Fulvalenes are a family of molecules built from two fully-conjugated rings, connected to one another by an exocyclic double bond. Some members of this family exhibit a relatively high dipole moment caused by charge transfer between the two rings. This occurs only when the two rings are of different sizes, if an electron transfer between them would produce two aromatic rings or one aromatic and one antiaromatic ring. Pentafulvalene, having two five-membered rings, does not induce such charge transfer because aromatization of one ring would antiaromatize the second. We investigated computationally various derivatives of pentafulvalene in order to study the effect different substituents can have on the charge transfer and aromaticity of this molecule. We found that placing strong electron withdrawing groups on one ring and strong electron donating groups on the second ring stabilizes the charge transfer structure, producing one aromatic and one antiaromatic ring. We also found that such derivatives can undergo π-system shifting via tunneling even at temperatures very close to 0 K. In addition, triplets of some pentafulvalene derivatives exhibit charge transfer and triplet localization on one of the rings, producing a novel neutral pentafulvalene having two aromatic rings.