Using ab initio density functional theory, here we systematically study the monolayer ${\mathrm{MoOCl}}_2$ with a $4d^2$ electronic configuration. Our main result is that an orbital-selective Peierls phase (OSPP) develops in ${\mathrm{MoOCl}}_2$, resulting in the dimerization of the Mo chain along the $b$ axis. Specifically, the Mo-$d_{xy}$ orbitals form robust molecular-orbital states inducing localized $d_{xy}$ singlet dimers, while the Mo-$d_{xz/yz}$ orbitals remain delocalized and itinerant. Our study shows that ${\mathrm{MoOCl}}_2$ is globally metallic, with the Mo-$d_{xy}$ orbital bonding-antibonding splittings opening a gap and the Mo-$d_{xz/yz}$ orbitals contributing to the metallic conductivity. Overall, the results resemble the recently much discussed orbital-selective Mott phase but with the localized band induced by a Peierls distortion instead of Hubbard interactions. Finally, we also qualitatively discuss the possibility of OSPP in the $3d^2$ configuration, as in ${\mathrm{CrOCl}}_2$.

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• Orbital order
• Peierls transition
• Phase transitions
• 1-dimensional systems
• Strongly correlated systems
• Density functional theory
• First-principles calculations