Mapping Back on a Valence-Only Model

A rigorous way to construct a valence-only model with ab initio methods is to make use of the effective Hamiltonian theory presented in Chap. 1. First, we define the basis of the model space as I, ba, aa, and use the matrix of Eq. 5.4 to 

To numerically illustrate the procedure, we will treat the magnetic coupling of two Cu + ions in the previously introduced SrCu203 compound with CU2O3 layers separated by Sr + ions (see Sect. 3.4.2). We recaii that the copper ions form a regular pattern that can best be described as a ladder structure as depicted in Fig. 5.9. Among 

U is given in eV, the other parameters in meV. Jp t is calculated using Eq. 5.8. The magnetic coupling extracted from the DDCI energies of the lowest singlet and triplet states is —158 meV. The dressed models are extracted from DDCI calculations using triplet orbitals 

8 Calculate the norm of the projections of I i on the model space and give the expressions of l [ 4. Are all mutually orthogonal Check that the biorthog- 

The Gram-Schmidt procedure provides a simpler ordu onalization scheme that leads to a hermitian effective Hamiltonian. Since and we already orthogonal to the other projections, we only have to worry about and This means that the coefficients of 4 are defined by that is, if I l = a ( afe + 6a ) -I- p ( aa -P bb ) 

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