= Solution
\b[Restricted Hartree–Fock incorrectly retains ionic configurations when a homonuclear bond dissociates.] As overlap vanishes, its symmetry-preserving occupied orbital approaches $(\phi_A+\phi_B)/\sqrt2$. The doubly occupied spatial product contains
$$
\psi(1)\psi(2)=\tfrac12\{\phi_A(1)\phi_A(2)+\phi_A(1)\phi_B(2)
+\phi_B(1)\phi_A(2)+\phi_B(1)\phi_B(2)\}.
$$
The first and last terms place both electrons on one separated atom. Their combined probability remains one half, while the correct neutral singlet has one electron on each atom. The resulting spurious Coulomb repulsion raises the restricted dissociation limit. This is missing <static electron correlation>, not a failure of the <Born-Oppenheimer approximation>.
A two-configuration expansion using both $\sigma_g^2$ and $\sigma_u^2$ can cancel the ionic terms and recover the Heitler–London separated-atom singlet. <Configuration interaction> in the appropriate active space or a multiconfigurational self-consistent treatment supplies this remedy. The <Unrestricted Hartree-Fock method> can instead localize opposite spins on different atoms and give the correct separated-atom energy, but its single determinant breaks spin symmetry and is not the pure singlet at intermediate separation. The distinction between restricted and symmetry-broken descriptions of stretched hydrogen is treated in the original analysis of Coulson and Fischer.<XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule by Charles Alfred Coulson and Inga Fischer-Hjalmars>[Philosophical Magazine 40 (1949), 386–393, molecular-orbital treatment of hydrogen and its dissociation]{ref}
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2a-dissociation.png]
{title=Restricted hydrogen dissociation failure contrasted with the helium hydride ion}
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