From Collinear to Noncollinear Spin Density Functionals: The Multicollinear Approach

ABSTRACT Most spin density functionals are collinear, assuming the spin magnetization has only one nonzero component. However, a fully defined functional should be noncollinear, treating all three components of the spin magnetization vector as variables. The multicollinear approach is introduced to bridge this gap by generalizing an arbitrary collinear functional to a noncollinear one. In contrast to the traditional scheme, which adopts the local projection of the spin magnetization vector field, the multicollinear method employs a global projection scheme. It offers several key advantages, including recovering the collinear limit, ensuring global spin rotational invariance, maintaining numerical stability, and providing nonzero local torque. Its broad applicability spans relativistic and nonrelativistic cases, molecular and periodic systems, ground and excited states, as well as static and dynamic simulations. Furthermore, for collinear systems, it provides capabilities that go beyond standard collinear functionals by establishing a rigorous framework for spin‐flip TDDFT. This makes it a powerful tool for treating challenging problems such as double excitations, conical intersections, bond dissociation, and diradicals. Overall, the multicollinear approach provides a unified and versatile framework for quantum chemistry. This article is categorized under: Electronic Structure Theory > Density Functional Theory