Spectator bonds

To illustrate the first point concerning a spectator bond for the abstraction reaction, Fig. 17 shows the total reaction probability for the abstraction reaction as a function of the translational energy for total angular momentum J = 0 on the YZCL2 PES with the H20 reactant in the ground rovibrational state [the (00)(0) state in the local mode notation], where the uncleaved bond OHb is treated in various ways. Using a limited number of one or five vibrational basis functions, VBF(OHb) = 1 or 5, means that the OHb bond is unreactive, a spectator. The abstraction reaction probability... 

We had earlier vindicated treating one of the OH bonds in the H2O molecule as a spectator bond in studying the abstraction reaction. Another key assumption that needed to be checked was the centrifugal sudden (CS) approximation which was invoked to reduce the number of rotational basis functions used in the computations.28 Under the CS approximation and using only the K = 0 rotational basis functions, there was a total of 220 million basis functions for J = 15 alone. Relaxing the CS approximation, for example, with K = 0,1 and J = 15 led to 650 million basis functions. To approach the fully coupled-channel (CC) results, i.e. without... 

In general, then, a band which is 1/3,1/4. .. l/p occupied is subject to Peierls instability with respect to a tri-, tetra-, / -merisation. It is important to remind you at this point that the possibility of a Jahn-Teller instability does not always mean the distortion occurs. The same applies for Peierls instability. There are several reasons. First of all, Peierls instability holds rigorously for ideal one-dimensional materials and reality is a more complicated three-dimensional space. Second, as in the case of molecules, when high-spin states are preferred, the distortion is not favored (see Problem 7 for an example). Third, even in the case of low-spin systems, the distortion may have additional consequences, e.g., weakening of spectator bonds. Coupled destabilizing effects can dampen or even prevent distortion. In the H2 case described above, there is no effect opposing the distortion, and dimerization is complete, i.e., fully independent H2 molecules result from our hypothetical chain. 

It can be seen from Eq. (7) that (1) the CD bond which is sometimes known as the spectator bond is indeed a spectator in that its velocity is unchanged, (2) unlike the case of a four-center AB + CD -> AC + BD reaction, here the A + BCD products have a finite relative velocity and so can recede from one another even if the reactants are not internally excited, and (3) the new BD bond is formed with considerable kinetic energy. 

Our focus here is on the abstraction reaction. It has a saddle point with H H O close to a collinear geometry hence the H atom should collide with the H2O molecule at totally different angles in order to abstract one H atom or the other. As a result, it should be possible to treat the unbroken OH bond as a spectator bond in the abstraction... 

In this approximate treatment, one simply freezes the nonreactive or spectator bond. The 6D Hamiltonian in this case becomes the effective 5D Hamiltonian by eliminating the kinetic energy operator for the r2 coordinate and fixed the r2 distance in the potential energy surface. The 5D potential is simply given by... 

In the PA5D treatment, one essentially treats the nonreactive bond vibration diabatically which is equivalent to including only one vibrational state in the 6D basis function expansion described previously. The net result of this treatment is a 5D Hamiltonian in which the effective 5D potential energy surface is given by averaging the 6D potential surface over the vibrational coordinate of the spectator bond. This is done by the simple procedure... 

Excitation of the OH stretching vibration does not signifieantly change the energy profile, in particular the barrier is lowered by only about 0.3 kcal/mol. Thus, the OH is definitely a spectator bond. 

The RBA is a general theory that has the particular advantage that it can treat explicitly both the bending mode of triatomic ABC and rotational states of AB in the reaction ABC + D AB + CD. The method has also been applied to the reactions OH + CO CO2 + H [14] and H + HCN H2 + CN [15]. It has also been extended to polyatomic reactions such as OH + CH4 H2O + CH3 [16] and, very recently, the Walden inversion reaction Cl" + CH3Br -> CH3CI + Br [17]. In these latter calculations the spectator bonds not taking part directly in the reaction were held fixed, an approximation which is expected to be reliable on the basis of our previous computations. 

After reading Chapter 14, you might be wondering why we can represent the a bonds in such a simple manner, because fully delocalized MOs without carbon hybridization are the results obtained from sophisticated electronic structure theory. Experience has shown that in pericyclic reactions there is no need to include "spectator bonds", bonds that remain intact throughout the reaction, in the analysis. Remember that orbitals and our notions of bonding are just models. Any model that explains experimental results and can predict them is useful, and the simplest is always the best. Here we show the simplest model that works. We could complicate our model by including the spectator bonds, but the results would be the same. 

Valero R, Kroes G-J (2006) Identifying spectator bonds in modeling reactions ... 

The adiabatic force constant associated with coordinate R3 does not change during the reaction, indicating that the CH bonds of the CH3 radical are spectator bonds. The changes in the R1 and bending angle force constants are related to the changes in the RP vector and the bifurcation of the RP. 

This study was shortly followed by a similar one in which the CN spectator bond was treated with a harmonic oscillator basis and the same main conclusions were found. Although these first calculations were very much of the model form, they did demonstrate that quantum scattering calculations on four-atom reactions are computationally feasible and were the start of a very intensive effort, by several of the leading groups working on chemical reaction theory, to make the theory more accurate and general for four-atom reactions. 

---