Trajectory sampling and finite-size effects in first-principles stopping power calculations

TL;DR

This paper introduces a quantitative metric for evaluating ion trajectories in first-principles stopping power calculations using TDDFT, revealing sampling issues, finite-size effects, and proposing cost-effective solutions for more accurate results.

Contribution

It develops a new trajectory evaluation metric, analyzes sampling and finite-size effects in TDDFT stopping power calculations, and offers methods to reduce computational costs while maintaining accuracy.

Findings

Nearly 30% of random trajectories are unrepresentative in FCC aluminium.

Unrepresentative trajectories can cause errors up to 60%.

Finite-size effects involve 'ouroboros' effects beyond plasmon models.

Abstract

Real-time time-dependent density functional theory (TDDFT) is presently the most accurate available method for computing electronic stopping powers from first principles. However, obtaining application-relevant results often involves either costly averages over multiple calculations or ad hoc selection of a representative ion trajectory. We consider a broadly applicable, quantitative metric for evaluating and optimizing trajectories in this context. This methodology enables rigorous analysis of the failure modes of various common trajectory choices in crystalline materials. Although randomly selecting trajectories is common practice in stopping power calculations in solids, we show that nearly 30% of random trajectories in an FCC aluminium crystal will not representatively sample the material over the time and length scales feasibly simulated with TDDFT, and unrepresentative choices incur errors of up to 60%. We also show that finite-size effects depend on ion trajectory via "ouroboros" effects beyond the prevailing plasmon-based interpretation, and we propose a cost-reducing scheme to obtain converged results even when expensive core-electron contributions preclude large supercells. This work helps to mitigate poorly controlled approximations in first-principles stopping power calculations, allowing 1-2 order of magnitude cost reductions for obtaining representatively averaged and converged results.