  The adiabatic Born-Oppenheimer approximation is considered to be a robust
approach that very rarely breaks down. Consequently, it is predominantly
utilized to address various electron-phonon properties in condensed matter
physics. By combining many-body perturbation and density functional theories we
demonstrate the importance of dynamical (nonadiabatic) effects in estimating
superconducting properties in various bulk and two-dimensional materials. Apart
from the expected long-wavelength nonadiabatic effects, we found sizable
nonadiabatic Kohn anomalies away from the Brillouin zone center for materials
with strong intervalley electron-phonon scatterings. Compared to the adiabatic
result, these dynamical phonon anomalies can significantly modify
electron-phonon coupling strength $\lambda$ and superconducting transition
temperature $T_c$. Further, the dynamically-induced modifications of $\lambda$
have a strong impact on transport properties, where probably the most
interesting is the rescaling of the low-temperature and low-frequency regime of
the scattering time $1/\tau$ from about $T^3$ to about $T^2$, resembling the
Fermi liquid result for electron-electron scattering. Our goal is to point out
the potential implications of these nonadiabatic effects and reestablish their
pivotal role in computational estimations of electron-phonon properties.
