Renormalization group approach to second-order Green’s function theory

In this work, we introduce a new approach for constructing a renormalized and regularized Fock matrix for self-consistent field calculations. The scheme relies on second-order perturbation theory and is conceptually related to quasiparticle self-consistent second-order Green's function theory (GF2). The regularization is derived within the framework of perturbative similarity renormalization group (SRG) theory. By optimizing both the regularization and spin-scaling parameters, we introduce three SRG-qsGF2 variants that enable accurate predictions of quasiparticle energies and dipole moments. Lastly, we demonstrate that formulating second-order perturbation theory for the total electronic energy using the renormalized SRG-qsGF2 Fock matrix as the unperturbed Hamiltonian mitigates divergence problems commonly observed in conventional Møller-Plesset perturbation theory.