Edwin Quashie edited section_Computational_and_Theoretical_Details__.tex  almost 9 years ago

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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} is used, and the core electrons are represented using norm-conserving pseudopotentials from Troullier and Martins\cite{Troullier_1991}.  Periodic boundary conditions were used throughout. The best supercell size was selected so as to reduce the specious effects of the duplication while maintaining controllable computational demands. The calculations used $(3\times3\times3)$ supercells containing 108 host Copper atoms plus a proton, represented by a Troullier-Martins pseudopotential (17 valence electrons per copper atom are explicitly considered). A single \textit{k} point ($\Gamma$) was used for integrations in the Brillouin zone. The density is sampled with 130 Ry mesh cutoff. The projectile was initially placed in the crystal and the time-independent DFT calculation was implemented to obtain the solutions for the initial condition of the electronic system for the ground state for subsequent evolution. We then perform TDDFT calculations on the electronic system. The projectile is moved with a constant velocity subjected to a straight uniform movement along a [100] channeling trajectory (also called hyper-channeling trajectory). This is done to minimize the collision of the projectile with the host atoms. Also the projectile is subjected to a random trajectory through the host material (also called off-center channeling) in order to assess sensitivity to the ideal hyper-channeling conditions. In this case, there is a stronger interaction between projectile and host atoms because the charge density in the proximity of the host atoms is larger.