Hartree-Fock algorithm

Our Hartree-Fock matrix is thus $$\hat{h}_{\alpha\beta}^{HF}=\langle \alpha | \hat{h}_0 | \beta \rangle+ \sum_{j=1}^A\sum_{\gamma\delta} C^*_{j\gamma}C_{j\delta}\langle \alpha\gamma|\hat{v}|\beta\delta\rangle_{AS}.$$ The Hartree-Fock equations are solved in an iterative waym starting with a guess for the coefficients $$C_{j\gamma}=\delta_{j,\gamma}$$ and solving the equations by diagonalization till the new single-particle energies $$\epsilon_i^{\mathrm{HF}}$$ do not change anymore by a prefixed quantity.