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Due to non-linear structure, iterative Green's function methods can result inmultiple different solutions even for simple molecular systems. In contrast tothe wave-function methods, a detailed and careful analysis of such molecularsolutions was not performed before. In this work, we use two-particle densitymatrices to investigate local spin and charge correlators that quantify thecharge-resonance and covalent characters of these solutions. When appliedwithin unrestricted orbital set, spin correlators elucidate the broken symmetryof the solutions, containing necessary information for building effectivemagnetic Hamiltonians. Based on GW and GF2 calculations of simple molecules andtransition metal complexes, we construct Heisenberg Hamiltonians,four-spin-four-center corrections, as well as biquadratic spin-spininteractions. These Hamiltonian parametrizations are compared to priorwave-function calculations.

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