Chapter 4
From Orbital Models to Accurate Predictions
Abstract Basic understanding and qualitative prediction of the isotropic magnetic
coupling between two magnetic centers can be obtained with two well-established
valence-only models. This chapter discusses the Kahn–Briat and Hay–Thibeault–
Hoffmann models, which have been (and still are) of fundamental importance for
understanding the basics of magnetism in polynuclear transition metal complexes.
After shortly presenting the basic model for magnetism in organic radicals, we review
the most evident magnetostructural relations and then move to the accurate prediction
of the magnetic coupling. An overview of the most widely used quantum chemical
methods is given, including wave function based methods and approaches within the
spin-unrestricted setting such as density functional theory. The last part of the chapter
is dedicated to the calculation of the interactions beyond the isotropic magnetic
coupling.
4.1 Qualitative Valence-Only Models
The simplest electronic structure models for magnetic interactions only consider the
unpaired electrons and their orbitals. All other electrons are taken as inactive and not
included in the description. This leads to very simple wave functions, especially in
the case of two identical S =
1
2 magnetic centers. Such valence-only models, where
valence is not used in its usual chemical context, are numerically not competitive with
large-scale all-electron calculations, but have provided chemists and other scientists
working in the field with important insights to control the magnetic interactions in
transition metal complexes and materials with organic radicals.
4.1.1 The Kahn–Briat Model
Based on valence bond reasoning with nonorthogonal atomic-like orbitals, Kahn and
Briat derived an elegant model that is capable of explaining and predicting magnetic
behavior of transition metal complexes based on the shape of the localized magnetic
© Springer International Publishing Switzerland 2016
C. Graaf and R. Broer, Magnetic Interactions in Molecules and Solids,
Theoretical Chemistry and Computational Modelling,
DOI 10.1007/978-3-319-22951-5_4
105
From Orbital Models to Accurate Predictions
Abstract Basic understanding and qualitative prediction of the isotropic magnetic
coupling between two magnetic centers can be obtained with two well-established
valence-only models. This chapter discusses the Kahn–Briat and Hay–Thibeault–
Hoffmann models, which have been (and still are) of fundamental importance for
understanding the basics of magnetism in polynuclear transition metal complexes.
After shortly presenting the basic model for magnetism in organic radicals, we review
the most evident magnetostructural relations and then move to the accurate prediction
of the magnetic coupling. An overview of the most widely used quantum chemical
methods is given, including wave function based methods and approaches within the
spin-unrestricted setting such as density functional theory. The last part of the chapter
is dedicated to the calculation of the interactions beyond the isotropic magnetic
coupling.
4.1 Qualitative Valence-Only Models
The simplest electronic structure models for magnetic interactions only consider the
unpaired electrons and their orbitals. All other electrons are taken as inactive and not
included in the description. This leads to very simple wave functions, especially in
the case of two identical S =
1
2 magnetic centers. Such valence-only models, where
valence is not used in its usual chemical context, are numerically not competitive with
large-scale all-electron calculations, but have provided chemists and other scientists
working in the field with important insights to control the magnetic interactions in
transition metal complexes and materials with organic radicals.
4.1.1 The Kahn–Briat Model
Based on valence bond reasoning with nonorthogonal atomic-like orbitals, Kahn and
Briat derived an elegant model that is capable of explaining and predicting magnetic
behavior of transition metal complexes based on the shape of the localized magnetic
© Springer International Publishing Switzerland 2016
C. Graaf and R. Broer, Magnetic Interactions in Molecules and Solids,
Theoretical Chemistry and Computational Modelling,
DOI 10.1007/978-3-319-22951-5_4
105