Is dipole moment a valid descriptor of excited state's charge-transfer character?

In the ongoing discussion on excited states of the pentacene crystal, dipole moment values have been recently invoked to gauge the CT admixture to excited states of Frenkel parentage in a model cluster. In the present paper, a simple dimer model is used to show that, in general, the dipole moment is not a valid measure of the CT contribution. This finding eliminates some apparent disagreement between the computational results published by different research groups. The implications of our results and other related aspects of cluster-type quantum chemistry calculations are discussed in the context of the standing literature dispute concerning the mechanism of singlet fission in the pentacene crystal, notably the role of charge transfer contributions vs the involvement of an excimer-like doubly excited intermediate (D state).