  Using the Becke-3-LYP functional, we have performed band structure
calculations on the high temperature superconductor parent compound, La2CuO4.
Under the restricted spin formalism (rho(alpha) equal to rho(beta)), the
R-B3LYP band structure agrees well with the standard LDA band structure. It is
metallic with a single Cu x2-y2/O p(sigma) band crossing the Fermi level. Under
the unrestricted spin formalism (rho(alpha) not equal to rho(beta)), the UB3LYP
band structure has a spin polarized antiferromagnetic solution with a band gap
of 2.0 eV, agreeing well with experiment. This state is 1.0 eV (per formula
unit) lower than that calculated from the R-B3LYP. 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 x2-y2 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 x2-y2/O p(sigma) and Cu z2/O' p(z). Since the Hohenberg-Kohn
theorem requires the spin restricted and spin unrestricted calculations give
exactly the same ground state energy and total density 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.
