General-Order Many-Body Green's Function Method.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Electron binding energies are fundamental properties in atomic and molecular systems.
• Accurate calculation of these energies is crucial for understanding chemical bonding and spectroscopy.
• Existing methods often involve approximations for electron correlation and self-energy effects.

Purpose of the Study:

• To evaluate electron binding energies using high-order Møller-Plesset perturbation (MPn) theory.
• To establish MPn energy differences as an alternative diagrammatic expansion for Koopmans-like binding energies.
• To investigate the inclusion of perturbation corrections from self-energy approximations.

Main Methods:

• Calculating total energies for N- and (N ± 1)-electron systems using MPn theory (n up to 30).
• Employing a determinant-based method for obtaining MPn energies.
• Comparing results with Dyson equation solutions under various self-energy approximations.

Main Results:

• MPn-derived binding energies agree with Dyson equation results in simpler approximations.
• MPn energy differences converge to exact basis-set solutions as n approaches infinity.
• The MPn approach naturally incorporates corrections from off-diagonal and frequency-dependent self-energy terms.

Conclusions:

• MPn energy differences provide a viable alternative diagrammatic expansion for electron binding energies.
• This method accounts for complex electron correlation and self-energy effects.
• The convergence rate and acceleration via Padé approximants are important considerations for practical application.