Towards a Quantitative Understanding

Abstract

Taking a binuclear copper complex as model system, the isotropic mag-netic 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 corre-lation 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 deter-minant 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-1,4,7-triaza-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].