Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF

Grofe, A.; Gao, J.; Li, X..  The Journal of Chemical Physics, 2021155, 014103. 

Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to a relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time-reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break the symmetry in order to lower the overall energy, just as unrestricted Hartree–Fock breaks spin symmetry. Overall, we demonstrate that time-reversal symmetry is roughly maintained when using Hartree–Fock, but less so when using Kohn–Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.