Comments on a paper by C. S. Sharma and C. A. Coulson, 'Hartree-Fock and correlation energies for 1s2s3S and1S states of helium-like ions'

Though the notation is identical with that of the standard Hartree-Fock formalism, the `Hartree-Fock parameter' of Sharma and Coulson, 12, cannot be taken as an off-diagonal Lagrangian multiplier for the general case of non-orthogonal orbitals. An alternative formulation of the singlet and triplet equations is derived in terms of standard Lagrangian multipliers in which 12 may be taken as an off-diagonal Lagrangian multiplier for either orthogonal or non-orthogonal orbitals.