Cyclooctatetraene can achieve a variety of geometries, tub, crown, chaise, and octagonal or distorted planar forms, depending on the system's charge and spin multiplicity. Our ab initio computations, which produce optimum geometries, relative energetics, and vibrational frequencies, provide a coherent story of the influences of charge and spin, consistent with a Walsh analysis. Since acceptor and donor substituents may alter the net charge on a cyclooctatetraene ring, such substituents might affect the geometry of the ring. We used the AM1 model for the wave function and electronic energy to evaluate the impact of substituents on charge distribution in the ring and on the inversion barrier. Qualitative perturbation molecular orbital analysis suggests that substituents would force charge alternation in the ring, reduce bond length alternation, and lower the inversion barrier. These predictions were borne out for a model donor (-CH2 anion) and a model acceptor (-CH2 cation). However, more easily accessible substituents, the donor methoxy and the acceptor formyl, had minor effects on the inversion barrier. Multiple acceptor or donor substitution and push-pull substituents exaggerated the charge alternation, but had little impact on inversion barriers. Fused-ring derivatives, such as the biscyclopentacyclooctatetraenes, suffered less of the bias arising from sigma-system strain toward a puckered singlet cyclooctatetraene ring, and in these systems electron donors were particularly effective in flattening the ring.