Table shows that TiOCl 2 or TiOBr 2 monolayer has quite large e 11 but small e 12 , compared to that of VOX 2 monolayers. We also notice that unlike 1Htype monolayers e.g., 1H-MoS 2 where e 11 = -e 12 due to 6m2 point group symmetry, MOX 2 monolayers exhibit highly anisotropic piezo-response, where e 11 is signicantly larger than e 12 . This is also expected as the monolayers have a strong in-plane electric polarization P 1 , hence atomic displacement in response to strain along a-direction can change P 1 directly. Interestingly, we observe a general trend that in-plane piezo-response (e 11 ) decreases as the in-plane polarization increases (see Table I and III). To understand the origin of large/small piezoelectric constant, we decompose e 11 and e 12 into two terms (i) the clamped-ion term ( e elc 11 or e elc 12 ), which is the electronic contribution where the atoms are xed at their equilibrium internal coordinates (u) and (ii) the ionic contribution term, e ion 11 (e ion 12 ) due to the atomic displacements in response to a macroscopic strain η 1 (η 2 ) along the a-direction ( b-direction). e ion 11 of TiOCl 2 and TiOBr 2 monolayers is almost twice larger than that of VOX 2 . Interestingly, we notice that both ionic and electronic parts of e 11 are positive (see Table ), thus they contribute positively to the total e 11 same like 1H-MoS 2 . That is why TiOCl 2 or TiOBr 2 monolayer has signicantly large e 11 , compared to that of VOX 2 , although e elc 11 of TiOCl 2 and TiOBr 2 monolayers is slightly smaller than that of VOX 2 . On the other hand, ionic and electronic part of e 12 are opposite in sign, hence they reduce the total e 12 . We see that because of their small positive e elc 12 but large negative e ion 12 , TiOCl 2 and TiOBr 2 monolayers have quite small e 12 (see Table ). We further decompose the ionic part :