Using the Becke-3–Lee-Yang-Parr (B3LYP) functional, we have performed band-structure calculations on the high-temperature superconductor parent compound, ${\mathrm{La}}_2{\mathrm{CuO}}_4.$ Under the restricted spin formalism $({\rho }_{\uparrow }={\rho }_{\downarrow }),$ B3LYP band structure agrees well with the standard local-density approximation (LDA) band structure. It is metallic with a single Cu $x^2-y^2/\mathrm{O}$ $p_{\sigma }$ band crossing the Fermi level. Under the unrestricted spin formalism $\left({\rho }_{\uparrow }\ne {\rho }_{\downarrow }\right),$ the B3LYP band structure has a spin-polarized antiferromagnetic solution with a band gap of 2.0 eV, agreeing well with experiment. This state is 0.52 eV (per formula unit) lower than that calculated under the restricted spin formalism. The apparent high energy of the spin-restricted state is attributed to an overestimate of on-site Coulomb repulsion, which is corrected in the unrestricted spin calculations. The stabilization of the total energy with spin polarization arises primarily from the stabilization of the $x^2-y^2$ band, such that the character of the eigenstates at the top of the valence band in the antiferromagnetic state becomes a strong mixture of Cu $x^2-y^2/\mathrm{O}$ $p_{\sigma }$ and Cu $z^2/{\mathrm{O}}^{\prime }$ $p_z.$ Since the Hohenberg-Kohn theorem requires the spin-restricted and spin-unrestricted calculations to give identical ground-state energies and total spatial densities for the exact functionals, this large disparity in energy reflects the inadequacy of current functionals for describing the cuprates. This calls into question the use of band structures based on current restricted spin-density functionals (including LDA) as a basis for single-band theories of superconductivity in these materials.

• Received 7 July 2000

DOI:https://doi.org/10.1103/PhysRevB.63.144510