Operator Formalism for Noncollinear Functionals in the Multicollinear Approach

Accurate modeling of spin–orbit coupling and noncollinear magnetism requires noncollinear density functionals within the two-component generalized Kohn–Sham framework, yet constructing and implementing noncollinear functionals remains challenging. Recently, a well-defined methodology called the multicollinear approach was proposed to extend collinear functionals into noncollinear ones. While previous research focuses on its matrix representation, the present work derives its operator formalism. We implement these new equations in our noncollinear functional ensemble named NCXC, which is expected to facilitate compatibility with most DFT software packages. Since the multicollinear approach was proposed for solving nonphysical properties and mathematical singularities in noncollinear functionals, we validate its accuracy in practical periodic systems, including noncollinear magnetism in spin spirals, band structures in topological insulators, and band gaps in semiconducting inorganic materials.