From “inverted” to “superdirect“ bonds: a general concept connecting substituent angles with sigma bond strengths. The case of the CC bonds in hydrocarbons.

30 June 2021, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


The C-C dissociation energy with respect to geometry frozen fragments (BE) has been calculated for C2H6 as a function of  = H-C-C angles. BE decreases rapidly when  decreases from its equilibrium value to yield the so-called “inverted bonds” for  < 90°; on the contrary BE increases
when  increases to yield somehow “superdirect” bonds, following a sigmoidal variation. The central bond in Si2H6, Ge2H6 and N 2H4 as well as the C-H bond in CH3-H behaves similarly. The concept of “invertedness”/”directedness” is generalized to any CC sigma bond in hydrocarbons and characterized by the mean angle value <> of substituents. Using dynamic orbital forces (DOF) as indices, the intrinsic  bond energies are studied as a function of <> for formally single bonds in a
panel of 22 molecules. This energy decreases from the strongest “superdirect” bonds in butadiyne, (<> = 180°) or tetrahedrylacetylene to the weakest “inverted bond” in cyclobutene, tetrahedrane, bicyclobutane and [1.1.1]propellane (<> = 60°), according to a sigmoidal variation. The <> parameter appears as a crude, but straightforward and robust, index of strain in cyclic molecules. Sigma bonds in multiple bonds of a panel of 11 molecules have most of time <> values less than 90°
and are significantly weaker than standard single bonds. Thus they can be considered as formally inverted or near inverted.


Chemical bonding
Molecular Orbitals
Inverted bond
Superdirect bond


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