Quantum reactive scattering: Dynamics of Gas Phase SN2 Reactions

Read our invited review article: ChemPhysChem 5, 601 (2004)

SN2 reactions are nucleophilic bimolecular substitution reactions. A nucleophilic species, e.g. Cl- attacks an electrophilic centre, the carbon atom of the methyl group of , for example, a CH3Br molecule. The C-Br bond breaks and a Cl-C bond is formed:

Cl- + CH3Br --> ClCH3 + Br-

This mechanism plays an important role in Organic Chemistry. In freshman's chemistry courses you learn that the reaction profile of an SN2 reaction shows a simple barrier. However, this is valid in the liquid phase only. In the gas phase the profile looks completely different:

Due to the attraction between the charge of the nucleophile and the dipole moment of the target molecule intermediate complexes are formed, one before and one after passage of the transition state. The corresponding potential wells are quite deep. It is possible that the reactive system is kept in one of these complexes for a while. The complex can either dissociate back to the educt side or surmount the barrier. In the second complex there are also two ways to react. If one takes one of the complexes as starting point, the reaction is essentially unimolecular. Being complex-forming bimolecular reactions, gas phase SN2 reactions are on the cutting egde of bi- and unimolecular reactions.

Because of the very special reaction profile the following questions arise:

v      What is the influence of the potential wells? How long are the lifetimes of the complexes? What can we say about the wavefunctions of the corresponding resonance states?

v      What is the effect of excitation of selected modes in the target species, e.g. the C-X stretching vibration or the CH3 umbrella bending vibration?

v      What is the influence of solvation on SN2 reactions?

v      How do different nucleophiles and leaving groups the reaction rates?

In order to answer the above questions we first construct potential energy hypersurfaces of the system which are based on results of high level ab initio calculations (mainly coupled cluster calculations with relatively big basis sets). We develop dimensionality reduced models in order to study the influence of selected modes. The time-independent Schrödinger equation is solved for continuum states by propagating (for a given total energy) the wavefunction from the classically forbidden strong interaction region out to the asymptotic region. The boundary conditions of the wavefunction yield -- via the S matrix -- information about reaction probabilites, reaction cross sections and rate constants. We also perform calculations in order to obtain insight into the wavefunctions of the resonances. Using the filter diagonalization method a lot of information can be obtained in selected energy windows.

 

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