Dependence of hydrocarbon sigma CC bond strength on bond angles: The concepts of "inverted", "direct" and "superdirect" bonds

The bond energy (BE) of CC in CH3-CH3 with respect to geometry frozen fragments follows a sigmoidal increase as a function of the theta = HCC pyramidalization angle. Using dynamic orbital forces as a BE index, the same behaviour as a function of a unique parameter, mean angle of the substituents, is found for 24 single CC bonds in various hydrocarbons. Thus the parameter appears as a straightforward and robust index of the geometrical constraints which can either strengthen or weaken a bond. This way, CC sigma bonds can be easily classified into weak "inverted" bonds for <90 degrees (eg. in [111]propellane and bicyclobutane), "direct" (or "normal") bonds for 90 degrees < 120 degrees (eg. ethane), and strong "superdirect" bonds for 120 degrees (eg. in tetrahedryl-tetrahedrane and butadiyne).