  Laser cooling of translational motion of small molecules is performed by
addressing transitions that ensure spontaneous emission cannot cause net
rotational excitation. This will not be possible once the rotational splitting
becomes comparable to the operational excitation linewidth, as will occur for
large molecules or wide bandwidth lasers. We show theoretically that in this
regime, angular momentum transfer from red-detuned Doppler cooling light can
also exert a damping torque on linear molecules, cooling rotation to the same
Doppler limit (typically $\approx$ 500 $\mu$K for molecules with $\approx$ 10
ns excited-state lifetimes). This cooling process is derived from photon spin,
and indicates that standard optical molasses can also cool molecular rotation
with no additional experimental resources.
