The geometries and stabilities of HCCH, ICCH, ICCI, IF3, IF2CCH, IF(CCH)2,I(CCH)3,I4(CC)44+, and four isomers of I4(CC)4F4 were calculated at the ab initio HF/LANL1DZ level. Final geometries were used for electron correlation calculations at the MP4/LANL1DZ level. The results of the calculations demonstrate considerable stability and suggest square planar structures for the macrocyclic tetraalkynyl tetraiodonium compounds. The tetracation I4C84+ is predicted to exist as a single isomer due to a pseudotetrahedral 8-1-2 configuration and to have a structure with only negligible deviations from a perfect square. In contrast, the neutral I4C8F4 species can exist as four different isomers as a consequence of the trigonal bipyramidal 10-I-3 configuration. These isomers have distinctly different geometries and energies due to the relative positions of the axial and equatorial C-I bonds. Macrocycles 16-19 have ring strain energy due to the existence of four unfavorable axial I-C bonds in each of the isomers. However, the calculated ring strain energy for the most stable isomer 16 is only 27 kcal/mol.