  Utilization of electron transfer methods for description of quantum transport
is popular due to simplicity of the formulation and its ability to account for
basic physics of electron exchange between system and baths. At the same time,
necessity to go beyond simple golden rule-type expressions for rates was
indicated in the literature and ad hoc formulations were proposed. Similarly,
kinetic schemes for quantum transport beyond usual second order
Lindblad/Redfield considerations were discussed. Here we utilize recently
introduced by us nonequilibrium Hubbard Green's functions diagrammatic
technique to analyze construction of rates in open systems. We show that
previous considerations for rates of second and fourth order can be obtained as
a particular case of zero and second order Green's function diagrammatic series
with bare diagrams. We discuss limitations of previous considerations, stress
advantages of the Hubbard Green's function approach in constructing the rates
and indicate that standard dressing of the diagrams is a natural way to account
for additional baths/degrees of freedom when formulating generalized
expressions for the rates.
