A. Table, 6: A list of the atoms position of the ice Ih crystal used in this manuscript

]. I. Abril, R. Garcia-molina, C. D. Denton, F. J. Pérez-pérez, and N. R. Arista, Dielectric description of wakes and stopping powers in solids, Physical Review A, vol.58, issue.1, pp.357-366, 1998.
DOI : 10.1103/PhysRevA.58.357

N. R. Arista and W. Brandt, Energy loss and straggling of charged particles in plasmas of all degeneracies, Physical Review A, vol.23, issue.4, pp.1898-1905, 1981.
DOI : 10.1103/PhysRevA.23.1898

R. Nestor and . Arista, Low-velocity stopping power of semidegenerate quantum plasmas, Journal of Physics C: Solid State Physics, vol.18, issue.26, p.5127, 1985.

D. Manuel and . Barriga-carrasco, Proton stopping using a full conserving dielectric function in plasmas at any degeneracy, Phys. Rev. E, vol.82, p.46403, 2010.

P. Bauer, W. Käferböck, and V. Ne?as, Investigation of the electronic energy loss of hydrogen ions in h 2 o: influence of the state of aggregation. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, Materials and Atoms, vol.93, issue.2, pp.132-136, 1994.

A. Baurichter, P. Sigmund, and A. H. Sørensen, Panel discussion on stopping of heavy ions. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, Materials and Atoms, vol.195, issue.1, pp.224-231, 2002.

M. J. Berger, J. S. Coursey, M. A. Zucker, and J. Chang, Estar, pstar, and astar: Computer programs for calculating stopping-power and range tables for electrons, protons, and helium ions, 2005.

H. Bethe, Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie, Annalen der Physik, vol.3, issue.3, pp.325-400, 1930.
DOI : 10.1002/andp.19303970303

H. A. Bethe, Bremsformel f???r Elektronen relativistischer Geschwindigkeit, Zeitschrift f???r Physik, vol.76, issue.5-6, p.293, 1932.
DOI : 10.1007/BF01342532

F. Bloch, Bremsverm???gen von Atomen mit mehreren Elektronen, Zeitschrift f???r Physik, vol.81, issue.5-6, p.363, 1933.
DOI : 10.1007/BF01344553

F. Bonsignori and A. Desalvo, A dielectric approach to electronic energy loss in real solids under channeling conditions, Lettere al Nuovo Cimento, vol.128, issue.12, pp.589-591, 1969.
DOI : 10.1007/BF02753963

F. Bonsignori and A. Desalvo, A dielectric calculation of energy loss to valence electrons under channeling conditions, Journal of Physics and Chemistry of Solids, vol.31, issue.10, pp.312191-2198, 1970.
DOI : 10.1016/0022-3697(70)90233-7

A. F. Burenkov, F. F. Komarov, and M. A. Kumakhov, Energy Loss of Charged Particles in Crystals, physica status solidi (b), vol.8, issue.1, pp.417-428, 1980.
DOI : 10.1002/pssb.2220990145

I. Campillo, J. Pitarke, and A. Eguiluz, Electronic stopping power of aluminum crystal, Physical Review B, vol.58, issue.16, pp.10307-10314, 1998.
DOI : 10.1103/PhysRevB.58.10307

I. Campillo, J. Pitarke, A. Eguiluz, and A. García, Electronic stopping power of periodic crystals. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, Materials and Atoms, vol.135, pp.1-4103, 1998.

M. Corradini, R. Del-sole, G. Onida, and M. Palummo, of the homogeneous electron gas, Physical Review B, vol.57, issue.23, pp.14569-14571, 1998.
DOI : 10.1103/PhysRevB.57.14569

C. D. Denton, I. Abril, R. Garcia-molina, J. C. Moreno-marín, and S. Heredia-avalos, Influence of the description of the target energy-loss function on the energy loss of swift projectiles, Surface and Interface Analysis, vol.61, issue.413, pp.401481-1487, 2008.
DOI : 10.1002/sia.2936

A. Desalvo and R. Rosa, A dielectric calculation of energy loss to valence electrons of channelled protons in silicon, Journal of Physics C: Solid State Physics, vol.10, issue.10, p.1595, 1977.
DOI : 10.1088/0022-3719/10/10/004

J. J. Dorado and F. Flores, Molecular-orbital theory for the stopping power of atoms in the low-velocity regime: The case of helium in alkali metals, Physical Review A, vol.47, issue.4, pp.3062-3072, 1993.
DOI : 10.1103/PhysRevA.47.3062

D. M. Duffy and A. M. Rutherford, Including the effects of electronic stopping and electron???ion interactions in radiation damage simulations, Journal of Physics: Condensed Matter, vol.19, issue.1, p.16207, 2007.
DOI : 10.1088/0953-8984/19/1/016207

. Ch, R. D. Eppacher, D. Mui-no, A. Semrad, and . Arnau, Stopping power of lithium for hydrogen projectiles. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, The Interaction of Swift Particles and Electromagnetic Fields with Matter, pp.639-642, 1995.

