Supercell Band Calculations and Correlation for High-T_C Copper Oxide Superconductors

First principle band calculations based on local versions of density functional theory (DFT), together with results from nearly free-electron models, can describe many typical but unusual properties of the high-TC copper oxides. The methods and a few of the most important results are reviewed. Some additional calculations are presented, and the problems with the commonly used approximate versions of DFT for oxides are discussed with a few ideas for corrections. It is concluded that rather modest corrections to the approximate DFT, without particular assumptions about strong correlation, can push the ground state towards antiferro magnetic (AFM) order. Spin fluctuations interacting with phonons are crucial for the mechanism of superconductivity in this scenario