The angular dependence of spin-state energy splittings in the core

Abstract

Spin-state energy splittings are highly relevant for catalysis, molecular magnetism, and materials science, yet continue to pose a challenge for electronic structure methods. For a Fe₂O²⁺ ₂ core, we evaluate the bridging angle dependence of energy splittings between ferromagnetically and antiferromagnetically coupled states for different exchange–correlation functionals, and compare with complete active space self-consistent field (CASSCF) values, also including second-order perturbative corrections (CASPT2). CASSCF and CASPT2 yield strong antiferromagnetic coupling, with the smallest coupling at 100°, and a smooth dependence on the angle for Fe−O−Fe angles of 70° to 120°. Interestingly, this is qualitatively the same behaviour as often found for stable dinuclear transition metal complexes. While all functionals show the same angular dependence as CASPT2, they favour the antiferromagnetic state less strongly. Pure functionals such as BP86, BLYP, SSB-D, and TPSS come closer to the CASPT2 results (with energy splittings by about 60 kJ/mol smaller than the CASPT2 ones) than hybrid functionals. The hybrid functionals B3LYP, B3LYP^⋆, and PBE0 favour the antiferromagnetic state even less strongly, resulting in ferromagnetic coupling for angles around 100°. The good qualitative agreement between CASPT2 and CASSCF on the one hand and CASPT2 and density functional theory on the other hand for angles between 70° and 110° suggests that the chosen active space of 18 electrons in 14 orbitals may be adequate for spin-state energy splitting of Fe₂O²⁺ ₂ in that region (possibly due to error cancellation), while angles of 60° or 120° may require larger active spaces. This study is complemented by an analysis of local spins, local charges, and CASSCF natural orbitals.

Keywords:

• electronic structure
• exchange spin coupling
• transition metal complexes
• local properties
• molecular orbitals

Acknowledgements

Financial support from the Free and Hanseatic City of Hamburg in the context of the Landesexzellenzinitiative Hamburg ‘Nanospintronics’ is gratefully acknowledged. We would further like to thank the University of Hamburg High Performance Computing Centre for computational resources, Markus Reiher at ETH Zurich for access to our implementations in a local version of Turbomole and Gemma C. Solomon at the University of Copenhagen for access to a MO postprocessing tool.