E. Fermi, Un metodo statistico per la determinazione di alcune priorieta dell'atome. Rend, Accad. Naz. Lincei, vol.6, pp.602-607, 1927.

E. Fermi and E. Teller, The Capture of Negative Mesotrons in Matter, Physical Review, vol.72, issue.5, pp.399-408, 1947.
DOI : 10.1103/PhysRev.72.399

G. Garcia, C. Elsässer, S. Louie, and M. Cohen, Use of gradient-corrected functionals in total-energy calculations for solids, Physical Review B, vol.46, issue.15, p.9829, 1992.
DOI : 10.1103/PhysRevB.46.9829

J. Gaunt, The Stopping Power of Hydrogen Atoms for ??-Particles according to the New Quantum Theory, Mathematical Proceedings of the Cambridge Philosophical Society, pp.732-754, 1927.
DOI : 10.1017/S0305004100011257

X. Gonze, B. Amadon, P. M. Anglade, J. M. Beuken, F. Bottin et al., ABINIT: First-principles approach to material and nanosystem properties, Computer Physics Communications, vol.180, issue.12, p.2582, 2009.
DOI : 10.1016/j.cpc.2009.07.007

E. K. Gross and W. Kohn, Local density-functional theory of frequency-dependent linear response, Physical Review Letters, vol.55, issue.26, pp.2850-2852, 1985.
DOI : 10.1103/PhysRevLett.55.2850

L. Hedin, New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem, Physical Review, vol.139, issue.3A, pp.796-823, 1965.
DOI : 10.1103/PhysRev.139.A796

G. H. Henderson, Lix. the decrease of energy of ? particles on passing through matter, Philosophical Magazine Series, vol.6, issue.44262, pp.680-688, 1922.

P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.136, issue.3B, pp.864-871, 1964.
DOI : 10.1103/PhysRev.136.B864

M. S. Hybertsen and S. G. Louie, Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies, Physical Review B, vol.34, issue.8, pp.5390-5413, 1986.
DOI : 10.1103/PhysRevB.34.5390

G. J. Iafrate and J. F. Ziegler, Numerical evaluation of Lindhard???s theory of stopping power for a charged particle in a free???electron gas, Journal of Applied Physics, vol.50, issue.9, pp.5579-5581, 1979.
DOI : 10.1063/1.326750

G. J. Iafrate, J. F. Ziegler, and M. J. Nass, Application of Lindhard???s dielectric theory to the stopping of ions in solids, Journal of Applied Physics, vol.51, issue.2, pp.984-987, 1980.
DOI : 10.1063/1.327679

F. J. Janni, Proton range-energy tables, 1 kev-10 gev, energy loss, range, path length, time-of-flight, straggling, multiple scattering, and nuclear interaction probability. part ii. for 92 elements. Atomic Data and Nuclear Data Tables, p.341, 1982.

R. O. Jones and O. , The density functional formalism, its applications and prospects, Reviews of Modern Physics, vol.61, issue.3, p.689, 1989.
DOI : 10.1103/RevModPhys.61.689

A. A. Kugler, Theory of the local field correction in an electron gas, Journal of Statistical Physics, vol.14, issue.1, pp.35-87, 1975.
DOI : 10.1007/BF01024183

J. Lindhard and M. Scharff, Energy loss in matter by fast particles of low charge, pp.1-31, 1953.

J. Lindhard and A. Winther, Stopping power of electron gasand equipartition rule, 1964.

J. Lindhard, On the properties of a gas of charged particles, Mat. Fys. Medd. Dan. Vid. Selsk, vol.28, issue.8, p.1, 1954.

M. A. Marques, C. A. Ullrich, F. Nogueira, A. Rubio, K. Burke et al., Time-Dependent Density Functional Theory, Lecture Notes in Physics, vol.706, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00438357

C. P. Martin and J. Schwinger, Theory of Many-Particle Systems. I, Physical Review, vol.115, issue.6, pp.1342-1373, 1959.
DOI : 10.1103/PhysRev.115.1342

G. Maynard and C. Deutsch, Energy loss and straggling of ions with any velocity in dense plasmas at any temperature, Physical Review A, vol.26, issue.1, p.665, 1982.
DOI : 10.1103/PhysRevA.26.665

C. Møller, Passage of hard beta rays through matter, Ann. Physik, vol.14, p.531, 1932.

E. Holm-mortensen, J. Oddershede, and J. R. Sabin, Polarization propagator calculations of generalized oscillator strengths and stopping cross sections of he. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, Materials and Atoms, vol.69, issue.1, pp.24-32, 1992.

