  Based on the first-principles plane wave calculations, we studied the
functionalization of the two-dimensional single layer MoS$_2$ structure via
adatom adsorption and vacancy defect creation. Minimum energy adsorption sites
are determined for sixteen different adatoms, each gives rise to diverse
properties. Bare, single layer MoS$_2$, which is normally a nonmagnetic, direct
band gap semiconductor, attains a net magnetic moment upon adsorption of
specific transition metal atoms, as well as silicon and germanium atoms. The
localized donor and acceptor states in the band gap expand the utilization of
MoS$_2$ in nanoelectronics and spintronics. Specific adatoms, like C and O,
attain significant excess charge upon adsorption to single layer MoS$_{2}$
which may be useful for its tribological applications. Each MoS$_{2}$-triple
vacancy created in a single layer MoS$_{2}$ gives rise to a net magnetic
moment, while other vacancy defects related with Mo and S atoms do not
influence the nonmagnetic ground state. Present results are also relevant for
the surface of graphitic MoS$_2$.
