  Despite being successfully synthesized [Zhang $et$ $al.$, Nat. Mater.
\textbf{20}, 1073 (2021)], the monolayer structure of stable hexagonal TiO$_2$
is unknown, and it is not even clear whether it can exist in a freestanding
form. Through first-principles calculations, we have identified two previously
uncharted stable structures, namely, distorted 1$\times$$\sqrt{3}$ 1T-TiO$_2$
and $\sqrt{3}$$\times$$\sqrt{3}$ 1T-TiO$_2$, both of which are energetically
more favourable than commonly adopted 1H and 1T phases. Here structural
distortions are characterized by the out-of-plane shifts of Ti atoms due to the
pseudo-Jahn-Teller interactions, which break one and all two inversion
symmetries of 1T configuration. As a consequence, the 1$\times$$\sqrt{3}$ 1T
remains centrosymmetric while the $\sqrt{3}$$\times$$\sqrt{3}$ 1T exhibits
out-of-plane ferroelectricity. Electronic structure calculations show that both
two are wide-bandgap semiconductors with bandgaps larger than their bulk
counterparts. Our study not only deepens the understanding of structural
instability in wide-gap semiconductors but also adds a new member to the rare
family of two-dimensional out-of-plane ferroelectrics.
