New concept of hybridization based on sp hybrid orbitals in three membered ring

Isomers hosting three epoxides prefer axial orientation by a huge margin (>40kcal/mol) despite having severe steric problems.  Among the two axial isomers, the ‘all-cis’ structure 1B is less stable than the cis-trans hy-brid 1A though the C-C bond alternation is moderate in 1B compared to 1A.  This reduced bond alternation in 1B along with the fact that it also has a planar cyclohexane ring unlike 1A suggests the possibility of cyclic conjuga-tion à la aromatic delocalization in 1B; however, it is not dominating the energetics compared to the repulsive O…..O interactions. The splaying of cis oxygen atoms that adversely affect C-C bonding is less in 1B (0.600Å) than 1A (0.624Å), facilitating cyclic delocalization in ‘all-cis’ form. 

Overlap Control of Conformations

Bonding in epoxides is usually explained by two classical models, though both have their own drawbacks.  The popular bent ‘banana bond’ model of Coulson is borrowed from cyclopropane that uses isovalent hybridization.  Coulson attributes shortening of exo-epoxide bonds to the increased s character but the absence of expected elongation of epoxide C-C bond forced him to assert that these bonds are bent outwards. 

 The alternate Walsh MO model assumes sp² hybridization for the carbon⁴¹ due to its propensity for addition like olefins, where the shortening of exo-epoxy bonds is attributed to conjugation.  In all the epoxide dimers, the central C-C bond is ~0.05Å shorter than standard C-C single bond, except for the transition state 2B which still experiences steric repulsion from oxygen lone-pairs.  This shortening is found even in 2F despite the fact that their epoxides are oriented orthogonally indicating that conjugation advocated by the Walsh model may not be the reason.  Similarly, the destabilization of 2E that has trans orientation of epoxides is hard to account for with the Walsh model of isovalent hybridization. It is clear that these simple models by Coulson and Walsh are not adequate to explain the energetic and C-C bond length variations of different conformations of epoxide dimers. 

   Analysis of the interaction of frontier MOS of epoxide fragments to form 1,3 trans inter and intra epoxide dimers show negligible conjugative stabilization due to the large HOMO-LUMO gap of epoxides as expected.   Though the diagrasm also shows inter to be more stable than intra as observed in nanosheets, its MO origins are difficult to trace from their fragment MOs.  This is mostly due to the low symmetry of the fragments forced by ipso hydrogen atoms of the dimer that allows the seamless mixing of many frontier MOs. 

  To avoid this complication, we use the frontier MOs of the epoxide fragment when two geminal hydrogens are removed from the carbon atom to construct the fragment MOs.   This gives two MOs dominated by the divalent carbon in the frontier; one is an sp hybrid pointing outwards and another p-type orbital perpendicular to the epoxide ring.  The orientation of these two types of FMOs (sp and p) forming the exo-C-C bond in different environments of the dimer is given in Figure 3.

   In the inter case, the dominant interaction is between the sp hybrid of one ipso carbon with the p orbital of the other.  Among these, trans has symmetrical distribution around the exo-epoxy bonds, while cis has electron density bent away from the epoxide bridges.  In the intra case, p-p and sp-sp overlap are dominant. Among these two, the overlap between sp hybrids in trans is poor as they are pointing away, while in cis they have the best overlap.  The variation in the bond-lengths of the C₂O nanosheets, particularly the computed energetic proximity of 3A and 3B nanosheets, supports the above reasoning.   Despite splaying, 3B shows the shortest C-O distances indicating that splaying is not detrimental to the stability of the carbon framework as it helps improve sp-p overlap in the exo C-C region.  This reasoning implies the bending of both epoxy and exo-epoxy bonds and can potentially be used to predict the mode and ease of nucleophilic attack.

  These facts naturally lead to a new model of epoxide bonding based on sp hybridization, in which s orbital and the radial p orbital of the epoxide ring is mixed to yield one sp hybrid pointing inwards and another pointing outward.  The inward-pointing sp hybrid, along with the p orbital tangential to the epoxide ring, is responsible for the bonding within the epoxide ring while the outward-pointing sp hybrid with the p orbital perpendicular to the epoxide ring is presumed to be involved in the exo-epoxy bonding.  This new hybridization model based on FMO theory is similar to sp hybrid model typically used in polyhedral boranes except that only one of the unhybridized p orbital (tangential to the epoxide ring) is involved in the bonding within the epoxide ring while the unhybridized p orbital perpendicular to the ring is engaged in exo-epoxy bonding. 

This model successfully addresses the shortcomings of the Walsh model, doing away with the conjugative stabilization as the reason for bond shortening.  It rather attributes to the overlap of the frontier orbitals away from the internuclear line making the exo-epoxy bonds also to have substantial electron density away from the inter-nuclear region, effectively extending the idea of bending to cover exo-epoxy bonds. Upon extension, the sp hybridization model can also explain the perceived instability of four-membered rings over three-membered rings as arising from repulsive 1,3 interactions between inward-pointing sp hybrids and will be described elsewhere.  With the observed trends in energetics and geometry successfully explained, our results provide the framework for understanding the origins of many of the mysterious observations surrounding the graphene oxide structure. 

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  https://pubs.acs.org/doi/10.1021/acs.jpcc.9b10262