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

TL;DR

This paper investigates multiple solutions in iterative Green's function methods for molecules by analyzing two-particle density matrices, revealing insights into their spin and charge properties and constructing effective magnetic models.

Contribution

It introduces a local analysis approach using two-particle density matrices to understand multiple solutions in GF2 and GW schemes, linking them to magnetic Hamiltonians.

Findings

Spin correlators reveal broken symmetry in solutions

Constructed magnetic Hamiltonians from GW and GF2 data

Compared Hamiltonian parameters with wave-function methods

Abstract

Due to non-linear structure, 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 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, as well as biquadratic spin-spin interactions. These Hamiltonian parametrizations are compared to prior wave-function calculations.