Bragg's additivity rule and core and bond model studied by real-time TDDFT electronic stopping simulations: The case of water vapor

The electronic stopping power (Se) of water vapor (H2O), hydrogen (H-2) and oxygen (O2) gases for protons in a broad range of energies, centered in the Bragg peak, was calculated using real-time time-dependent density functional theory (rt-TDDFT) simulations with Gaussian basis sets. This was done for a kinetic energy of incident protons (Ek) ranging from 1.56 keV/amu to 1.6 MeV/amu. Se was calculated as the average over geometrically pre-sampled short ion trajectories. The average Se(Ek) values were found to rapidly converge with 25-30 pre sampled, 2 nm-long ion trajectories. The rt-TDDFT Se(Ek) curves were compared to experimental and SRIM data, and used to validate the Bragg's Additivity Rule (BAR). Discrepancies were analyzed in terms of basis set effects and omitted nuclear stopping at low energies. At variance with SRIM, we found that BAR is applicable to our rt-TDDFT simulations of 2H(2) + O-2 -> 2H(2)O without scaling for E-k > 40 keV/amu. The hydrogen and oxygen Core and Bond (CAB) contributions to electronic stopping were calculated and found to be slightly smaller than SRIM values as a result of a red-shift in our rt-TDDFT S-e(E-k) curves and a re-distribution of weights due to some bond contributions being neglected in SRIM.

Automated summary

The electronic stopping power (Se) of water vapor, hydrogen, and oxygen gases for protons was calculated using real-time time-dependent density functional theory. The results were compared to experimental and SRIM data, and the applicability of the Bragg's Additivity Rule was validated. The contributions of hydrogen and oxygen atoms to the electronic stopping power were also analyzed, revealing slight differences due to the neglected bond contributions in SRIM.