Unimolecular transition structure

In contrast, applying frontier orbital theory to unimolecular reactions like electrocyclic reactions and sigmatropic rearrangements is inherently contrived, since we have artificially to treat a single molecule as having separate components, in order to have any frontier orbitals at all. Furthermore, frontier orbital theory does not explain why the barrier to forbidden reactions is so high—whenever it has been measured, the transition structure for the forbidden pathway has been 40 kJ mol-1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. 

Under this treatment, the reaction order of an elementary unimolecular or bimolecular reaction must identify with molecularity, and K is related in Equation 9.3 to the standard molar free energy difference, AG, between reactants and transition state (a hypothetical construct comprising one mole of transition structures, see below) ... 

A similar description applies to a unimolecular reaction except that formation of the transition structure is initiated by energy accumulation in the solvated reactant by collision. 

Transition structures of CH4 elimination in MMes have been investigated in detail with ab initio see Ab Initio Calculationi) quantum mechanics calculations. The most favorable transition structure for the elimination is close to a trigonal-bipyramidal geometry. A dimeric mechanism through intermolecular hydrogen abstraction is found to be much lower in activation free energy than the unimolecular mechanism. The dimeric transition structure is mainly stabilized by an M-CH2-M bridge. ... 

Another complication with gas phase pyrolyses is that many possible nonconcerted reaction pathways are possible. Alkyl halides xmdergo elimination in the gas phase, and some compounds, such as ethyl chloride, appear to undergo unimolecular elimination. Their unimolecular decompositions may involve transition structures with significant carbocation character. For example, p5u-olysis of (-l- )-2-chlorooctane in the gas phase at 325-385°C was found to produce racemization of the starting material as well as elimination of HCl. Some compounds appear to react by radical chain mechanisms, and heterogeneous radical reactions often complicate studies that are not carried out in "well-seasoned" (i.e., coated with a layer of organic material) vessels. Furthermore, there appears to be a significant radical (but not radical chain) component to the pyrolysis of sulfoxides. These complications mean that many control studies are necessary to clarify the mechanism of gas phase elimination reactions. 

In this equation k is called the transmission coefficient and is taken to be equal to unity in simple transition-state theory calculations, but is greater than imity when tunneling is important (see below), c° is the inverse of the reference volume assumed in calculating the translational partition function (see below), m is the molecularity of the reaction (ie, m = 1 for unimolecular, 2 for bimolecular, and so on), is Boltzmann s constant (1.380658 x 10 J molecule K ), h is Planck s constant (6.6260755 x 10 J s), Eq (commonly referred to as the reaction barrier) is the energy difference between the transition structure and the reactants (in their respective equiUbriiun geometries), Qj is the molecular partition function of the transition state, and Qi is the molecular partition function of reactant i. 

By ab initio MO and density functional theoretical (DPT) calculations it has been shown that the branched isomers of the sulfanes are local minima on the particular potential energy hypersurface. In the case of disulfane the thiosulfoxide isomer H2S=S of Cg symmetry is by 138 kj mol less stable than the chain-like molecule of C2 symmetry at the QCISD(T)/6-31+G // MP2/6-31G level of theory at 0 K [49]. At the MP2/6-311G //MP2/6-3110 level the energy difference is 143 kJ mol" and the activation energy for the isomerization is 210 kJ mol at 0 K [50]. Somewhat smaller values (117/195 kJ mor ) have been calculated with the more elaborate CCSD(T)/ ANO-L method [50]. The high barrier of ca. 80 kJ mol" for the isomerization of the pyramidal H2S=S back to the screw-like disulfane structure means that the thiosulfoxide, once it has been formed, will not decompose in an unimolecular reaction at low temperature, e.g., in a matrix-isolation experiment. The transition state structure is characterized by a hydrogen atom bridging the two sulfur atoms. 

Marcus and Rice6 made a more detailed analysis of the recombination from the point of view of the reverse reaction, the unimolecular decomposition of ethane, C2Ha - 2CH3. By the principle of microscopic reversibility the transition states must be the same for forward and reverse paths. Although they reached no definite conclusion they pointed out that a very efficient recombination of CH3 radicals would imply a very high Arrhenius A factor for the unimolecular rate constant of the C2H6 decomposition which in turn would be compatible only with a very "loose transition state. Conversely, a very low recombination efficiency would imply a very tight structure for the transition state and a low A factor for the unimolecular decomposition. 

---