  Two-dimensional layered transition metal dichalcogenide (TMDC) materials
often exhibit exotic quantum matter phases due to the delicate coupling and
competitions between the charge, lattice, orbital, and spin degrees of freedom.
Surprisingly, we here present, based on first-principles density-functional
theory calculations, the incorporation of all such degrees of freedom in a
charge density wave (CDW) of monolayer (ML) TMDC 1$T$-TaS$_2$. We reveal that
the CDW formed via the electron-phonon coupling is significantly stabilized by
the orbital hybridization. The resulting lattice distortion to the "David-star"
superstructure constituted of one cental, six nearest-neighbor, and six
next-nearest-neighbor Ta atoms is accompanied by the formation of
quasimolecular orbitals due to a strong hybridization of the Ta $t_{\rm 2g}$
orbitals. Furthermore, the flat band of the quasimolecular orbital at the Fermi
level has a spin splitting caused by an intramolecular exchange, yielding a
full spin polarization with a band-gap opening. Our finding of the intricate
charge-lattice-orbital-spin coupling in ML 1$T$-TaS$_2$ provides a framework
for the exploration of various CDW phases observed in few-layer or bulk
1$T$-TaS$_2$.
