Strongly anisotropic electronic and magnetic structures in oxide dichlorides <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">RuOCl</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">OsOCl</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

Here, using density functional theory and matrix renormalization group methods, we investigate the electronic magnetic properties of RuOCl$_2$ OsOCl$_2$ with $d^4$ configurations. Different from a previous study VOI$_2$ $d^1$ configuration, these systems $4d^4$ or $5d^4$ do not exhibit ferroelectric instability along $a$-axis. Due to fully-occupied $d_{xy}$ orbital in OsOCl$_2$, Peierls distortion disappears $b$-axis, leading an undistorted I${\rm mmm}$ phase (No. 71). Furthermore, observe strongly anisotropic structures The large crystal-field splitting energy (between $d_{xz/yz}$ orbitals) hopping between nearest-neighbor Ru Os atoms suppresses spin-orbital effect $M$OCl$_2$ ($M$ = Os) $n 4$, resulting spin-1 system instead $J 0$ singlet ground state. Moreover, find staggered antiferromagnetic order $\pi$ wavevector $M$-O chain direction ($a$-axis) while coupling $b$-axis is weak. Based on Wannier functions first-principles calculations, calculated relevant amplitudes energies $t_{2g}$ orbitals for construct multi-orbital Hubbard model chains. Staggered AFM $\uparrow$-$\downarrow$-$\uparrow$-$\downarrow$ spin structure dominates our DMRG agreement DFT calculations.