Multireference-state Rayleigh–Schrödinger perturbation theory applied to the electronic states X 1Σ+g and E F 1Σ+g of H2

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Abstract
The effect of the reference space on the convergence of Rayleigh–Schrödinger perturbation series within the molecular‐orbitals framework is studied for the ground X 1Σ+g and excited EF 1Σ+g electronic states of H2 over a wide range of internuclear separations. Near the ground‐state equilibrium distance of 1.4 bohr each state is well described by a single spin‐adapted configuration function. This no longer holds for the EF 1Σ+g state around 3.0 bohr because of forbidden curve crossing. In general, the quasidegeneracy increases with the internuclear distance due to improper dissociation of molecular orbitals. A rigorous approach to define a proper reference space is discussed. It is based on analysis of convergence with emphasis on identifying intruder states. A reference space of nine spin‐adapted functions is adequate in the range 1.4–8.0 bohr; giving third‐order results within less than 1×10−3 hartree from the basis limit. Other findings are: (i) Epstein–Nesbet breakup of the Hamiltonian usually gives faster convergence as compared with the Mo/ller–Plesset scheme. (ii) Padé approximants improve the results but only when the reference space is capable of describing the state. When this is not the case the Padé sequence is erratic and physically meaningless. (iii) With suitably defined reference space there is only a marginal difference in the results between different breakups of the Hamiltonian, and little improvement is gained by employing Padé approximants.