Spectra of Clusters

Abstract

The spin hamiltonian appropriate to describe the EPR spectra of clusters of three or more weakly interacting paramagnetic centers can be written as an obvious extension of (3.1−3) and takes the form $${\text{H = }}{\Sigma _{\text{i}}}{{\text{H}}_{{\text{i < j}}}}{{\text{H}}_{{\text{ij}}}}.$$ (4.1) In (4.1) Hi is the spin hamiltonian (3.1) of the individual spin center i and Hij is the interaction hamiltonian (3.3) between couples of spins assumed to be symmetric with respect to the i and j indices. The sums in (4.1) extend over all the paramagnetic centers forming the cluster. It must be stressed here that (4.1) is not the most general hamiltonian to describe the magnetic and exchange interactions in a cluster. Such a hamiltonian, in fact, has the only requisite to be invariant with respect to the symmetry operations of the cluster and should include n-center interactions as well as spin operators of the form jijSi · Sj)2. Hamiltonian (4.1) is, however, the most widely used to interpret the EPR spectra and we will use this operator in the following. A number of general equations, which we will report in this chapter, can be, however, easily modified to include the jij terms.