Toward Practical Corrections of Artificial Symmetry Breaking in Molecular Self-Consistent Field Calculations

Spin symmetry breaking is a critical part of practical molecular electronic structure calculations. A commonly cited example is the so-called “strongly correlated” dissociation limit of ground-state singlet hydrogen molecule. Spin-restricted singlet Hartree-Fock or Kohn-Sham density functional theory calculations give an artificially high energy, while spin-unrestricted calculations localize spin-up and spin-down electrons to different atoms and return a reasonable dissociation energy. A number of literature reports have documented unexpected spin symmetry breaking in the Hartree-Fock ground states of conjugated π-systems as common as benzene. Such symmetry breaking is typically identified by restricted/unrestricted instability and the resulting broken-symmetry and spin-contaminated unrestricted Hartree-Fock wave functions and Kohn-Sham determinants. We show that symmetry breaking degrades predicted properties of many of these systems. Moreover, we demonstrate that practical spin purification models can improve the quality of calculated minimum energy geometries and vibrational frequencies while retaining reasonable computational cost. These results show that careful consideration of spin symmetry can be important in simulating even "normal" systems.