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Two state-of-the-art computational approaches: quantum Monte Carlo and GW with exciton effects [GW-BSE (Bethe-Salpeter equation)] are employed to calculate ionization potentials, electron affinities, and first excited singlet and triplet energies for the silane and methane molecules. Results are in excellent agreement between these dramatically different approaches and with available experiment. The optically forbidden triplet excitation in silane is predicted to lie roughly 1 eV higher than previously reported. In the GW-BSE method, we demonstrate that inclusion of off-diagonal matrix elements in the self-energy operator is crucial for an accurate picture.

High Accuracy Many-Body Calculational Approaches for Excitations in Molecules