Noncollinear generalization of nonlocal pure exchange–correlation functionals

We have recently proposed a method for extending collinear functionals to noncollinear functionals, referred to as the multicollinear approach. While previous studies have applied this method to local and semilocal functionals, demonstrating its effectiveness, the present work extends the approach to nonlocal pure functionals via a novel implementation scheme. As an example, we generalize the weighted spin density approximation functional from its original collinear form to a noncollinear one, introducing the first pure functional that is both nonlocal and noncollinear. Our numerical tests demonstrate that the generalized noncollinear functional satisfies the correct collinear limit, preserves spin rotational invariance, provides nonzero local torque, and maintains numerical stability. This work highlights the broad applicability of the multicollinear approach and provides a reference for developing more sophisticated noncollinear functionals beyond local and semilocal forms.