The performance of density cumulant functional theory (DCT) for capturing static correlation effects is reported and discussed. In this respect, DCT is competitive with the popular coupled-cluster methods CCSD and CCSD(T), and the DCT natural orbital occupation numbers provide a convenient diagnostic for the appearance of multireference effects. In addition, ab initio computational studies of tetrafluoroethylene (C2F4) and tetragermacyclobutadiene (Ge4H4) are reported. First, a theoretical investigation of the low-lying electronic states and conical intersections of C2F4 provides a complementary description of nonadiabatic processes that were recently probed by femtosecond photoionization spectroscopy. Second, a coupled-cluster study of the ground-state potential energy surface of Ge4H4 demonstrates its preference for unusual bonding arrangements in contrast to the planar ring structure of cyclobutadiene (C4H4).