On the validity of the McConnell-I model of ferromagnetic interactions: The [2.2]paracyclophane example

A formal comparison between a rigorous implementation of a Heisenberg Hamiltonian model in a VB space with the McConnell-I model shows that the validity of the McConnell model rests upon a heuristic one-to-one correspondence between spin density products in the latter with the difference of the spin exchange density matrix elements in the former. Using a rigorous Heisenberg Hamiltonian, a numerical model computation of the singlet/quintet stability for pseudo ortho, pseudometa, and pseudopara bis(phenylmethylenyl)[2.2]paracyclophanes (modeled with the correponding singlet/triplet bis(methyl)[2.2]paracyclophanes) shows that the McConnell model makes the correct prediction of low and high spin stability only because the contributions from "closest contact" carbon atoms that are not directly aligned is rather small. In systems where the alignment is not perfect, this cancelation may not hold. The association between spin density products in the McConnell model with the difference of the spin exchange density matrix elements in the VB Heisenberg Hamiltonian is shown to be valid because the McConnell model correctly predicts the leading configuration terms in the VB expansion.