Branching ratios

Seeley J V, Morris R A, Viggiano A A, Wang FI and Flase W L 1997 Temperature dependencies of the rate constants and branching ratios for the reactions of Cr(Fl20)g 3 with CFIjBr and thermal dissociation rates for CI (CFl3Br) J. Am. Chem. Soc. 119 577-84... 

The conceptually simplest approach towards controlling systems by laser field is by teaching the field [188. 191. 192 and 193]. Typically, tire field is experimentally prepared as, for example, a sum of Gaussian pulses with variable height and positions. Each experiment gives an outcome which can be quantified. Consider, for example, an A + BC reaction where the possible products are AB + C and AC + B if the AB + C product is preferred one would seek to optimize the branching ratio... 

Other possible choices are to use two pairs of frequencies which together have the same energies. The key point is that quantum interference between the two pathways can be used to control the branching ratio. This coherent-control approach is very general and can be used in virtually any branch of molecular dynamics, including scattering and photo-dissociation. 

The 0X0 process is not limited to simple olefins. The terrninal-to-branched ratio of products can be controlled by ligand addition (130). Butanol is produced from propylene and CO using a similar process (see Butyl alcohols). The catalyst in this case is Fe(CO) (131). 

Fig. 13.11. A schematic drawing of the potential energy surfaces for the photochemical reactions of stilbene. Approximate branching ratios and quantum yields for the important processes are indicated. In this figure, the ground- and excited-state barrier heights are drawn to scale representing the best available values, as are the relative energies of the ground states of Z- and E -stilbene 4a,4b-dihydrophenanthrene (DHP). [Reproduced from R. J. Sension, S. T. Repinec, A. Z. Szarka, and R. M. Hochstrasser, J. Chem. Phys. 98 6291 (1993) by permission of the American Institute of Physics.]...

For example, consider the two trees shown in figure 12.4. The tree in figure 12.4-a has equal (binary) subtrees, so that its diversity V = 1 and complexity C = 0. The same is true for any tree all of whose nodes have a constant branching ratio. On the other hand, the tree shown in figure 12.4-b has two distinct subtrees, each of which has a diversity of 2 = 1. The diversity of the entire tree is therefore X) = 22 - 1 = 3. 

The results of Fig. 2 therefore show that for the chosen frequency, almost total dissociation is attainable for a range of field amplitudes and we can get more I + Br or I + Br (the desired selectivity) with simple cw fields employed in the FOIST scheme. We may therefore infer that considerable dissociation and selectivity (almost any branching ratio) may be achieved using the scheme (18,19) presented here. The extent of optimization however varies with field amplitude and at the two ends of the field range, the FOIST results do not provide much improvement over the maximum available from one of the pure vibrational states in the optimization manifold. It should however be noted that FOIST alone can provide which of the v=0, 1 or 2 is optimal for the chosen objective. 

The mechanism of the FOIST based selective control of IBr photodissociation has been further probed by the use of and V iii the TDWP calculation of IBr absorption spectrum (Fig. 5) and branching ratio (Fig. 6). 

The branching ratio F(Br / Br) with 4>a, and as the initial conditions are plotted in Fig. 6. At all energy values, F(Br / Br) is much larger in magnitude with as the initial condition compared to that with (j>Q or as the initial condition and F(Br / Br) is uniformly smaller with... 

The branching ratio for geometric dimensions (g,) was defined by Zimm and Stockmayer as... 

The product branching ratio / is defined as the quantity of each chemically distinguishable set of reaction products n compared to the quantity of all products. As an example, consider the hypothetical reaction... 

The ability to probe specific pathways using these statistical approaches relies completely on the geometric structures determined from the calculated stationary points of the PES. In other words, the knowledge that, for example, two particular stationary points represent a three- and four-member ring intermediate, respectively, allows one to calculate rates, and therefore pathway branching ratios through these channels. 

The kinetics study [38] utilized a Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometer to measure the pathway branching ratios. The ability to eject selected masses and the extremely high mass resolution of this technique ensured that the observed CD3CH2 was in fact a primary product of the reaction. Temporal profiles from this reaction are shown in Fig. 1. Noticeably absent from the mass spectrum are the cations C2D2H3 and... 

The measured [ OH]/[ OH] branching ratio versus inverse temperature is plotted in Fig. 4. If the two species are produced by two parallel pathways, the total reaction rate is a simple sum of the two pathway-resolved rates. In this case, the data points in an Arrhenius plot should fall on a straight line with a slope proportional to the difference in activation energies for the two competing pathways. A fit to the data in Fig. 4 yields the result that the barrier to O atom abstraction is 1.0 0.4kcal mol larger than for H atom abstraction. Although... 

Figure 4. The [ OH]/[ OH] branching ratios versus inverse temperature for the H 02 + reaction. Reprinted with permission from [41]. Copyright 1994 American Chemical Society.

For both statistical and dynamical pathway branching, trajectory calculations are an indispensable tool, providing qualitative insight into the mechanisms and quantitative predictions of the branching ratios. For systems beyond four or five atoms, direct dynamics calculations will continue to play the leading theoretical role. In any case, predictions of reaction mechanisms based on examinations of the potential energy surface and/or statistical calculations based on stationary point properties should be viewed with caution. 

The branching ratio will determine the value of w for either EtO... 

---