The delocalization of a-electrons from bonds to bonds in three and four-membered ring molecules was studied in a theoretical manner. The antibonding property of the u-electron delocalization between geminal C-C bonds increases in perfluorocyclopropane (5) and cyclopropene (8) while it decreases in cyclopropane (2). This accounts for the fact that the three-membered rings (5 and 8) are more strained than the four-membered rings (6 and 9) while the ring strains of 2 and cyclobutane (3) are comparable. The geminal delocalization between ring bonds is bonding in the threemembered ring molecules 0 9 (14) and S3 (23) and less antibonding in N3H3 (11). Ab initiomolecularorbital calculations of the strain energies revealed that the three-membered rings (11,14, and 23) should surprisingly be less strained than the four-membered rings (12,15, and 24). The present findings contribute to establishing the geminal delocalization theory for ring strains.There are some interesting problems about the strains of small ring molecules. von Baeyerl proposed that the deviation in bond angles from the normal tetrahedral value should be responsible for the instability of three-and four-membered ring compounds. However, measured heats of combustion showed that cyclopropane (2) and cyclobutane (3) have nearly the same strain energies (27.5 and 26.5 kcal/mol, respectively).2 The bond angle is not an exclusive cause of the ring strains. There have appearedvarious ideas about components of the ring strain^.^.^ Torsional strains destabilize the small-ring molecules due to eclipsed or nearly so C-H bonds. 1,3-Nonbonded interaction was pointed out to contribute to the instability of 3, while the repulsion is absent in 2. The rehybridization caused by the acute bond angles should strengthen the C-H bonds due to highs characters to compensate to some extent for the weakening of the C-C bonds in 2. The concepts of the u-aromaticity5 and the surface delocalization6 were proposed to account for the stability of 2.The strain energies of perfluorocycloalkanes and cycloalkenes are remarkably different between the three-and four-membered rings. The strain energy of perfluorocyclopropane (5) was evaluated from the experimentally-determined enthalpy of formation (the heat of the homodesmotic reaction) to be 76.7 kcal/m01.~ Perfluorocyclobutane (6) is much less strained (45.3 kcal/m01).~ Cyclopropene (8) is highly strained (53.8 kcal/mol) relative tocyclobutene (9) (30.0 kcal/mol).* The perfluorination or the introduction of a double bond strains the three-more than the four-membered rings.The strains of the small rings of the second row elements are intriguing. The three-membered ring cyclotrisilane (17) is more strained than the four-membered ring 18. The calculated strain

The origin of the inverted tetrahedral configurations of the bridgehead carbons in bicyclo[1.1.0]butane has been investigated in a theoretical manner. The delocalization of σ-electrons between the central C 1 -C 3 bond and the side C 1 -C 2 bonds was found to be bonding to relax the angle strains, while the delocalization between the geminal C-C bonds is antibonding in propane and cyclopropane, etc. The bonding property of the geminal delocalization was shown to be related to the inversion of the configurations. Inverted and normal tetrahedral bridgehead configurations in the bicyclo[1.1.0]butane frameworks were designed by controlling the geminal delocalization and confirmed by ab initio molecular orbital calculations.