  It is well known that fewest-switches surface hopping (FSSH) fails to
correctly capture the quadratic scaling of rate constants with diabatic
coupling in the weak-coupling limit, as expected from Fermi's golden rule and
Marcus theory. To address this deficiency, the most widely used approach is to
introduce a `decoherence correction', which removes the inconsistency between
the wavefunction coefficients and the active state. Here we investigate the
behavior of a new nonadiabatic trajectory method, called the mapping approach
to surface hopping (MASH), on systems that exhibit incoherent rate behavior.
Unlike FSSH, MASH hops between active surfaces deterministically, and can never
have an inconsistency between the wavefunction coefficients and the active
state. We show that MASH is not only able to describe rates for intermediate
and strong diabatic coupling, but can also accurately reproduce the results of
Marcus theory in the golden-rule limit, without the need for a decoherence
correction. MASH is therefore a significant improvement over FSSH in the
simulation of nonadiabatic reactions.
