Green's function in computational chemistry: Insights and theoretical approaches.

[Display omitted] • Correlation energy through Green function formalism. • Computing ionization energies and electron affinities of diatomic molecules. • Feynman diagrammatic expansion method for improving correlation energy estimation. • Partition energy procedure and the problem of particle number conservation. In this study, we revisit Green's function formalism in theoretical chemistry. Specifically, we investigate how it allows refining the Hartree-Fock model by introducing the self-energy's first and second-order corrections. Two distinct approaches are considered: the energy partition procedure and the Feynman diagrammatic expansion. These approaches are applied to the study of the π bond of ethylene, demonstrating that both provide better numerical results than those obtained using the Hartree-Fock model but worse than those obtained using the Configuration Interaction method. An optimization process of the energy partition procedure, capable of reproducing the results obtained by applying the Configuration Interaction method and solving the problem of the violation of particle number conservation, is also proposed. [ABSTRACT FROM AUTHOR]