L. C. Northcliffe, Passage of Heavy Ions Through Matter, Annual Review of Nuclear Science, vol.13, issue.1, pp.67-102, 1963.
DOI : 10.1146/annurev.ns.13.120163.000435

A. Ojanperä, A. V. Krasheninnikov, and M. Puska, Electronic stopping power from first-principles calculations with account for core electron excitations and projectile ionization, Physical Review B, vol.89, issue.3, p.35120, 2014.
DOI : 10.1103/PhysRevB.89.035120

G. Onida, L. Reining, and A. Rubio, Electronic excitations: density-functional versus many-body Green???s-function approaches, Reviews of Modern Physics, vol.74, issue.2, pp.601-659, 2002.
DOI : 10.1103/RevModPhys.74.601

J. Ortner and I. M. Tkachenko, Stopping power of strongly coupled electronic plasmas: Sum rules and asymptotic forms, Physical Review E, vol.63, issue.2, p.26403, 2001.
DOI : 10.1103/PhysRevE.63.026403

J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Gerber et al., Screened hybrid density functionals applied to solids, The Journal of Chemical Physics, vol.124, issue.15, 2006.
DOI : 10.1063/1.2187006

URL : https://hal.archives-ouvertes.fr/hal-00204683

H. Paul, Stopping power for light ions

H. Paul and A. Schinner, An empirical approach to the stopping power of solids and gases for ions from 3li to 18ar. Nuclear Instruments and Methods in, Physics Research B, vol.179, pp.299-315, 2001.

H. Paul and A. Schinner, Judging the reliability of stopping power tables and programs for protons and alpha particles using statistical methods. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, Materials and Atoms, vol.227, issue.4, pp.461-470, 2005.

H. Paul and A. Schinner, An empirical approach to the stopping power of solids and gases for ions from 3li to 18ar -part ii. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with, Materials and Atoms, vol.195, issue.12, pp.166-174, 2002.

D. R. Penn, Electron mean-free-path calculations using a model dielectric function, Physical Review B, vol.35, issue.2, p.482, 1987.
DOI : 10.1103/PhysRevB.35.482

M. Petersilka, U. J. Gossmann, and E. K. Gross, Excitation Energies from Time-Dependent Density-Functional Theory, Physical Review Letters, vol.76, issue.8, pp.1212-1215, 1996.
DOI : 10.1103/PhysRevLett.76.1212

J. M. Pitarke and I. Campillo, Band structure effects on the interaction of charged particles with solids. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, pp.164-165147, 2000.

J. M. Pruneda, D. Sánchez-portal, A. Arnau, J. I. Juaristi, and E. Artacho, Electronic Stopping Power in LiF from First Principles, Physical Review Letters, vol.99, issue.23, p.99235501, 2007.
DOI : 10.1103/PhysRevLett.99.235501

J. M. Pruneda, D. Sánchez-portal, A. Arnau, J. I. Juaristi, and E. Artacho, Heating electrons with ion irradiation: A first-principles approach. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Proceedings of the 17th International Workshop on Inelastic Ion-Surface Collisions, pp.590-593, 2009.

M. Quijada, A. G. Borisov, I. Nagy, R. P. Mui, and P. M. Echenique, Time-dependent density-functional calculation of the stopping power for protons and antiprotons in metals, Physical Review A, vol.75, issue.4, p.42902, 2007.
DOI : 10.1103/PhysRevA.75.042902

URL : https://hal.archives-ouvertes.fr/hal-00306539

C. P. Race, D. R. Mason, M. W. Finnis, W. M. Foulkes, A. P. Horsfield et al., The treatment of electronic excitations in atomistic models of radiation damage in metals, Reports on Progress in Physics, vol.73, issue.11, p.73116501, 2010.
DOI : 10.1088/0034-4885/73/11/116501

L. Reining, V. Olevano, A. Rubio, and . Onida, Excitonic Effects in Solids Described by Time-Dependent Density-Functional Theory, Physical Review Letters, vol.88, issue.6, p.66404, 2002.
DOI : 10.1103/PhysRevLett.88.066404

URL : https://hal.archives-ouvertes.fr/hal-00122419

R. H. Ritchie and A. Howie, Electron excitation and the optical potential in electron microscopy, Philosophical Magazine, vol.39, issue.2, pp.463-481, 1977.
DOI : 10.1143/JPSJ.12.618

K. Röttger, A. Endriss, J. Ihringer, S. Doyle, and W. Kuhs, between 10 and 265 K, Acta Crystallographica Section B Structural Science, vol.50, issue.6, pp.644-648, 1994.
DOI : 10.1107/S0108768194004933

