Asymptotic behavior of atomic Hartree–Fock orbitals

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Abstract
The restricted Hartree–Fock equations are solved at large r for closed shell atomic states. Except for states containing only s orbitals, the Hartree–Fock orbitals obey the formula, φi(r)∼kiYlimi(ϑ,φ) rβ−λ−1 exp(−ζr), where −1/2ζ2=εho, the highest occupied orbital energy, where β= (nuclear charge – number of electrons +1−ζ)/ζ, where λ+1=0 for the highest occupied orbital, where λ=‖ li−lho ‖ if li≠lho, where λ=2 if li=lho≠0 and i≠ho, where λ=2lmin+1 if li=lho, and where lmin is the smallest nonzero l value of the occupied Hartree–Fock orbitals.