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.