Bragg's Additivity Rule and Core and Bond model studied by real-time TDDFT electronic stopping simulations: the case of water vapor

TL;DR

This study uses real-time TDDFT simulations to analyze the electronic stopping power of water vapor and related gases for protons, validating Bragg's Additivity Rule and exploring core and bond contributions at various energies.

Contribution

It provides the first rt-TDDFT-based validation of Bragg's Additivity Rule for water vapor and decomposes electronic stopping into core and bond contributions, highlighting differences from SRIM predictions.

Findings

Bragg's Additivity Rule holds for water vapor above 40 keV/amu in rt-TDDFT simulations.

Core and bond contributions to stopping power are slightly smaller than SRIM estimates.

Simulations converge with 25-30 short ion trajectories, confirming efficiency.

Abstract

The electronic stopping power ($S_e$) of water vapor (H$_2$O), hydrogen (H$_2$) and oxygen (O$_2$) 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 ($E_k$) ranging from 1.56 keV/amu to 1.6 MeV/amu. $S_e$ was calculated as the average over geometrically pre-sampled short ion trajectories. The average $S_e(E_k)$ values were found to rapidly converge with 25-30 pre-sampled, 2 nm-long ion trajectories. The rt-TDDFT $S_e(E_k)$ 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 $\mathrm{2H_2+O_2}$ $\mathrm{\rightarrow 2H_2O}$ 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.