Optimized structures of the isoelectronic cumulenes (CCCB)(-), CCCC, and (CCCN)(+) and of their isomers formed by rearrangement have been calculated at the B3LYP/6-311+ G(3df) level of theory with relative energies and electronic states determined at the CCSD(T)/aug-cc-pVTZ level of theory. The ground states of CCCC and (CCCN)(+) are triplets, whereas the ground state of (CCCB)(-) is a quasi-linear singlet structure that is only 0.6 kcal mol(-1) more negative in energy than the linear triplet. When energized, both triplet and singlet CCCC cyclize to planar rhomboids, of which the singlet is the lowest-energy configuration. Ring-opening of rhomboid C-4 reforms CCCC with the carbons partially randomized. Similar rear-rangements occur for (CCCB)(-) and (CCCN)(+), but the reactions are different in the detail. In the case of (CCCN)(+), rearrangement of atoms is supported both experimentally and theoretically. Because (CCCB)(-) and (CCCN)(+) are not symmetrical, two fully cyclized forms are possible; the one more resembling a rhomboid structure is called a "kite" structure, and the other is called a "fail" structure. The rearrangement of (CCCB)(-) is more favored via the triplet with equilibrating kite and fan structures being formed, whereas the singlet (CCCN)(+) ring closes to give the singlet kite structure, which may ring open to give a mixture of (CCCN)(+) and (CCNC)(+). Intersystem crossing may occur for the triplet and singlet forms of CCCC and (CCCB)(-) but not for (CCCN)(+).