Two current gas-phase chemical models of interstellar clouds have been extended to include hydrocarbons and bare carbon clusters through 64 carbon atoms in size. The new molecules comprise linear, monocyclic, tricyclic, and fullerene/ane species but do not include polycyclic aromatic hydrocarbons (PAHs). The reaction networks used to produce and destroy these species have been adopted from a laboratory synthesis of fullerenes. The models have been used to investigate the chemistry of complex molecules in a number of dispersive clouds, which begin as dense clouds but end up as diffuse material. The calculated abundances of large molecules are discussed in terms of candidates for the carriers of the diffuse interstellar bands (DIBs). We find that both gas-phase models utilized can produce large abundances of 64 carbon atom species, considered to represent molecules of this size and larger. Such species are DIB candidates only if the abundances are not spread too thinly over many species. One of the two gas-phase models used leads to large abundances of fullerenes and fulleranes. If this model is accurate, the fullerenes/anes represent reasonable candidates for the carriers of the DIBs. If small hydrocarbon ''seeds'' are assumed to be present on dust particles and to photodesorb during cloud dispersion, we find that large abundances of linear and monocyclic hydrocarbons can also be produced and maintained via gas-phase chemistry, so that these molecules become additional DIB-carrier candidates.