Decomposition of the Four-Center Interactions

11 Equation 5.43 assumes that the energies of and are strictly the same. Is this correct Hint Assume that A, B, C and D are uncharged in Pj and calculate the Coulomb interaction along the path in a simple point charge 

The contribution of the anti-clockwise pathways is the same, increasing the prefactor to 10. By accounting for the pathways that start at the other magnetic centers, we can derive the total effective matrix element and a perturbative estimate of Jr 

12 Write down an anti-clockwise path from P/ to Pj starting at center A that goes through a di-ionic determinant. 

43 Complex Interactions with Single Determinant Approaches 

The fourth-order perturbation estimates give us expressions in terms of t, U and K, and hence, we can relate X to these electronic structure parameters, which can be calculated with spin-unrestricted single determinant methods. To simplify the perturbation estimates we neglect a, fi and y, and all intersite exchange integrals in the interaction matrices derived in Sect. 5.4.1. The interaction matrices for triplet and singlet states then become 

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