The “Inverted Bonds” Revisited: Analysis of “In Silico” Models and of [1.1.1]Propellane by Using Orbital Forces

Abstract

This article dwells on the nature of “inverted bonds”, which refer to the σ interaction between two sp hybrids by their smaller lobes, and their presence in [1.1.1]propellane. Firstly, we study H3C−C models of C−C bonds with frozen H‐C‐C angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane and [1.1.1]bicyclopentane are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate bond energies. Triplet and cationic states of [1.1.1]propellane species are also considered to confirm the bonding/antibonding character of MOs in the parent molecule. These approaches show an essentially non‐bonding character of the σ central C−C interaction in propellane. Within the MO theory, this bonding is thus only due to π‐type MOs (also called “banana” MOs or “bridge” MOs) and its total energy is evaluated to approximately 50 kcal mol−1. In bicyclopentane, despite a strong σ‐type repulsion, a weak bonding (15–20 kcal mol−1) exists between both central C−C bonds, also due to π‐type interactions, though no bond is present in the Lewis structure. Overall, the so‐called “inverted” bond, as resulting from a σ overlap of the two sp hybrids by their smaller lobes, appears highly questionable.

Comment on “The ‘Inverted Bonds’ Revisited. Analysis of ‘in Silico’ Models and of [1.1.1]Propellane Using Orbital Forces“

“…It is noteworthy that the BOVB method, the same as the one that characterized the σ bridgehead bond of [1.1.1]propellane and whose results are challenged in Ref. , yields a bonding energy of 30.4 kcal mol −1 for F 2 − , in perfect agreement with experiment.…”

“…In a recent publication in this journal, Laplaza, Contreras‐Garcia, Fuster, Volatron and Chaquin (LCFVC) report an application of the Dynamical Orbital Forces (DOF) method, which was used by the authors to challenge the presence of an inverted central C−C bond in [1.1.1]propellane ( 1 in Scheme ), which was suggested to exist long ago by Jackson and Allen, then by Feller and Davidson, and recently given theoretical support on the basis of ab initio valence bond calculations …”

“…As an extension of this model, the DOFs with respect to a given interatomic distance are summed over all the MOs (ϕ i ) of a molecule, and the result Σ(DOF i ) is considered as the central quantity that determines the nature and strength of a particular bond. A large positive Σ(DOF i ) corresponds to a strong bond, while a negative Σ(DOF i ) signifies a repulsive interaction . This method was recently applied to a series of hydrocarbons and a linear correlation was found between the CC bonding energies and the CC Σ(DOF i ) …”

“…To check the effect of changing the Hartree–Fock MOs to Kohn–Sham MOs, as done in Ref. , and argued to tentatively bring in electron correlation, we restarted the DOF calculations by using the density functional that was shown to yield the best (2c,3e) bonding energies, the BHandHLYP functional, in the spin‐unrestricted version to maximize accuracy. The results are displayed in Table , and are quite similar to the ROHF results, with a negative ΣDOF i of −0.251 a.u., hence still predicting a dissociative F 2 − anion.…”

“…In Ref. , the MOs are divided into two categories, π (e’ and e“) and σ (a’ 1 and a“ 2 ), and all the MOs of the latter category are arbitrarily associated to the central bond, whereas two of these MOs, 9a“ 2 and 13a’ 1 , are in fact mixtures of wing and central bonds. In particular, the 9a“ 2 MO should rather be considered as a negative combination of bonding fragment orbitals localized on wing bonds, as indicated by its shape, the absence of axial p atomic orbitals, and the low orbital energy (−0.533 hartrees, this work).…”