||Ab-initio calculations were performed at the D95V** level of theory to determine the equilibrium geometries of difluorocyclopropane (DFCP) with the two fluorines on different carbon atoms. The calculated energy difference between the cis and trans isomers is in excellent agreement with the accepted experimental value. Similar calculations were carried out on the 1,2 and 1,3-difluorotrimethylenes (DFTM). Both species are expected to be intermediates or transition states in the conversion of cis to trans difluorocyclopropane. As the difluorotrimethylenes are diradicals, they exist in both singlet and triplet states. For the singlet and triplet twenty-one dimensional potential energy hypersurfaces for 1,2 and 1,3-difluorotrimethylenes, the Unrestricted Hartree-Fock method (UHF) was used, while the Restricted Hartree-Fock method (RHF) was applied to the singlet difluorocyclopropane minima. Furthermore, to correct for the electron correlation, single point calculations using the MP (Moller-Plesset) method, were performed. For the singlet difluorotrimethylenes, three cols and no minima were found, with energies (UHF level) between 77 and 93 kcal/mol above the energy of trans difluorocyclopropane. One col corresponds to 1,3-difluorotrimethylene and the other two to 1,2-difluorotrimethylenes. Using the steepest descent procedure, it was found that the cols lead to cis or trans difluorocyclopropane. Also, one of the cols leads to singlet 3,3-difluoropropylene. Two triplet difluorotrimethylene surfaces, corresponding to 1,2 and 1,3-difluorotrimethylenes, were studied. Between both surfaces, ten minima and cols were found. The highest energy difference between the minima and the cols is about 5 kcal/mol, making the potential energy hypersurface wavy and shallow. The triplet hypersurfaces are between 30 and 35 kcal/mol (UHF level) above the energy of trans difluorocyclopropane and about 40 kcal/mol below those of the singlet hypersurfaces. It is postulated that the interconversion between cis and trans difluorocyclopropanes occurs by means of intersystem crossing through the formation of triplet difluorotrimethylene.