Among the measurable quantities associated to the interaction between ions and solids, the stopping power \(\mathrm(S)\) \cite{Ferrell_1977} has received much attention; it provides information regarding the energy transfer between the incoming projectile and the solid target. When a fast ion moves through a material, it loses most of its kinetic energy due to the excitations of the target electrons along its trajectory in what constitutes a fundamentally non-adiabatic process. This energy-loss phenomenon plays an important role in many experimental studies involving radiation in solids, surfaces, and nanostructures \cite{Chenakin_2006,Figueroa_2007,Markin_2008,Kaminsky_1965,Lehmann_1978,Sigmund_2014,Nastasi_1996}.

Various models and theories have been proposed to calculate stopping cross sections due to electrons. Employing the First Born Approximation, Bethe \cite{Bethe_1930_EN} has introduced the first calculations of inelastic and ionization cross section. The Bloch correction \cite{Bloch_1933} provides a convenient link between the Bohr and the Bethe scheme. Fermi and Teller \cite{Fermi_1947} using electron gas models had reported electronic stopping for various targets. The Bethe formula for stopping has been studied in details by Lindhard and Winther \cite{Lindhard_Winther} on the basis of the generalized linear-response theory. In particular, the condensed matter community has introduced sophisticated numerical computer simulation techniques for this fundamentally non-adiabatic problem as spearheaded by Echenique et al.  \cite{Echenique_1989} aimed to overcome limitations of historical approaches \cite{Bethe_1930,Bloch_1933,Fermi_1947,Lindhard_Winther}. A unified ab initio theoretical approach suitable for different projectiles and energies is in its developing stages \cite{Pruneda_2007,Schleife_2015,Ullah_2015}. A review on the topic can be found in Ref. \cite{Race_2010} and references therein.

Using a Kohn-Sham (KS) scheme of time-dependent density functional theory (TDDFT) where the KS wave functions are expanded in a basis set of spherical harmonics, Quijada et al. \cite{Quijada_2007} have studied the energy loss of protons and anti-protons moving inside metallic spherical \(\mathrm{Al}\) (Jellium) clusters and obtained good results for the projectile-target energy transfer over a restricted energy range. Recently Uddin et al. \cite{Alfaz_Uddin_2013} and Haque et al. \cite{Haque_2015} have calculated stopping cross sections for various media using atomic density functions from Dirac-Hartree-Fock-Slater wave functions in the Lindhard-Schraff theory \cite{Lindhard_Scharff} with fitted parameters and obtained close agreement with the experimental and Srim data. Srim \cite{Ziegler_2010} provides both a fitted model for electronic stopping as well as a large set of experimental points.