  Nonadiabatic transition dynamics lies at the core of many electron/hole
transfer, photoactivated, and vacuum field-coupled processes. About a century
after Ehrenfest proposed "Phasenraum" and the Ehrenfest theorem, we report a
conceptually novel trajectory-based nonadiabatic dynamics approach,
nonadiabatic field (NaF), based on a generalized exact coordinate-momentum
phase space formulation of quantum mechanics. It does not employ the
conventional Born-Oppenheimer or Ehrenfest trajectory in the nonadiabatic
coupling region. Instead, in NaF the equations of motion of the independent
trajectory involve a nonadiabatic nuclear force term in addition to an
adiabatic nuclear force term of a single electronic state. A few benchmark
tests for gas phase and condensed phase systems indicate that NaF offers a
practical tool to capture the correct correlation of electronic and nuclear
dynamics for processes where the states remain coupled all the time as well as
for the asymptotic region where the coupling of electronic states vanishes.
