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\section{Computational and Theoretical Details}  In this work we employed the formalism of TDDFT coupled with Ehrenfest molecular dynamics (EMD)\cite{Gross_1996}\cite{Calvayrac_2000}\cite{Mason_2007}\cite{Alonso_2008}\cite{Andrade_2009} to simulate the collision processes between the target electrons and the ion (proton). In TDDFT-EMD, the dynamics of the electrons are treated quantum mechanically described by TDDFT and the nuclei are point particles treated classically using EMD. The strength of this method is used to calculate the electronic stopping power $\mathrm(S_e)$ for metals. We compared our results with those contained in \textit{SRIM} database for the case of proton in Cu.   The simulations of the collisions consist of a well-defined trajectories of the projectile (proton) in the metallic bulk. The calculations were done using the code package \textsc{Qbox}\cite{Gygi_2008}. The Kohn-Sham (KS) orbitals are expanded in the plane-wave basis around the atoms and the projectile. These KS orbitals are evolved in time with a self-consistent Hamiltonian that is a functional of the density. The algorithm for evolution of the orbitals is done using the fourth-order Runge-Kutta scheme (RK4)\cite{Schleife_2012}. The advantages of using plane-wave approach is that, it conquers basis-size effects which was a drawback for earlier approaches and finite-size error in the simulations are overcome by considering large simulation cells\cite{Schleife_2015}. The Perdew-Zunger's exchange-correlation\cite{Perdew_1992} exchange-correlation functional\cite{Perdew_1992}  is used, and the core electrons are represented using norm-conserving pseudopotentials from Troullier and Martins\cite{Troullier_1991}.    
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