deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index acf9a68..bdd006c 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.tex 
...
The calculations were done using the code \textsc{Qbox} \cite{Gygi_2008} with time-dependent modifications \cite{Schleife_2012}.   The Kohn-Sham (KS) orbitals are expanded in a supercell plane-wave basis.   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 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 with the earlier observation \cite{Schleife_2015}.  Periodic boundary conditions along with Ewald summation~\cite{Amisaki_2000,Roy_2007} are used throughout this study to ensure finite range due to screening length of $\mathrm{Cu}$ is close to the interatomic spacing.