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Rayleigh—Schrödinger perturbation calculations are carried out for the ground state of the HeH+ + molecular ion. The zeroth-order wavefunction is ψ=Nexp(−αZArA−βZBrB).The expectation value of the Hamiltonian calculated with the wavefunction accurate through first order, E(1), is compared with the accurate series calculations of Bates and Carson and found to agree up to five places. Also the values of the normalized wavefunction accurate through the first order agree quite well with Bates and Carson, particularly for small values of the internuclear separation.
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Matcha et al. (1965) studied this question.
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