  We present the orbital resolved electronic properties of structurally
distorted 1T-TaS2 monolayers. After optimizing the crystal structures, we
obtain the lattice parameters and atomic positions in the star-of-David
structure, and show the low-temperature band structures of distorted bulk are
consistent with recent angle resolved photoemission spectroscopy (ARPES) data.
We further clearly demonstrate that $5d$ electrons of Ta form ordered
orbital-density-wave (ODW) state with dominant $5d_{3{z}^2-{r}^2}$ character in
central Ta, driving the one-dimensional metallic state in paramagnetic bulk and
half-filled insulator in monolayer. Meanwhile, the star-of-David distortion in
monolayers favors charge density wave and the flat band stabilizes
ferromagnetic density wave of Ta spins with the same wavevector of ODW 4/13
b_1+1/13 b2. We propose that $1$T-TaS$_{2}$ monolayer may pave a new way to
study the exciton physics, exciton-polaron coupling, and potential applications
for its exciton luminescence.
