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

TL;DR

This work develops a SRG-based regularization for quasiparticle self-consistent GF2 (SRG-qsGF2), addressing divergences in second-order perturbation theory and improving predictive accuracy for quasiparticle energies and molecular dipoles. By performing a perturbative SRG analysis and incorporating spin-component scaling, the authors obtain three variants (SRG-qsGF2, SRG-SOS-qsGF2, SRG-SCS-qsGF2) that balance regularization with correlation contributions, achieving MAEs for IPs/EAs comparable to GW methods and CCSD(T)-level dipole accuracy in benchmark sets. The framework extends to ground-state energy corrections via QP-PT2, where the SRG-renormalized Fock matrix mitigates divergence and stabilizes dissociation curves. Overall, the SRG-qsGF2 approach offers improved reliability and transferability across molecular properties and suggests avenues for excited-state extensions and computational optimizations.

Abstract

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.

Figures (3)

• Figure 1: Violinplots of the HOMO a) and LUMO energy b) error distributions in the GW50 benchmark set for SRG-qsGF2, SRG-SOS-qsGF2 and SRG-SCS-qsGF2, as well as SRG-qsGWmarieSRG. The data for SRG-qsGW are taken from marieSRG. All qsGF2 calculations were performed using the aug-cc-pVTZ basisaugccpvtz_1augccpvtz_2augccpvtz_3augccpvtz_4.
• Figure 2: Histogram of the errors with respect to $\Delta$CCSD(T) for the IPs of the GW100 benchmark set bruneval2021gwGW100: a) SRG-qsGF2, b) SRG-SOS-qsGF2 and c) SRG-SCS-qsGF2. All calculations were performed using the def2-TZVPP basis set. def2svp_tzvp_tzvppddef2_RI
• Figure 3: Dissociation curves for a) H$_{2}$ (cc-pVDZ), b) N$_{2}$ (sto-3g) and c) a linear H$_{10}$ (cc-pVTZ). The MRCI+Q results were taken from Ref. mrci