Reactive space

The Reactivity Space, In many reaction types the situation is not as well defined as in the chemical reactions so far investigated. If either fewer and less accurate reactivity data are available, or the chemical system is under the influence of many effects, then MLRA is no longer the appropriate analytical method. 

For such situations we have developed a different approach. The parameters calculated by our methods are taken as coordinates in a space, the reactivity space, A bond of a molecule is represented in such a space as a specific point, having characteristic values for the parameters taken as coordinates. Figure 6 shows a three-dimensional reactivity space spanned by bond polarity, bond dissociation energy, and the value for the resonance effect as coordinates. 

Figure 6, Reactivity space having bond polarity, Q, bond dissociation energy, BDE, and resonance effect parameter, R, as coordinates ...

With Figure 6 a three-dimensional reactivity space is shown. Whereas this is the limit for pictorial representation, statistical methods can deal with spaces of higher dimensionalities. In a study aimed at modelling the reactivity of single bonds in aliphatic chemistry a data set of 28 molecules representing that field was chosen. Table II gives this data set. 

The entire set of molecules contained 782 bonds out of which 111 a-bonds were selected. The parameters were calculated by our methods to build a reactivity space with electronegativity difference, resonance effect parameter, bond polarizability, bond polarity, a-charge distribution, and bond dissociation energy as six coordinates. 

Linear hydrocarbon radicals have been the subject of intensive laboratory spectroscopic and radio-astronomical research since the early 1980s. In recent years, a considerable number of rotational spectroscopic studies of medium to longer hydrocarbon chains such as C5H, CeH, CgH, and ChH have been carried out using a pulsed molecular beam FTMW spectrometer. The high resolution offered by such a spectrometer allowed the detection of the hyperfine sphtting of rotational transitions. These measurements improved fine and hyperfine coupling constants and provided rest frequencies with accuracies better than 0.30 km s in equivalent radial velocity up to 50 GHz. Indeed, some of the small C H radicals with n < 9 have subsequently been detected in space, in molecular cloud cores, and in certain circumstellar shells. These hydrocarbon chains are among the most abundant reactive space molecules known. 

Gasteiger, J., Rdse, P. and Sailer, H. (1988). Multidimensional Explorations into Chemical Reactivity The Reactivity Space. J.MolGraphics, 6,87. 

The complicating situation with chemical reactions is that their reactivity is simultaneously influenced by many factors and it is so to various extents. To account for that dependence on many variables, the multidimensionality of chemical reactivity, we have taken the various chemical effects as co-ordinates of a space, the reactivity space. (Figure 10). 

Figure 10, A three-dimensioned reactivity space spanned by polarisability, a, and the differences in charge, Aq, and electronegativity, AX.

In Figure 11 various single bonds of acetaldol are shown in a reactivity space spanned by the polarity in the sigma electron distribution, the bond dissociation energy, BDE, and the resonance effect, R. 

As an additional feature, the bonds of aldol represented in the three-dimensional reactivity space of Figure 11 were marked according to their reactivity. Bonds that... 

Figure 11. Reactivity space representing the polar breaking of various bonds in acetaldol.

It can be seen that reactive and non-reactive bonds clearly separate. Non-reactive bonds are found in the lower and left parts and more to the front of this perspective of the 3-D reactivity space. Reactive bonds are moved more to upper regions, to the right, and further away from the observer. The clear separation of breakable and non-breakable bonds shows that the property that is under investigation, chemical reactivity, is well represented in this space. 

Figure 12. The reactivity space of Figure 11 containing additional points for bonds of the two ions derived from aldol and showing the representation of increases in reactivity.

Removal of a proton from carbon atom 4 of aldol was considered not easy (point) In the carbocation, however, this proton should be much more acidic as again the carbanion can be stabilised by the adjacent positive charge. Thus, this bond becomes reactive and the point representing this heterolysis is again shifted more to the right of the reactivity space. However, the product is a p,y-unsaturated carbonyl compound, which is not as stabilised as the a,p-isomer. This is reflected in the fact that point 12 is not as far to the right as point 11. 

To summarise, the three variables used in constructing the reactivity space of Figures 11 and 12 and quantified by our methods are very well-suited to the representation of the reactivity of aldol and the ions derived from it. In this space, bonds that are classified by a chemist as either reactive or non-reactive are clearly separated. Furthermore, the distance between points in such a space is of chemical significance. The more reactive a bond, the further the point representing the breaking of this bond will be from the plane of separation. 

Figures 10-12 have shown reactivity spaces with three dimensions. However, in general, reactivity spaces of higher dimensionality have to be considered as chemical reactivity might depend on more than three factors.

We haveemployed a variety of unsupervised and supervised pattern recognition methods such as principal component analysis, cluster analysis, k-nearest neighbour method, linear discriminant analysis, and logistic regression analysis, to study such reactivity spaces. We have published a more detailed description of these investigations. As a result of this, functions could be developed that use the values of the chemical effects calculated by the methods mentioned in this paper. These functions allow the calculation of the reactivity of each individual bond of a molecule. 

Fig. 4.4 Variation of NH3 and NO concentrations in the front half of the Fe-zeolite catalyst during SCR reactivity. Space velocity of entire catalyst is 30,000 h (GHSV) 200 ppm NO, 200 ppm NH3, 10 % O2, 5 % H2O, 325 °C...

---