A model wavefunction including electron correlation for the ground state of the helium isoelectronic sequence

From the form of the exact ground-state wavefunction psi , of a helium-like atom, the dependence on the first power of the interparticle coordinates r ₁, r₂ and r₁₂ is easily obtained. The authors construct a simple model wavefunction phi that (a) agrees with the exact wavefunction to first order in r₁, r₂ and r₁₂, (b) is finite everywhere, is normalisable and satisfies the derivative cusp conditions as r₁, r₂ or r₁₂ to 0, and (c) satisfies the virial theorem. If the exact wavefunction psi is written psi = phi chi , then chi satisfies a transformed Schrodinger equation, H' chi =E chi where H' has no poles at the electron-nucleus or electron-electron coalescences. It is shown, by a linear transformation of the interparticle coordinates, that all integrals required for the evaluation of the energy reduce to products of gamma functions.