Carbocations and Free Radicals

The structure, reactivity and stability of organic carbocations and free radicals



Carbocations are organic compounds with a tricoordinated, sp2-hybridized, carbon atom with a formally empty 2p orbital.  They are positively charged electron deficient compounds with often very fluid structures.  Very few are stable isolable entities; they are usually postulated as reactive intermediates in SN1 and E1 mechanisms.

The most interesting features of carbocations are their nonclassical structures and ready conformational interconversions.  The first are very amenable to ab initio electronic structure calculations, while the second are also susceptible to experimental strong acid NMR techniques.  In the 1980a and 1990s, my group had a fruitful collaboration with the Sorensen group, beginning with his seminal discovery in 1980 of novel cyclohexyl cations which can be described as hydride-bridged dications [T. S. Sorensen, et al., JACS, 1981, 103, 588 – 596; T. S. Sorensen, et al., JACS, 1981, 103, 597 – 604].  The empty 2p orbital has a tendency to delocalize electrons from nearby s bonds and will distort from a planar structure to maximize p-type overlap [T.S. Sorensen et al., JACS, 1989, 111, 9024 - 9029].  This is dramatically illustrated in the structure of the 2-adamantyl cation shown at right.

2-adamantyl cation

Computed structure of the 2-adamantyl cation, showing distortion from nonplanar geometry to maximize orbital overlap with adjacent C-C bonds. The lowest unoccupied molecular orbital is shown.

Organic Free Radicals

The central feature of organic free radicals is an sp2 hybridized carbon atom with a singly occupied 2p orbital.

For a variety of theoretical and technical reasons, computation of open shell systems is difficult at the Hartree-Fock level.  Post-HF methods, e.g., UMP2 with a large basis set, were required to yield reliable structures, energies and thermodynamic functions.  It became very much easier with the advent of Density Functional Theory (DFT) in the early 1990s.  Nevertheless, I enjoyed a very fruitful collaboration in the 1980s with the late Eugene (Gene) Tschuikow-Roux and his student Yonghua Chen, investigating the structures of a variety of 2- and 3-C hydrocarbons with varying degrees of fluorination.  Gene was a kineticist whose modus operandi was gas-phase shock tube, which yielded experimental data in the gaseous phase, ideal for computations, since the effects of solvation were difficult to accommodate in those days. The structures of mono- di- and trifluoroethyl radicals are shown at right [Y. Chen, A. Rauk, and E. Tschuikow-Roux, J. Chem. Phys. 1990, 93, 6620 – 6629].

Radical Stabilization

Stabilization of carbon free radical by an electron donor (left), an electron acceptor (middle), and by the captodative effect (right) - image from "Orbital Interaction Theory of Organic Chemistry, 2nd Ed.", John Wiley & Sons, 2000.

Alpha-C Radicals in Peptides

As the orbital interaction diagram above shows, extra stabilization of a C-centred radical, called captodative stabilization, ensues if the radical is substituted by at least one p-electron donor (O, N, double bond, etc), and one p-electron acceptor (-NO2, C=O, nitrile, double bond, etc).  While a normal C-H bond dissociation enthalpy (BDE) is above 400 kJ/mol (CH4 440), much lower values of BDE are measured and calculated for captodative systems:H2NCH2CH=O 320; H2NCH2BH2 333, CH2=CHCH2CH=CH2 250).  For maximum stabilization, the p-systems of the donor, acceptor and C. must be coplanar. We realized in the late 1990s that the a-CH bond common to all amino acid residues and proteins may similarly be weakened by the captodative effect of the flanking amide groups, one of which presents a carbonyl group and the other of which presents the NH group. The carbonyl group of an amide is a weak p-acceptor and the NH group is a weak p-donor, so it was not clear how much captodative stabilization actually ensues.  The question is important in the biological context because removal of the a-CH hydrogen atom constitutes oxidative damage to the peptide/protein.  Oxidative damage is usually repaired by transfer of an H atom from glutathione (GSH), the endogenous reducing agent present in millimolar concentrations.  Repair may not be possible if the a-CH bond is weaker than the S-H bond of GSH, 367 kJ/mol. The graphic at the right represents the results of a careful theoretical investigation of the BDEs of all peptidic a-CH bonds (A Rauk , D Yu, J Taylor, G V Shustov, D A Block, D A Armstrong, Biochemistry, 1999, 38, 9089-9096. doi: 10.1021/bi990249x)

Fluoroethyl radicals

The UHF/6-31G(d) structures of 2-fluoro-, 2,2-difluoro-, and 2,2,2-trifluoroethyl radicals.

Stabilization of Free Radicals

Throughout the 1990s, we had a very fruitful collaboration with the late David Armstrong and a shared PDF, Dake Yu, investigating radicals with a more biological relevance.  With the advent of DFT and more sophisticated theoretical and computational techniques, answers to more complex questions could be obtained.  Orbital interaction theory (OIT) predicts that radicals can be stabilized by delocalizing nearby electrons into the singly occupied 2p orbital of the radical centre, and counterintuitively, also by delocalizing the single electron into nearby empty p-type orbitals.  Clearly, since every molecule has within it a source of both occupied and empty orbitals, as do external molecules, including the medium, all radicals should be stabilized.  While OIT provides only a crude estimate of the extent of stabilization, DFT methods can provide a quantitative number, in the form af an enthalpy of interaction (R. + X à R.X), or the strength of a bond (R:H à R.  +  H.)


Bond dissociation enthalpies of all of the amino acid peptides.