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 (nearly D4h) H4 molecule is performed.
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Research Article| November 20 2018
Global elucidation of broken symmetry solutions to the independent particle model through a Lie algebraic approach
Lee M. Thompson; Global elucidation of broken symmetry solutions to the independent particle model through a Lie algebraic approach. J. Chem. Phys. 21 November 2018; 149 (19): 194106. https://doi.org/10.1063/1.5049827
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