Long-Range Behavior of Hartree-Fock Orbitals

The widely held belief that Hartree-Fock orbitals φ₁ behave asymptotically like exp[-(-2εᵢ)1/2r], where εᵢ is the orbital energy of φᵢ, is shown to be incorrect, with one exception: atomic configurations consisting entirely of s orbitals. The correct asymptotic form of φᵢ is a sum of terms like exp[-(-2×εⱼ)1/2r], in which all εⱼ appear. The former misconception apparently resulted from too superficial a treatment of the exchange potential at large r.