The coefficients \( C \) result from the solution of the eigenvalue problem. The energy of say the ground state is then $$ E=E_{ref}+\Delta E, $$ where the so-called reference energy is the energy we obtain from a Hartree-Fock calculation, that is $$ E_{ref}=\langle \Phi_0 \vert \hat{H} \vert \Phi_0 \rangle. $$