{\em Hartree-Fock equations}
\begin{eqnarray}
\label{eq:hf}
\left( \frac{{\bf p_i^2}}{2m} - \frac{e^{2}}{4\pi\epsilon_{0}}
\frac{Z}{r} \right) \psi_a(i) 
+
\left[ \sum_b^{occ} \int \psi_b(j) \frac{e^{2}}{4\pi\epsilon_{0}} 
\frac{1}{r_{ij}}
\psi_b(j) dV_j \right] \psi_a(i) \nonumber \\
\nonumber \\
- \left[ \sum_b^{occ} \int \psi_b(j) \frac{e^{2}}{4\pi\epsilon_{0}} 
\frac{1}{r_{ij}}
\psi_a(j) dV_j \right] \psi_b(i) = \varepsilon_a \psi_a(i).
\end{eqnarray}