Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

Abstract: The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C₂ singlet ground state is known to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B_2, C₂, O₂, and F₂ in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C₂. This work shows that spin symmetry breaking in singlet C₂, the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that under-binding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry-breaking with an advanced density functional might reliably describe strong correlation. This talk also discusses some general aspects of symmetry breaking, and the insights into strong correlation that symmetry-breaking can bring.