  In this article we show how Ehrenfest mean field theory can be made both a
more accurate and efficient method to treat nonadiabatic quantum dynamics by
combining it with the generalized quantum master equation framework. The
resulting mean field generalized quantum master equation (MF-GQME) approach is
a non-perturbative and non-Markovian theory to treat open quantum systems
without any restrictions on the form of the Hamiltonian that it can be applied
to. By studying relaxation dynamics in a wide range of dynamical regimes,
typical of charge and energy transfer, we show that MF-GQME provides a much
higher accuracy than a direct application of mean field theory. In addition,
these increases in accuracy are accompanied by computational speed-ups of
between one and two orders of magnitude that become larger as the system
becomes more nonadiabatic. This combination of quantum-classical theory and
master equation techniques thus makes it possible to obtain the accuracy of
much more computationally expensive approaches at a cost lower than even mean
field dynamics, providing the ability to treat the quantum dynamics of
atomistic condensed phase systems for long times.
