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.
Bibliographical noteFunding Information:
X.L. acknowledges support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, in the Heavy-Element Chemistry program (Grant No. DE-SC0021100), for the development of relativistic electronic structure methods. The development of excited state methods was supported by the Computational Chemical Sciences (CCS) Program of the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division in the Center for Scalable and Predictive methods for Excitations and Correlated phenomena (SPEC) at the Pacific Northwest National Laboratory. The development of the open source software package was supported by the U.S. National Science Foundation (Grant Nos. OAC-1663636 and CHE-1856210). Work carried out at the Shen-zhen Bay Laboratory was supported by a grant from the Shenzhen Municipal Science and Technology Innovation Commission (Grant No. KQTD2017-0330155106581 to J.G.).
© 2021 Author(s).