Self-Consistent Energy Bands of Cu via theXαβMethod

The energy bands of Cu have been calculated self-consistently through use of the improved exchange approximation of Herman, Van Dyke, and Ortenburger (the so-called $X_{\alpha \beta }$ method). The resulting bands are compared with the self-consistent energy bands calculated by the $X_{\alpha }$ method with $\alpha =1.\mathrm{}00$, $\frac{5}{6}$, 0.721, and $\frac{2}{3}$. The $X_{\alpha }$ and $X_{\alpha \beta }$ energy-band widths ($s-p$, $d$) are compared with photoemission data. The differences between the energy-band calculations and the atomic calculations are described. A brief discussion is given of the role of the virial theorem and the variational principle.