Realistic Electronic Structure Calculations for Magnetic Insulators Like La_{2}CuO_{4}

We suggest that Hartree-Fock theory is a good starting point for the solution of ab initio-derived extended Hubbard Hamiltonians for magnetic insulators like ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$, as indicated by surprisingly accurate results for the superexchange frequencies and insulating gaps for this material and isostructural ${\mathrm{La}}_2$Ni${\mathrm{O}}_4$, ${\mathrm{K}}_2$Cu${\mathrm{F}}_4$, and ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$. Limited configuration interaction beyond Hartree-Fock theory is then used to demonstrate that admixtures of $a_1 \left(d_{3z^2-r^2}\right)$ symmetry states at energies somewhat away from the gap edge are essential to the dispersion of the first quasiparticle branch in ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$ for doped-in holes.