Strong electron correlation plays an important role in the determination of double ionization energy, which is required for removing or adding two electrons, particularly in small-sized systems. Starting from the state-of-the-art GW approximation, we evaluate the particle-particle ladder diagrams up to the infinite order by solving the Bethe-Salpeter equation of the T-matrix theory to calculate the double-ionization energy spectra of atoms and molecules (Be, Mg, Ca, Ne, Ar, Kr, CO, C(2)H(2), Li(2), Na(2), and K(2)) from first principles. The ladder diagrams up to the infinite order are significant to calculations of double-ionization energy spectra. The present results are in good agreement with available experimental data as well as the previous calculations using, e.g., the configuration-interaction method.
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