The Dyson self-energy, wherein electron correlation and final-state orbital relaxation are embedded, may be expressed in terms of the elements of a superoperator Hamiltonian matrix that suffices to derive several approximations. Herein, a new generation of diagonal self-energy approximations in ab initio electron propagator theory for the calculation of electron removal energies of molecules and molecular ions has been derived from a metric that produces Hermitian super-operator matrices. The performance of the new self-energy approximations (several members of which may be derived from an intermediately normalized, Hermitized super-operator metric) and their widely used antecedents are tested with respect to a data set of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calculations whose accuracy approaches that of full configuration interaction. Several modifications of the diagonal second-order self-energy, a version of G0W0 theory based on Tamm-Dancoff excitations (HF-TDA G0W0), the three versions of the outer valence Green’s function (OVGF) and several non-diagonal self-energies, such as the third-order algebraic diagrammatic construction (ADC3), also are included in the tests. All new methods employ canonical Hartree–Fock orbitals and avoid adjustable or empirical parameters. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are 1) the opposite-spin, non-Dyson, diagonal, second-order or os-nD-D2; 2) the approximately renormalized, third-order quasiparticle or Q3+; 3) the renormalized, third-order quasiparticle or RQ3; 4) the approximately renormalized, linear, third-order or L3+; and 5) the renormalized, linear, third-order or RL3 self-energies.

New generation of diagonal electron propagator self-energies for the calculation of electron removal energies

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