Effect of Exact Exchange on the Energy Landscape in Self-Consistent Field Theory

Density functional
approximations can reduce the spin
symmetry
breaking observed for self-consistent field (SCF) solutions compared
to Hartree–Fock theory, but the amount of exact Hartree–Fock
(HF) exchange appears to be a key determinant in broken Ŝ2 symmetry. To elucidate the precise role of exact exchange,
we investigate the energy landscape of unrestricted Hartree–Fock
and Kohn–Sham density functional theory for benzene and square
cyclobutadiene, which provide paradigmatic examples of closed-shell
and open-shell electronic structures, respectively. We find that increasing
the amount of exact exchange leads to more local SCF minima, which
can be characterized as combinatorial arrangements of unpaired electrons
in the carbon π system. Furthermore, we studied the pathways
connecting local minima to understand the relationships between different
solutions. Our analysis reveals a subtle balance between one- and
two-body interactions in determining SCF symmetry breaking, shedding
new light on the physical driving forces for spin-symmetry-broken
solutions in SCF approaches.