Orbital occupation selects structural dimensionality in binary transition-metal oxides
Orbital-lattice coupling in transition-metal oxides is usually discussed within a given bonding framework, where orbital occupation is intertwined with local coordination, strain, or symmetry breaking. Here, we show that orbital occupation can also select the bonding framework itself, thereby determining structural dimensionality. Using first-principles calculations, we identify CrO as a prototype in which the single active $3d\,e_g$ electron of high-spin Cr$^{2+}$ gives rise to two competing orbital-structure states. The $d_{x^2-y^2}$ occupation favors a three-dimensionally connected covalent phase, whereas the $d_{z^2}$ occupation stabilizes a weakly coupled layered phase. Constrained-occupation calculations show that increasing the $d_{z^2}$ filling continuously contracts the in-plane lattice while expanding the structure along the layer normal. The two phases exhibit distinct magnetic ground states and ferroelastic responses. Moreover, the layered phase is robust against exchange-correlation functional and on-site ($U$) variations, remains dynamically stable down to the monolayer limit, and has a low exfoliation energy of 46 meV/Angstrom^2. Extending the analysis across related $3d$ binary oxides reveals a filling-dependence relation between accessible orbital filling and the preference for 2D or 3D connected bonding motifs, providing a microscopic basis for exploring low-dimensional oxide materials.