deletions | additions       diff --git a/geometry optimization.tex b/geometry optimization.tex  index 1b68b74..81c66e8 100644  --- a/geometry optimization.tex  +++ b/geometry optimization.tex 
...
%  \begin{equation}  \label{eq:acceleration_fire}  \dot{\vec{\mathrm{v}}}{(t)} \dot{\mathrm{\vec{v}}}{(t)}  = \dfrac{\vec{F}{(t)}}{m} - \dfrac{\alpha}{\Delta t}|\vec{\mathrm{v}}(t)|\left[\hat{\mathrm{v}}(t)-\hat{F}(t)\right]\ t}|\mathrm{\vec{v}}(t)|\left[\hat{\mathrm{\vec{v}}(t)-\hat{F}(t)\right]\  , \end{equation}  %  where the second term is an introduced acceleration in a direction``steeper'' than the usual direction of motion. Obviously, if $\alpha = 0$ then $\vec{\mathrm{V}}(t) $\mathrm{\vec{V}}(t)  = \vec{v}(t)$, \mathrm{\vec{v}}(t)$,  meaning the velocity modification vanish, and the acceleration $\dot{\vec{\mathrm{v}}}{(t)} $\dot{\mathrm{\vec{v}}}{(t)}  = \vec{F}{(t)}/m$, as usual. We illustrate the dynamic of the algorithm with a simple case: the geometry optimization of a methane molecule. The input geometry consist of one carbon atom at the center of a tetrahedral structure, and four hydrogen atoms at the vertices, where the initial C-H distance is 1.2~\AA. In Fig.~\ref{fig:go_fire} we plot the energy  difference $\Delta E_{\text{tot}}$ respect to the equilibrium conformation, the maximum component of the force acting on the ions $F_{\text{max}}$, and the C-H bond length of the molecule being optimized. On the first iterations the geometry approaches to the equilibrium position, but moves away on the 3th, this means a change on the direction of the gradient, therefore there is no movement on the 4th iteration, the adaptive parameters are reseted, resuming the sliding on the 5th iteration.