Electron correlation in molecular many-electron systems by diagrammatic many-body perturbation theory: Correlation energies and dipole polarizabilities of the hydrogen molecule

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Abstract
Diagrammatic many‐body perturbation theory is used to calculate the electronic energy and the static electric dipole polarizability of the hydrogen molecule in its ground state. An amply extended discrete basis set of Gaussian orbitals is employed to minimize basis set errors and single‐electron states are generated by the Hartree–Fock VN potential. The correlation energy is evaluated through third order and with some higher‐order corrections included by denominator shifts to recover about 95% of the total correlation energy. Dipole polarizabilities are calculated through second order in electron correlation with an accuracy of ∼2%. Also the energy‐denominator decoupling theorem is explicitly proved by invoking combinatorial analysis to implement extensive denominator shifts. Considering the values obtained, some comments are given on the application of partial summation techniques to molecular problems.