The electronic and molecular structure of the CeB6 molecular unit has been probed by anion PE spectroscopy and DFT calculations to gain insight into structural and electronic relaxation on edge and corner sites of this ionic material. While boron in bulk lanthanide hexaboride materials assumes octahedral B-6(3-) units, the monomer assumes a less compact structure to delocalize the charge. Two competitive molecular structures were identified for the anion and neutral species, which include a boat-like structure and a planar or near-planar teardrop structure. Ce adopts different orbital occupancies in the two isomers; the boat-like structure has a 4f superconfiguration while the teardrop favors a 4f 6s occupancy. The B-6 ligand in these structures carries a charge of -4 and -3, respectively. The teardrop structure, which was calculated to be isoenergetic with the boat structure, was most consistent with the experimental spectrum. B-6 -local orbitals crowd the energy window between the Ce 4f and 6s (HOMO) orbitals. A low-lying transition from the B-based orbitals is observed slightly less than 1 eV above the ground state. The results suggest that edge and corner conductivity involves stabilized, highly diffuse 6s orbitals or bands rather than the bulk-favored 5d band. High-spin and open-shell low-spin states were calculated to be very close in energy for both the anion and neutral, a characteristic that reflects how decoupled the 4f electron is from the B(6 )2p- and Ce 6s-based molecular orbitals.