deletions | additions       diff --git a/geometry optimization.tex b/geometry optimization.tex  index aec4a7c..44eff4a 100644  --- a/geometry optimization.tex  +++ b/geometry optimization.tex 
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\dot{\mathrm{\vec{v}}}{(t)} = \dfrac{\vec{F}{(t)}}{m} - \dfrac{\alpha}{\Delta t} \left| \mathrm{\vec{v}}(t) \right| \left[\hat{\mathrm{\vec{v}}}(t)-\hat{F}(t)\right]\ ,  \end{equation}  %  where the second term is an introduced acceleration in a direction``steeper'' direction ``steeper''  than the usual direction of motion. Obviously, if $\alpha = 0$ then $\mathrm{\vec{V}}(t) = \mathrm{\vec{v}}(t)$, meaning the velocity modification vanishes, and the acceleration $\dot{\mathrm{\vec{v}}}{(t)} = \vec{F}{(t)}/m$, as usual. We illustrate how the algorithm works with a simple case: the geometry optimization of a methane molecule. The input geometry consists of one carbon atom at the center of a tetrahedron, 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. On the first iterations, the geometry approaches the equilibrium position, but moves away on the 3th. This means a change oin the direction of the gradient, so there is no movement on the 4th iteration, the adaptive parameters are reset, and sliding resumes on the 5th iteration.