The electronic energy loss for low-velocity protons channeled in the [
100] direction of single-crystal Au and Al is calculated. The proton t
rajectories are determined by solving the equation of motion. In the p
roton dynamics two forces are included, a repulsive term arising from
the nuclei and core electrons and a friction ford, depending on proton
velocity, arising from the valence electrons. The repulsive force on
the proton is evaluated using a superposition of conservative potentia
ls. The friction coefficient is evaluated by using the local density o
f valence electrons, and a quantum-mechanical transport cross-section
approach with a self-consistent model based on Friedel's sum rule. The
results allow us to describe the nonlinear behavior of energy loss wi
th ion velocity observed experimentally in Au, as well as the linear b
ehavior observed in Al. [S1050-2947(97)05311-0].