  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.
