According to recent Stern-Gerlach measurements of the one-dimensional sandwich clusters, M-2(C6H6)(3) (M = Sc, Ti, V), the magnitudes of their magnetic moments are known to be reduced effectively from their spin-only values by a factor of 1/4 for M = Sc and Ti, and 3/5 for V. To clarify the origin of this reduction, the spin state of each cluster has been analyzed and the axial zero-field splitting parameters D have been evaluated by the second-order perturbation of spin-orbit interactions. The magnitude of D for the V-2(C6H6)(3) cluster is less than 10% of those for the Sc and Ti analogs, which is in accord with the experimental findings. (c) 2008 Elsevier B.V. All rights reserved.