First-principles study of bulk stacking, J_eff picture, magnetic Hamiltonian, $g$-factors, and structural distortions of α-RuCl₃

α-RuCl₃ is a prominent candidate for realizing the Kitaev quantum spin liquid, but its low-temperature crystal structure remains debated. Although experiments now agree that the high- and low-temperature phases correspond to the $C2/m$ and $R\bar{3}$ space groups, theoretical support for the $R\bar{3}$ structure has been lacking. Here, using constrained density functional theory, we show that the $R\bar{3}$ phase is energetically favored over the $C2/m$ phase, consistent with experiment. We further analyze the conduction band edge states and find that they predominantly exhibit J_eff=1/2 and m_eff=-1/2 character when the angular momentum quantization axis aligns with the Néel vector, underscoring the importance of this alignment in describing electronic states. In addition, we calculate anisotropic exchange parameters and $g$-factors for monolayer α-RuCl₃, revealing the significance of second-nearest-neighbor interactions and magnetic moments beyond atomic orbital projections. The computed $g$-factor anisotropy agrees well with experiments. Finally, we show that octahedral distortions, especially the relative twist of Cl triangles in RuCl₆ octahedron, strongly influence magnetic anisotropy, offering a route to magnetism engineering in Kitaev materials.