Ce has been found experimentally to be preferentially incorporated into the C-82 isomer of C-2v symmetry as have other lanthanoids in M@C-82 (M = La, Pr, Nd, etc.). We have investigated the underlying reason for this preference by calculating structural and electronic properties of Ce@C-82 using density functional theory. The ground-state structure of Ce@C-82 is found to have the cerium atom attached to the six-membered ring on the C-2 axis of the C-82-C-2v cage, and the encapsulated atom is found to perturb the carbon cage due to chemical bonding. We have found Ce to favor this C-2v chemisorption site in C-82 by 0.62 eV compared to other positions on the inside wall of the cage. The specific preference of the metal atom to this six-membered ring is explained through electronic structure analysis, which reveals strong hybridization between the d orbitals of cerium and the pi orbitals of the cage that is particularly favorable for this chemisorption site. We propose that this symmetry dictated interaction between the cage and the-lanthanide d orbital plays a crucial role when C-82 forms in the presence of Ce to produce Ce@C-82 and is also more generally applicable for the formation of other lanthanoid M@C-82 molecules. Our theoretical computations are the first to explain this well-established fact. Last, the vibrational spectrum of Ce@C-82 has been simulated and analyzed to gain insight into the metal-cage vibrations.