The H2+ cation has a single electron, so there is no electron–electron repulsion and hence no correlation energy. This means that the Hartree–Fock method for calculating properties of molecular systems is exact for a given orbital basis set; every difference between two basis sets is a pure basis-set effect. I computed the gerade bonding sigma orbital (σg) and ungerade antibonding sigma orbital (σu) states at 501 different bond lengths, equally spaced on a logarithmic scale from 1 pm to 105 pm, with two basis sets: STO-3G, which gives each hydrogen atom a single contracted 1s function with a set exponent (ζ = 1.24) fixing its orbital size, and aug-cc-pV6Z. The aug-cc-pV6Z basis set reproduces a near-exact Born–Oppenheimer curve (Re=105.69 pm, Emin=−0.602633 Eh against the exact Emin=−0.602634 Eh). The 1s basis fails at both ends of the curve: by up to 0.9 Eh for the σu state and 0.3 Eh for the σg state in the united 2He+ atom’s limit, and by 0.033 Eh for the separated atoms. I explain the kinetic-energy errors through confinement and the gradient of the wave function. I explain the potential-energy errors through where the charge sits relative to the nuclei and, for σu , through the node. The virial theorem shows why the 1s basis fails: with a fixed exponent the 1s charge density cannot shrink or expand as R changes, so it cannot reach the size at which kinetic and potential energy balance.
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