Calculation of Coulomb-interaction parameters forLa2CuO4using a constrained-density-functional approach
The constrained-density-functional approach is used to calculate the energy surface as a function of local charge fluctuations in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. This energy surface is then mapped onto a self-consistent mean-field solution of the Hubbard model which allows extraction of the Coulomb interaction parameters when combined with one-electron parameters derived from band-structure results. Variations in the local Cu d charges and in-plane O p charge are considered for the prototypical high-${T}_{c}$ parent oxide ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. To isolate the charge fluctuations, the calculations are done in a supercell of size up to 2\ifmmode\times\else\texttimes\fi{}2 in the basal plane. The local density-functional calculations are done using the linear muffin-tin orbital approach with the atomic sphere approximation. In the Hubbard Hamiltonian, the Cu d(${x}^{2}$-${y}^{2}$) and O p(x,y) orbitals are included in the pd\ensuremath{\sigma} configuration. The one-electron parameters consist of bare on-site energies (${\ensuremath{\varepsilon}}_{p}$,${\ensuremath{\varepsilon}}_{d}$) and first-neighbor hopping from Cu to O (${t}_{\mathrm{pd}}$) and from O to O (${t}_{\mathrm{pp}}$) while the Coulomb-interaction parameters include on-site (${U}_{d}$,${U}_{p}$) and intersite (${U}_{\mathrm{pd}}$,${U}_{\mathrm{pp}}$) terms. Results of the present calculation indicate that ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ is intermediate between the extreme spin or charge fluctuation regimes. This places strong constraints on the available parameter space for theories of high-${T}_{c}$ superconductivity based on the extended Hubbard model.