The variational-perturbation method has been applied to the study of correlation effects in the helium atom. Starting from the Hartree-Fock Hamiltonian as zeroth-order approximation, we have evaluated the correlation energy through fifth order in perturbation theory. With a ten-parameter trial wave function we get Ecorr=-0.0419 atomic units, which differs from the exact value by 0.4% and shows the rapid convergence of this type of Hartree-Fock perturbation theory. Comparison is also made with similar calculations using Hartree or hydrogenic Hamiltonians as starting points.
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Byron et al. (1966) studied this question.
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