Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices

Due to the presence of non-linear equations, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular solutions was not performed before. In this work, we use two-particle density matrices to investigate local spin and charge correlators that quantify the charge resonance and covalent characters of these solutions. When applied within the unrestricted orbital set, spin correlators elucidate the broken symmetry of the solutions, containing necessary information for building effective magnetic Hamiltonians. Based on GW and GF2 calculations of simple molecules and transition metal complexes, we construct Heisenberg Hamiltonians, four-spin-four-center corrections, and biquadratic spin-spin interactions. These Hamiltonian parameterizations are compared to previous wave-function calculations. Published under an exclusive license by AIP Publishing.

Automated summary

Iterative Green's function methods can lead to multiple solutions for simple molecular systems due to non-linear equations, while a detailed analysis of these molecular solutions has not been conducted before. This study utilizes two-particle density matrices to investigate the charge resonance and covalent characters of these solutions, providing necessary information for effective magnetic Hamiltonian construction. The obtained Hamiltonian parameterizations are compared to previous wave-function calculations using GW and GF2 calculations for simple molecules and transition metal complexes.