Efficient ab initio calculation of electronic stopping in disordered systems via geometry pre-sampling: Application to liquid water

Knowledge of the electronic stopping curve for swift ions, S-e(v), particularly around the Bragg peak, is important for understanding radiation damage. Experimentally, however, the determination of such a feature for light ions is very challenging, especially in disordered systems such as liquid water and biological tissue. Recent developments in real-time time-dependent density functional theory (rt-TDDFT) have enabled the calculation of S-e(v) along nm-sized trajectories. However, it is still a challenge to obtain a meaningful statistically averaged S-e(v) that can be compared to observations. In this work, taking advantage of the correlation between the local electronic structure probed by the projectile and the distance from the projectile to the atoms in the target, we devise a trajectory pre-sampling scheme to select, geometrically, a small set of short trajectories to accelerate the convergence of the averaged S-e(v) computed via rt-TDDFT. For protons in liquid water, we first calculate the reference probability distribution function (PDF) for the distance from the proton to the closest oxygen atom, phi (R)(r(p -> O)), for a trajectory of a length similar to those sampled experimentally. Then, short trajectories are sequentially selected so that the accumulated PDF reproduces phi (R)(r(p -> O)) to increasingly high accuracy. Using these pre-sampled trajectories, we demonstrate that the averaged S-e(v(p)) converges in the whole velocity range with less than eight trajectories, while other averaging methods using randomly and uniformly distributed trajectories require approximately ten times the computational effort. This allows us to compare the S-e(v(p)) curve to experimental data and assess widely used empirical tables based on Bragg's rule.