Not Carbon s–p Hybridization, but Coordination Number Determines C−H and C−C Bond Length

Abstract

Af undamental and ubiquitous phenomenon in chemistry is the contraction of both CÀHa nd CÀCb onds as the carbon atoms involved vary,i ns -p hybridization, along sp 3 to sp 2 to sp. Our quantum chemical bonding analyses basedo nK ohn-Sham molecular orbital theory show that the generally accepted rationaleb ehind this trend is incorrect. Inspection of the molecular orbitals and their corresponding orbitalo verlapsr eveals that the above-mentioned shortening in CÀHa nd CÀCb onds is not determinedb ya ni ncreasinga mount of s-character at the carbon atom in these bonds. Instead, we establish that this structuralt rend is caused by ad iminishing steric (Pauli)r epulsion between substituents aroundt he pertinent carbon atom, as the coordinationn umber decreases along sp 3 to sp 2 to sp.

Cooperative Self‐Assembly in Linear Chains Based on Halogen Bonds

“…[29,30] The black MO diagram shows the donor‐acceptor interaction between the σ HOMO and σ* LUMO of two monomers, and the blue energy levels are the σ HOMO and σ* LUMO of two interacting dodecamers. The stability of the σ* LUMO orbital of the C−X bond lowers significantly when we vary the system from X−CN or X−CC−CN to X−C 6 H 4 −CN, for instance, for X = Br, the σ* LUMO orbital goes from −2.5 eV to −2.3 eV to −1.6 eV, for Br−CN to Br−CC−CN to Br−C 6 H 4 −CN, respectively (Table 3), which is in line with our previous work [42] . In that paper, we showed that the σ* LUMO of a C−X bond becomes more stable when we go from an sp 2 ‐hybridized C−X bond to an sp‐hybridized C−X bond, because the SOMO of the sp 2 ‐hybridized carbon radical, which participates in the electron‐pair bond formation with X yielding the C−X bond, is more stable than the sp‐hybridized analog.…”

“…The stability of the σ* LUMO orbital of the CÀ X bond lowers significantly when we vary the system from XÀ CN or XÀ CCÀ CN to XÀ C 6 H 4 À CN, for instance, for X = Br, the σ* LUMO orbital goes from À 2.5 eV to À 2.3 eV to À 1.6 eV, for BrÀ CN to BrÀ CCÀ CN to BrÀ C 6 H 4 À CN, respectively (Table 3), which is in line with our previous work. [42] In that paper, we showed that the σ* LUMO of a CÀ X bond becomes more stable when we go from an sp 2 -hybridized CÀ X bond to an sp-hybridized CÀ X bond, because the SOMO of the sp 2hybridized carbon radical, which participates in the electronpair bond formation with X yielding the CÀ X bond, is more stable than the sp-hybridized analog. Furthermore, σ* LUMO becomes more stable when the CÀ X bond contains a larger halogen due to the more diffuse halogen np σ atomic orbital which gives rise to a decrease in the overlap of the antibonding combination of the carbon 2 s and halogen np σ atomic orbital (AO).…”

The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn–Teller effect

“…Thus, the bond elongation in the TS is a result of DE Pauli -lowering, similar to the recently described effects for CH-bond lengths in the series of sp n (n ¼ 1-3) hybridized carbon atoms. 111 The differences in preparation energy (DDE Prep ) need to be added to reproduce the nal inversion barrier energies. DDE Prep can be understood as the part of the inversion barrier caused by substituentsubstituent repulsion.…”

Theoretical Study of a Derivative of Chlorophosphine with Aliphatic and Aromatic Grignard Reagents: SN2@P or the Novel SN2@Cl Followed by SN2@C?

“…29 The occurrence of activation barriers was explained using the distortion/interaction-activation strain model (D/I-ASM) of chemical reactivity. 30,31 The mechanisms that we determined do not only explain the experimental outcome 25 but also constitute a novel synthetic route, via SN2@Cl mechanism, for organophosphorus derivatives which experimentalists may explore in cases where a control over stereoselectivity is required. In addition, to the best of our knowledge, SN2@Cl is being proposed for the first time.…”

“…Moreover, the D/I-ASM of chemical reactivity was employed to explain the trends in reactivity along the reaction. 30,31,45,46 In the D/I-ASM, the energy along the reaction coordinate is decomposed into its strain and interaction contributions [Equation S1; supplementary information (SI)] which originate from the rigidity and orbital overlap of deformed reactants, respectively. The D/I-ASM was also applied in THF to investigate the effect of solvation (ΔEsolvation) (Equations S2 and S3).…”