Two-component natural spinors from two-step spin-orbit coupled wave functions.

We developed an algorithm to obtain the natural orbitals (natural spinors) from the two-step spin-orbit coupled wave functions. These natural spinors are generally complex-valued, mixing two spin components, and they can have similar symmetry properties as the j-j spinors from the one-step spin-orbit coupling calculations, if the reduced density equally averages all the components of a multi-dimensional irreducible representation. Therefore, the natural spinors can serve as an approximation to the j-j spinors and any wave function analysis based on the j-j spinors can also be performed based on them. The comparison between the natural spinors and the j-j spinors of three representative atoms, Tl, At, and Lu, shows their close similarity and demonstrates the ability of the natural spinors to approximate the j-j spinors.