GVB and SD-CI calculations have been performed with the 6-31G* basis set in order to explore the potential surface for the stereomutation of 1,1-difluorocyclopropane (1) by ring opening to 2,2-difluorotrimethylene (2) and 1,1-difluorotrimethylene (3) diradicals. The calculations predict that the presence of the geminal fluorines in 1 should (1) enhance the preference for stereomutation by coupled methylene rotations over that in cyclopropane, (2) change the preferred stereochemistry of ring opening and closure from conrotatory in the hydrocarbon to disrotatory in the fluorocarbon, (3) cause the preference for coupled rotation to be enhanced, rather than obscured, by alkyl substituents, and (4) result in the singlet lying below the triplet at the (0,0) geometry of diradical 2. The reasons for these differences between the hydrocarbon and the fluorocarbon are traced to the strong through-bond coupling that is provided by the C-F sigma* orbitals at the (0,0) geometry of 2. Experimental tests of the computational predictions are proposed.