There is often a disconnect between how a text-book (schematically) represents a reaction and a more quantitive “reality” revealed by quantum mechanics. Is the bromination of ethene to give 1,2-dibromoethane one such example?
Text-books will show how ethene interacts with bromine to form a cyclic bromonium cation, which with the liberated bromide anion makes for an ion-pair. Using quantum mechanics (DFT ωB97XT/6-311G(d,p)/SCRF=dichloromethane), one soon realises that the ion-pair will need to be stabilised, both by solvation and possibly by interacting the bromide anion with a further bromine to form a tribromide anion (as shown above). A transition state for this process can indeed be located, and this is shown below, together with the IRC for the process.
The barrier (~ 7 kcal/mol) is appropriately small for what is a rapid reaction. The ion-pair formed is only stable by ~ 1 kcal/mol towards a reverse reaction. Here however, the limitations of this relatively simple solvation model (a continuum solvent and an extra bromine molecule) may be under-estimating its stability.
The interesting bit comes next. The ion-pair has got to relocate itself to a position where the tribromide anion can back-side attack the bromonium cation.‡ Ion-pairs are unlike normal molecules, where covalent bonds determine fairly clearly what the geometry and its conformations might be. There are no straightforward rules for establishing what the geometry of an ion-pair might be, or indeed what its energy relative to other poses might be, other than perhaps simply minimising its dipole moment. In this example, quantum mechanics tells us that in fact the ion-pair is about 2 kcal/mol MORE stable in its new location, and so it can presumably diffuse over with a clear driving force.† Once it is back-side located, the reaction completes without any enthalpic barrier; it is downhill all the way!
This is a fairly simple model for the reaction between bromine and ethene. Modelling it however is not that simple. Any reaction which undergoes a transition from covalency to ionicity in one or more bond is always a challenge. And ionic systems may not always be best represented by (non-statistical) models which include only one molecule (as is the case with ionic solids). But the picture I have shown here takes the text-book schemes up one level, and we now have at least an estimate of the energies involved, as well as geometries.
† The geometry of TS2 is shown below. It has a dipole moment of 19.3D and is some 9.6 kcal/mol in ΔG above TS1, which has a dipole moment of 18.7D. It may of course not be the lowest energy pathway for reorganisation of the ion-pair.
‡Where backside attack is prevented by steric bulk, this very ion-pair can actually be isolated as a crystal
It is also possible to isolate the bromonium cation using a different counter-anion, by the same subterfuge of steric hindrance. This structure also is unusual in revealing an isolated hydronium ion cation, H3O+.
- H. Slebocka-Tilk, R.G. Ball, and R.S. Brown, "The question of reversible formation of bromonium ions during the course of electrophilic bromination of olefins. 2. The crystal and molecular structure of the bromonium ion of adamantylideneadamantane", J. Am. Chem. Soc., vol. 107, pp. 4504-4508, 1985. http://dx.doi.org/10.1021/ja00301a021
- R.S. Brown, R.W. Nagorski, A.J. Bennet, R.E.D. McClung, G.H.M. Aarts, M. Klobukowski, R. McDonald, and B.D. Santarsiero, "Stable Bromonium and Iodonium Ions of the Hindered Olefins Adamantylideneadamantane and Bicyclo[3.3.1]nonylidenebicyclo[3.3.1]nonane. X-Ray Structure, Transfer of Positive Halogens to Acceptor Olefins, and ab Initio Studies", J. Am. Chem. Soc., vol. 116, pp. 2448-2456, 1994. http://dx.doi.org/10.1021/ja00085a027