  Sulphur depletion in the interstellar medium (ISM) is a long-standing issue,
as only 1% of its cosmic abundance is detected in dense molecular clouds (MCs),
while it does not appear to be depleted in other environments. In addition to
gas phase species, MCs also contain interstellar dust grains, which are
irregular, micron-sized, solid aggregates of carbonaceous materials and/or
silicates. Grains provide a surface where species can meet, accrete, and react.
Although freeze-out of sulphur onto dust grains could explain its depletion,
only OCS and, tentatively, SO$_2$ were observed on their surfaces. Therefore,
it is our aim to investigate the interaction between sulphur-containing species
and the exposed mineral core of the grains at a stage prior to when sulphur
depletion is observed. Here, the grain core is represented by olivine
nanoclusters, one of the most abundant minerals in the ISM, with composition
Mg$_4$Si$_2$O$_8$ and Mg$_3$FeSi$_2$O$_8$. We performed a series of quantum
mechanical calculations to characterize the adsorption of 9 S-bearing species,
both neutral and charged, onto the nanoclusters. Our calculations reveal that
the Fe-S interaction is preferred to Mg-S, causing sometimes the chemisorption
of the adsorbate. These species are more strongly adsorbed on the bare dust
grain silicate cores than on water ice mantles, and hence therefore likely
sticking on the surface of grains forming part of the grain core. This
demonstrates that the interaction of bare grains with sulphur species in cloud
envelopes can determine the S-depletion observed in dense molecular clouds.
