Global elucidation of broken symmetry solutions to the independent particle model through a Lie algebraic approach Available to Purchase

Broken symmetry solutions—solutions to the independent particle model that do not obey all symmetries required by the Hamiltonian—have attracted significant interest for capturing multireference properties with mean-field scaling. However, identification and optimization of broken-symmetry solutions is difficult owing to the non-linear nature of the self-consistent field (SCF) equations, particularly for solutions belonging to low-symmetry subgroups and where multiple broken symmetry solutions are sought. Linearization of SCF solution space results in the Lie algebra, which this work utilizes as a framework for elucidation of the set of solutions that exist at the desired symmetry. To demonstrate that searches constructed in the Lie algebra yield the set of broken symmetry solutions, a grid-based search of real-restricted, real-unrestricted, complex-restricted, paired-unrestricted, and real-general solutions of the $C2v$ (nearly D_4h) H₄ molecule is performed.