An analytical evaluation of matrix elements of single spin operators in tetranuclear mixed-valence metal clusters is presented. The case of a ground state of the cluster with one strongly anti-ferromagnetic coupled spin pair and the second pair with undefined spin state is considered in detail. Such spin states have been discussed as a model for the water-oxidizing complex in photosystem II. Consequences of the structure of the ground state apparent in the hyperfine structure observed by EPR are discussed. The spin coupling algebra is presented and evaluated using the Mathematica software system.