  We describe a multiple electronic state adaptation of the mapping approach to
surface hopping introduced recently by Mannouch and Richardson (J. Chem. Phys.
158, 104111 (2023)). This adaptation treats populations and coherences on an
equal footing and is guaranteed to give populations in any electronic basis
that tend to the correct quantum-classical equilibrium values in the long-time
limit (assuming ergodicity). We demonstrate its accuracy by comparison with
exact benchmark results for three- and seven-state models of the
Fenna-Matthews-Olson complex, obtaining electronic populations and coherences
that are significantly more accurate than those of fewest switches surface
hopping and at least as good as those of any other semiclassical method we are
aware of. Since these results were obtained by adapting the scheme of Mannouch
and Richardson, we go on to compare our results with theirs for a variety of
problems with two electronic states. We find that their method is sometimes
more accurate, and especially so in the Marcus inverted regime. However, in
other situations the accuracies are comparable, and since our scheme can be
used with multiple electronic states it can be applied to a wider variety of
systems.
