  Using {\it ab initio} density functional theory and single-orbital Hubbard
model calculations via the density matrix renormalization group method, we
systematically studied the monolayer VOI$_2$ with a $3d^1$ electronic
configuration. Our phonon calculations indicate that the orthorhombic $Pmm2$
FE-II phase is the most likely ground state, involving a ferroelectric
distortion along the $a$-axis and V-V dimerization along the $b$-axis.
Specifically, the "pseudo Jahn-Teller" effect caused by the coupling between
empty V ($d_{xz/yz}$ and $d_{3z^2-r^2}$) and O $2p$ states is proposed as the
mechanism that stabilizes the ferroelectric distortion from the paraelectric
phase. Moreover, the half-filled metallic $d_{xy}$ band displays a Peierls
instability along the $b$-axis, inducing a V-V dimerization. We also found very
short-range antiferromagnetic coupling along the V-V chain due to the formation
of nearly-decoupled spin singlets in the ground state.
