  To understand superconductivity in Chevrel phase compounds and guide the
search for interesting properties in materials created with Chevrel phase
molecules as building blocks, we use ab-initio methods to study the properties
of single Mo$_6$X$_8$ molecules with $X=S$, $Se$, $Te$ as well as the bulk
solid PbMo$_6$S$_8$. In bulk PbMo$_6$S$_8$, the different energy scales from
strong to weak are: the band kinetic energy, the intra-molecular Coulomb
interaction, the on-molecule Jahn-Teller energy and the Hund's exchange
coupling. The metallic state is stable with respect to Mott and polaronic
insulating states. The bulk compound is characterized by a strong
electron-phonon interaction with the largest coupling involving phonon modes
with energies in the range from 11 meV to 17 meV and with a strong
inter-molecule (Peierls) character. A two-band Eliashberg equation analysis
shows that the superconductivity is strong-coupling, with different gaps on the
two Fermi surface sheets. A Bergman-Rainer analysis of the functioanl
derivative of the transition temperature with respect to the electron-phonon
coupling reveals that the Peierls modes provide the most important contribution
to the superconductivity. This work illustrates the importance of
inter-molecular coupling for collective phenomena in molecular solids.
