deletions | additions       diff --git a/Forces and geometry optimization.tex b/Forces and geometry optimization.tex  index 097a21c..cf15b98 100644  --- a/Forces and geometry optimization.tex  +++ b/Forces and geometry optimization.tex 
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The egg-box effect is particularly problematic for calculations where the atoms are allowed to move, for example to study its dynamics (molecular dynamics) or to find the minimum energy configuration (geometry optimization).  The first step In Octopus we have studied several scheme  to control the egg-box effect effect\cite{Andrade2010thesis}. The first step  is to usesome sort of  pseudo-potential filtering to eliminate Fourier components of the potential that cannot be represented in on  the grid. In Octopus we use the scheme of Tafipolosky and Schmid~\cite{Tafipolsky_2006}. Additionally, the formulation used to calculate certain properties can reduce the spurious  effect of the grid on the calculations. For example, the calculation of forces requires the evaluation of the derivative of the energy with respect to the ionic position  \(\vec{R_A}\)(for simplicity we have considered local ionic  potentials but our results are valid for non-local potentials  as well.)  that can be evaluated as the expectation value of the derivative of the ionic potential (for simplicity, we have considered local ionic  potentials but the results are valid for non-local potentials  as well)  %  \begin{equation}  \label{eq:forcespot}