[Paper Review] Broken symmetry $G_0W_0$ approach for the evaluation of exchange coupling constants

Akseli Mansikkamäki, Zhishou Huang+2 more|arXiv (Cornell University)|Mar 13, 2020

Magnetism in coordination complexes4 citations

TL;DR

This paper proposes a broken symmetry $G_0W_0$ approach to improve the calculation of isotropic exchange coupling constants ($J_{ij}$) in quantum materials. It shows consistent improvement over broken symmetry DFT and Hartree-Fock in a minimal H–He–H model system, but limited gains in realistic Cu(II) complexes due to inconsistent treatment of spin- and charge-polarization effects outside the magnetic orbital space.

ABSTRACT

The applicability of a broken symmetry version of the $G_0W_0$ approximation to the calculation of isotropic exchange coupling constants has been studied. Using a simple H--He--H model system the results show a significant and consistent improvement of the results over both broken symmetry Hartree--Fock and broken symmetry density functional theory. In the case of more realistic bimetallic Cu(II) complexes, inclusion of the $G_0W_0$ correction does not lead to obvious improvement in the results. The discrepancies are explained by improved description of the interactions within the magnetic orbital space upon inclusion of the $G_0W_0$ corrections but deterioration of the description of charge- and spin-polarization effects outside the magnetic orbital space. Overall the results show that computational methods based on the $GW$ method have a potential to improve computational estimates of exchange coupling constants.

Motivation & Objective

• To assess the applicability of the broken symmetry $G_0W_0$ method for computing isotropic exchange coupling constants ($J_{ij}$) in magnetic systems.
• To address the limitations of broken symmetry DFT, which suffer from strong dependence on the exchange–correlation functional and lack theoretical consensus.
• To test whether $G_0W_0$ can systematically improve $J_{ij}$ estimates by reducing reliance on approximate functionals.
• To investigate the role of spin- and charge-polarization effects in $G_0W_0$-based calculations and their impact on accuracy.
• To determine whether $G_0W_0$ can outperform standard DFT in realistic transition metal complexes, particularly bimetallic Cu(II) systems.

Proposed method

• Adapts the $G_0W_0$ approximation to the broken symmetry formalism for open-shell magnetic systems.
• Applies the method to a minimal H–He–H model system with varying H–He bond lengths (1.5–2.5 Å) to probe exchange coupling behavior.
• Performs calculations using the Molgw code with HF orbitals as input for $G_0W_0$ corrections.
• Compares $G_0W_0$ results with broken symmetry DFT and Hartree-Fock, using high-level configuration interaction as a reference for the H–He–H system.
• Extends the analysis to experimentally characterized bimetallic Cu(II) complexes to test transferability.
• Analyzes the role of orbital delocalization and polarization effects in the accuracy of $J_{ij}$ evaluation at the $G_0W_0$ level.

Experimental results

Research questions

• RQ1 Does the broken symmetry $G_0W_0$ approach improve the accuracy of isotropic exchange coupling constants compared to broken symmetry DFT and Hartree-Fock in a minimal model system?
• RQ2 How does the $G_0W_0$ correction affect the description of kinetic exchange and polarization contributions to $J_{ij}$ in the H–He–H system?
• RQ3 Why does the $G_0W_0$ correction fail to improve results in realistic Cu(II) complexes despite success in the model system?
• RQ4 To what extent do spin- and charge-polarization effects outside the magnetic orbital space limit the performance of $G_0W_0$ in $J_{ij}$ calculations?
• RQ5 Can self-consistent $GW$ schemes further improve $J_{ij}$ estimates, and what is the role of the XC functional in $G_0W_0$-based calculations?

Key findings

• In the H–He–H model system, the $G_0W_0$ correction leads to a significant and consistent improvement in $J_{ij}$ values over both broken symmetry Hartree-Fock and DFT, with the best results at the HF + $G_0W_0$ level.
• The $G_0W_0$ method correctly describes the kinetic exchange contribution in the H–He–H system, indicating improved treatment of the exchange mechanism in minimal models.
• In more realistic bimetallic Cu(II) complexes, the $G_0W_0$ correction does not lead to improved agreement with experimental $J_{ij}$ values compared to DFT.
• The lack of improvement in Cu(II) complexes is attributed to inconsistent or deteriorated description of spin- and charge-polarization effects outside the magnetic orbital space at the $G_0W_0$ level.
• The results suggest that $G_0W_0$ is most effective when spin- and charge-polarization effects are negligible, such as in systems with localized orbitals and minimal delocalization.
• Self-consistent $GW$ calculations were attempted but did not visibly improve results, indicating that full self-consistency may be necessary for further progress, though this requires further investigation.