Molecular orbital calculations using CASPT2 ab initio and AM1/CI methods show that polymeric hydrocarbons with multiple nonbonding pi-orbitals can attain higher spin states than their smaller analogs due to (a) the quadratic increase of the quantity of exchange (K-ij) terms as one unpairs the spins of additional electrons and (b) the removal of the disjoint relationship between nonbonding orbitals (NBO’s) upon low-energy excitations from the highest doubly occupied molecular orbital (HDOMO) to a NBO or LUMO. We illustrate the effect with the example of the dimethylenepolycyclobutadienes containing up to nine cyclobutadiene rings. AM1/ CI calculations (which are in good agreement with CASPT2 calculations for systems where the complete pi-active space could be accommodated) predict that all dimethylenepolycyclobutadienes with three or more rings will have spin states S greater than or equal to (n/2) + 1, where n is the number of rings, in contrast to earlier reports that suggested that S = 0 when n is even and S = 1 when n is odd.