  There is currently much interest in the development of improved
trajectory-based methods for the simulation of nonadiabatic processes in
complex systems. An important goal for such methods is the accurate calculation
of the rate constant over a wide range of electronic coupling strengths and it
is often the nonadiabatic, weak-coupling limit, which being far from the
Born-Oppenheimer regime, provides the greatest challenge to current methods. We
show that in this limit there is an inherent sign problem impeding further
development which originates from the use of the usual quantum flux correlation
functions, which can be very oscillatory at short times. From linear response
theory, we derive a modified flux correlation function for the calculation of
nonadiabatic reaction rates, which still rigorously gives the correct result in
the long-time limit regardless of electronic coupling strength, but unlike the
usual formalism is not oscillatory in the weak-coupling regime. In particular,
a trajectory simulation of the modified correlation function is naturally
initialized in a region localized about the crossing of the potential energy
surfaces. In the weak-coupling limit, a simple link can be found between the
dynamics initialized from this transition-state region and an generalized
quantum golden-rule transition-state theory, which is equivalent to Marcus
theory in the classical harmonic limit. This new correlation function formalism
thus provides a platform on which a wide variety of dynamical simulation
methods can be built aiding the development of accurate nonadiabatic rate
theories applicable to complex systems.
