  In part I, we presented the ring-polymer instanton with explicit friction
(RPI-EF) method and showed how it can be connected to the \textit{ab initio}
electronic friction formalism. This framework allows the calculation of
tunneling reaction rates that incorporate the quantum nature of the nuclei and
certain types of non-adiabatic effects (NAEs) present in metals. In this second
part, we analyze the performance of RPI-EF on model potentials and apply it to
realistic systems. For a 1D double-well model, we benchmark the method against
numerically exact results obtained from multi-layer multi-configuration
time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for
medium and high friction strengths and less accurate for extremely low friction
values. We also show quantitatively how the inclusion of NAEs lowers the
cross-over temperature into the deep tunneling regime, reduces the tunneling
rates, and in certain regimes, steers the quantum dynamics by modifying the
tunneling pathways. As a showcase of the efficiency of this method, we present
a study of hydrogen and deuterium hopping between neighboring interstitial
sites in selected bulk metals. The results show that multidimensional
vibrational coupling and nuclear quantum effects have a larger impact than NAEs
on the tunneling rates of diffusion in metals. Together with part I, these
results advance the calculations of dissipative tunneling rates from first
principles.
