We start with fully optimized centrosymmetric paraelectric (and also ferromagnetic for VOX 2 ) phase (space group: P mmm) of MOX 2 monolayers and calculate their phonon dispersion. We nd that there is an imaginary (soft) optical vibration mode at the center of the Brillouin zone ( Γ-point) for the PE phase (see Fig for TiOBr 2 and also Supporting Information for other MOX 2 ). The frequency (iω Γ ) associated with the polar soft mode is given in the Table . This suggests that there is a spontaneous atomic displacement of Ti(V) along the Ti-O (V-O) chain, breaking the inversion symmetry, thus producing a spontaneous in-plane (along a-direction) electric polarization. This can also be understood in terms of long and short Ti-O (V-O) bonds along the a-direction in FE phase (space group: P mm2), whereas all M-O bonds are same in PE phase. Therefore, a lattice parameter of FE phase becomes slightly larger than that of PE phase, although b lattice parameter remains almost unchanged (see Table ). As Ti 4+ and V 4+ have almost same ionic radius, their lattice parameters are close. We see increase in b as radius of X increases from F to Br, which is expected because X atoms are only along the bdirection. With the exception of TiOF 2 (FE), the phonon Table . Structural information of the monolayers: optimized lattice parameters (a and b; see the rectangular cells in Figure ). M-O (M-X) represents the bond length between metal (M) and oxygen (halogen; X) atoms. Z11 is the Born eective charge in |e| unit. The values in the parentheses are for paraelectric phases. P1 and △E are the in-plane electric polarization in 2D unit (C/m) and energy dierence between ferroelectric and paraelectric phase (positive △E value suggests FE phase is lower in energy compared to PE). iωΓ stands for the lowest imaginary frequency of PE phase at the Γ-point.