C. C. Rousseau, W. K. Chu, and D. Powers, Calculations of Stopping Cross Sections for 0.8- to 2.0-MeV Alpha Particles, Physical Review A, vol.4, issue.3, p.1066, 1971.
DOI : 10.1103/PhysRevA.4.1066

E. Runge and E. K. Gross, Density-Functional Theory for Time-Dependent Systems, Physical Review Letters, vol.52, issue.12, pp.997-1000, 1984.
DOI : 10.1103/PhysRevLett.52.997

R. John, J. Sabin, and . Oddershede, Shell corrections to electronic stopping powers from orbital mean excitation energies, Phys. Rev. A, vol.26, pp.3209-3219, 1982.

R. John, J. Sabin, and . Oddershede, Theoretical stopping cross sections of c-h, c-c and c=c bonds for swift protons, Nucl. Instrum. Meth. B, vol.27, issue.2, pp.280-286, 1987.

W. M. Saslow and G. F. Reiter, Plasmons and Characteristic Energy Loss in Periodic Solids, Physical Review B, vol.7, issue.7, pp.2995-3003, 1973.
DOI : 10.1103/PhysRevB.7.2995

A. Schleife, Y. Kanai, and A. A. Correa, Accurate atomistic first-principles calculations of electronic stopping, Physical Review B, vol.91, issue.1, p.14306, 2015.
DOI : 10.1103/PhysRevB.91.014306

W. Schülke, Electron dynamics by inelastic X-ray scattering, OUP Oxford, 2007.

P. Sigmund, Particle Penetration and Radiation Effects-General Aspects and Stopping of Swift Point Charges, 2006.

L. H. Thomas, The calculation of atomic fields, Proc. Camp. Philos. Soc, pp.542-548, 1927.

J. J. Thomson, Ionization by moving electrified particles, pp.449-57, 1912.

D. I. Thwaites, Bragg's Rule of Stopping Power Additivity: A Compilation and Summary of Results, Radiation Research, vol.95, issue.3, pp.495-518, 1983.
DOI : 10.2307/3576096

T. M. Tielens, G. E. Bauer, and T. H. Stoof, Dielectric theory of the electronic stopping power of fast ions in crystals, Physical Review B, vol.49, issue.8, pp.5741-5744, 1994.
DOI : 10.1103/PhysRevB.49.5741

I. V. Tokatly and O. Pankratov, Many-Body Diagrammatic Expansion in a Kohn-Sham Basis: Implications for Time-Dependent Density Functional Theory of Excited States, Physical Review Letters, vol.86, issue.10, pp.2078-2081, 2001.
DOI : 10.1103/PhysRevLett.86.2078

C. A. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications, 2012.
DOI : 10.1093/acprof:oso/9780199563029.001.0001

G. S. Was, Fundamentals of Radiation Materials Science, 2007.
DOI : 10.1007/978-1-4939-3438-6

H. Weissker, J. Serrano, S. Huotari, F. Bruneval, F. Sottile et al., Signatures of Short-Range Many-Body Effects in the Dielectric Function of Silicon for Finite Momentum Transfer, Physical Review Letters, vol.97, issue.23, p.237602, 2006.
DOI : 10.1103/PhysRevLett.97.237602

H. Weissker, J. Serrano, S. Huotari, E. Luppi, M. Cazzaniga et al., calculations, Physical Review B, vol.81, issue.8, p.85104, 2010.
DOI : 10.1103/PhysRevB.81.085104

URL : https://hal.archives-ouvertes.fr/hal-01454997

W. A. Wenzel and W. Whaling, O Ice, Physical Review, vol.87, issue.3, pp.499-503, 1952.
DOI : 10.1103/PhysRev.87.499

J. A. White and D. M. Bird, Implementation of gradient-corrected exchange-correlation potentials in Car-Parrinello total-energy calculations, Physical Review B, vol.50, issue.7, pp.4954-4957, 1994.
DOI : 10.1103/PhysRevB.50.4954

J. F. Ziegler, Srim-the stopping and range of ions in matter

J. F. Ziegler, Stopping of energetic light ions in elemental matter, Journal of Applied Physics, vol.85, issue.3, pp.1249-1272, 1999.
DOI : 10.1063/1.369844

J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions in Matter, 1985.
DOI : 10.1007/978-1-4615-8103-1_3

A. Zupan, P. Blaha, K. Schwartz, and J. P. Perdew, and Fe: Performance of local-spin-density and generalized-gradient-approximation density functionals, Physical Review B, vol.58, issue.17, p.11266, 1998.
DOI : 10.1103/PhysRevB.58.11266