deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index e2f5dee..801cf9b 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.tex 
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The fourth-order Runge-Kutta scheme (RK4) \cite{Schleife_2012} is used to propagate these orbitals in time.   The advantages of using the plane-wave approach is that it systematically deals with basis-size effects which was a drawback for earlier approaches \cite{Pruneda_2007, Correa_2012}.  Finite size effects are studied between 108 and 256 atoms in a supercell of $(3\times3\times3)$ and $(4\times4\times4)$ respectively in this simulation, the errors remain within 3\% in conformity within the earlier observation \cite{Schleife_2015}.  %Finite-size errors in the simulations are overcome by considering large simulation cells \cite{Schleife_2015}.% Periodic boundary conditions are used throughout this study.   The supercell size was chosen so as to reduce the specious size effects while maintaining controllable computational demands.