  Some chemical reactions are described by electron transfer (ET) processes.
The underlying mechanism could be modeled as a polaron motion in the molecular
crystal-the Holstein model. By taking spin degrees of freedom into
consideration, we generalize the Holstein model (molecular crystal model) to
microscopically describe an ET chemical reaction. In our model, the electron
spins in the radical pair simultaneously interact with a magnetic field and
their nuclear-spin environments. By virtue of the perturbation approach, we
obtain the chemical reaction rates for different initial states. It is
discovered that the chemical reaction rate of the triplet state demonstrates
its dependence on the direction of the magnetic field while the counterpart of
the singlet state does not. This difference is attributed to the explicit
dependence of the triplet state on the direction when the axis is rotated. Our
model may provide a possible candidate for the microscopic origin of avian
compass.
