  Using first-principles density functional theory calculations, we investigate
the structure, stability, optical modes and electronic band gap of a distorted
tetragonal MoS$_2$ monolayer (T'-MoS$_2$). Our simulated scanning tunnel
microscopy (STM) images of T'-MoS$_2$ are dramatically similar with those STM
images which were identified as K$_{x}$(H$_{2}$O)$_{y}$MoS$_{2}$ from a
previous experimental study. This similarity suggests that T'-MoS$_2$ might
have already been observed in experiment but was unexpectedly misidentified.
Furthermore, we verify the stability of T'-MoS$_2$ from thermal, mechanical and
dynamic aspects, by \emph{ab initio} molecular dynamics simulation, elastic
constants evaluation and phonon band structure calculation based on density
functional perturbation theory, respectively. In addition, we calculate the
eigenfrequencies and eigenvectors of the optical modes of T'-MoS$_2$ at
$\Gamma$ point and distinguish their Raman and infrared activity by pointing
out their irreducible representations using group theory; at the same time, we
compare the Raman modes of T'-MoS$_2$ with those of H-MoS$_2$ and T-MoS$_2$.
Our results provide a useful guidance for further experimental identification
and characterization of T'-MoS$_2$.
