Interaction energy between two ground-state helium atoms using many-body perturbation theory

Diagrammatic many-body perturbation theory is applied to the calculation of potential-energy curves for ${\mathrm{He}}_2$. Both model and shifted perturbative procedures are described. The shifted scheme produces a spurious $R$ dependence for the long-range interatomic potential in both second and third order. Variational-perturbative upper-bound methods produce energies that approach an incorrect asymptotic limit at large internuclear distances. In contrast, the model-perturbative scheme in both second and third order achieves a proper distance dependence for the ${\mathrm{He}}_2$ potential curve. Four basis sets are employed to illustrate basis-set effects.