Chapter 5
Towards a Quantitative Understanding
Abstract Taking a binuclear copper complex as model system, the isotropic magnetic coupling is decomposed into different contributions. Perturbative expressions
of the main contributions are derived and illustrated with numerical examples. An
effective Hamiltonian is constructed that incorporates all important electron correlation effects and establishes a connection between the complex N -electron wave
functions and the simpler qualitative methods discussed in the previous chapter.
Subsequently an outline is given of the analysis of the coupling with a single determinant approach and the biquadratic and four-center interactions are decomposed.
The chapter closes with the recently proposed method to extract DFT estimates for
these complex interactions.
5.1 Decomposition of the Magnetic Coupling
The production of accurate electronic structure parameters is of course an important
result for computational chemistry. However, it should not be the final goal and one
has to go one step further on the road towards understanding. The qualitative valence
methods described in the first sections of the previous chapter of this book are mainly
focused on this understanding of the coupling, but here we discuss three approaches to
analyse the results of the computational schemes that aim at a quantitative agreement
with experiment. In this way quantitative accuracy can be combined with qualitative
understanding.
The binuclear complex [L 2 Cu 2 (µ-1,3-N 3 ) 2 ] 2+ (L = N,N’,N”-trimethyl-1,4,7triaza-cyclononane) shows a large antiferromagnetic coupling with J =− 800 cm,
nicely reproduced with a DDCI calculation using a CAS(2,2)SCF reference wave
function on the model complex [(NH 3 ) 6 Cu 2 (µ-1,3-N 3 ) 2 ] 2+ [1]. In this section, we
will closely follow the work of Calzado and co-workers, decompose this 800 cm −1
into small pieces and ascribe each individual contribution to well defined physical
mechanisms [2, 3].
© 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_5
141
Towards a Quantitative Understanding
Abstract Taking a binuclear copper complex as model system, the isotropic magnetic coupling is decomposed into different contributions. Perturbative expressions
of the main contributions are derived and illustrated with numerical examples. An
effective Hamiltonian is constructed that incorporates all important electron correlation effects and establishes a connection between the complex N -electron wave
functions and the simpler qualitative methods discussed in the previous chapter.
Subsequently an outline is given of the analysis of the coupling with a single determinant approach and the biquadratic and four-center interactions are decomposed.
The chapter closes with the recently proposed method to extract DFT estimates for
these complex interactions.
5.1 Decomposition of the Magnetic Coupling
The production of accurate electronic structure parameters is of course an important
result for computational chemistry. However, it should not be the final goal and one
has to go one step further on the road towards understanding. The qualitative valence
methods described in the first sections of the previous chapter of this book are mainly
focused on this understanding of the coupling, but here we discuss three approaches to
analyse the results of the computational schemes that aim at a quantitative agreement
with experiment. In this way quantitative accuracy can be combined with qualitative
understanding.
The binuclear complex [L 2 Cu 2 (µ-1,3-N 3 ) 2 ] 2+ (L = N,N’,N”-trimethyl-1,4,7triaza-cyclononane) shows a large antiferromagnetic coupling with J =− 800 cm,
nicely reproduced with a DDCI calculation using a CAS(2,2)SCF reference wave
function on the model complex [(NH 3 ) 6 Cu 2 (µ-1,3-N 3 ) 2 ] 2+ [1]. In this section, we
will closely follow the work of Calzado and co-workers, decompose this 800 cm −1
into small pieces and ascribe each individual contribution to well defined physical
mechanisms [2, 3].
© 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_5
141