At The Transition State

Both of the out-of-plane modes are non-degenerate. The kernel of the a2u mode is C4V, the point group of a tetragonal pyramid, such as would be generated by the approach of a fifth ligand atom along z. Continued displacement along the 62 coordinate takes square-planar NiFj into D2d, and eventually converts it into a tetrahedral complex this interconversion will be discussed in detail in a Chapter 11. 

Up to now, we have been assuming that the molecular entity being considered is stable, in the sense that it is in a geometry of minimum potential energy, so that all of its 3A — 6 values of A are positive. This geometry need not be the most stable one on the potential energy surface it can be at a local minimum. It follows that even a chemical species that would normally be classified as an unstable intermediate as distinguished from a transition state, is stable in this restricted sense. 

When the molecular entity involved is a transition state, one of its normal coordinates is the reaction coordinate, motion along which is not opposed by a restoring force. The transition state is situated at a saddle point on the potential energy surface [25, Chap. 5] [26, pp. 101-107], at which A, the force constant for motion along the reaction coordinate is negative and is consequently imaginary, so a non-linear transition state can have no more than 

For mathematical convenience, is usually assumed to be zero in formal derivations of Transition State Theory, whereupon the reaction coordinate approximates a translation. 

In their now classic monograph [1], Wooodward and Hoffmann concentrate on three basic types of no mechanism reaction Electrocyclic reactions -notably polyene cyclizations, cycloadditions, and sigmatropic rearrangements. These three reaction types will be taken up in this and the next two chapters from the viewpoint of Orbital Correspondence Analysis in Maximum Symmetry (OCAMS) [2, 3, 4], the formalism of which follows naturally from that developed in Chapter 4. The similarities to the original WH-LHA approach [5, 6], and the points at which OCAMS departs from it, will be illustrated. In addition, a few related concepts, such as allowedness and forbiddenness , global vs. local symmetry, and concertedness and synchronicity , will be taken up where appropriate. 

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The photoelectron spectrum of FH,is shown in figure A3.7.6 [54]. The spectrum is highly structured, showing a group of closely spaced peaks centred around 1 eV, and a smaller peak at 0.5 eV. We expect to see vibrational structure corresponding to the bound modes of the transition state perpendicular to the reaction coordinate. For this reaction with its entrance chaimel barrier, the reaction coordinate at the transition state is... 

The interplay between favourable reactivity at a collinear geometry and electrostatic forces favouring a T-shaped geometry leads to a bent geometry at the transition state. 

Equation (A3.11.183) is simply a fommla for the number of states energetically accessible at the transition state and equation (A3.11.180) leads to the thenual average of this number. If we imagine that the states of the system fonu a continuum, then PJun, 1 Ican be expressed in tenus of a density of states p as in... 

The tenn (E-E ) is tire sum of states at the transition state for energies from 0 to E-E. Equation (A3.12.15) is the RRKM expression for the imimolecular rate constant. 

One way to overcome this problem is to start by setting up the ensemble of trajectories (or wavepacket) at the transition state. If these bajectories are then run back in time into the reactants region, they can be used to set up the distribution of initial conditions that reach the barrier. These can then be run forward to completion, that is, into the products, and by using transition state theory a reaction rate obtained [145]. These ideas have also been recently extended to non-adiabatic systems [146]. 

More specifically, the geometry of the molecule at the transition state is used to... 

The structure that exists at the transition state is some times referred to as the tran sition structure or the activated complex... 

In principle cis 2 butene and trans 2 butene may be mterconverted by rotation about the C 2=C 3 double bond However unlike rotation about the C 2—C 3 single bond in butane which is quite fast mterconversion of the stereoisomeric 2 butenes does not occur under normal circumstances It is sometimes said that rotation about a carbon-carbon double bond is restricted but this is an understatement Conventional lab oratory sources of heat do not provide enough energy for rotation about the double bond m alkenes As shown m Figure 5 2 rotation about a double bond requires the p orbitals of C 2 and C 3 to be twisted from their stable parallel alignment—m effect the tt com ponent of the double bond must be broken at the transition state... 

The regioselectivity of elimination is accommodated m the E2 mechanism by noting that a partial double bond develops at the transition state Because alkyl groups... 

Although both stereoisomers yield 4 tert butylcyclohexene as the only alkene they do so at quite different rates The cis isomer reacts over 500 times faster than the trans The difference in reaction rate results from different degrees of rr bond develop ment in the E2 transition state Since rr overlap of p orbitals requires their axes to be parallel rr bond formation is best achieved when the four atoms of the H—C—C—X unit he in the same plane at the transition state The two conformations that permit this are termed syn coplanar and anti coplanar... 

Hughes and Ingold interpreted second order kinetic behavior to mean that the rate determining step is bimolecular that is that both hydroxide ion and methyl bromide are involved at the transition state The symbol given to the detailed description of the mech anism that they developed is 8 2 standing for substitution nucleophilic bimolecular... 

Carbon is partially bonded to both the incoming nucleophile and the departing halide at the transition state Progress is made toward the transition state as the nucleophile begins to share a pair of its electrons with carbon and the halide ion leaves taking with it the pair of electrons m its bond to carbon... 

Because carbocatwn character develops at the transition state substitution is favored at the carbon that can better support a developing positive charge Thus m... 

Although nucleophilic participation at the transition state is slight it is enough to ensure that substitution proceeds with inversion of configuration... 

What will be the product isolated after thermal decarboxyla tion of each of the following Using curved arrows represent the bond changes that take place at the transition state... 

Unimolecular (Section 4 8) Describing a step in a reaction mechanism in which only one particle undergoes a chemi cal change at the transition state... 

The average flux across the transition state dividing surface will be proportional to the relative probability of being found at the transition state,... 

We counted the contribution of only those trajectories that have a positive momentum at the transition state. Trajectories with negative momentum at the transition state are moving from product to reactant. If any of those trajectories were deactivated as products, their contribution would need to be subtracted from the total. Why Because those trajectories are ones that originated from the product state, crossed the transition state twice, and were deactivated in the product state. In the TST approximation, only those trajectories that originate in the reactant well are deactivated as product and contribute to the reactive flux. We return to this point later in discussing dynamic corrections to TST. 

In practice, we can compute K as follows [19,23]. We start with a set of trajectories at the transition state q = q. The momenta have initial conditions distributed according to the normalized distribution functions... 

It is interesting that the molecular structure in the transition state is also subject to a solvent effect. Compared to the gas phase, the solute molecular geometry at the transition state shifts toward the reactant side in aqueous solution the C—N and C—Cl distances... 

Because the product composition is kinetically controlled, the isomer ratio will be governed by the relative magnitudes of AG, AGI, and AG, the energies of activation for the ortho, meta, and para transition states, respectively. In Fig. 4.7 a qualitative comparison of these AG values is made. At the transition state, a positive charge is present on the benzene ring, primarily at positions 2, 4, and 6 in relation to the entering bromine. 

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