Catalysis of Organic..

306 Catalyst Library Designd−(b 0+ b 1 α ⋅α)−(eα )α= e(1)Similar function can also be applied for the selectivity as well. In these formulas the b 0and b 1 parameters can be determined if two corresponding d and α values areavailable. These values are usually arbitrary selected by the researcher. d can havevalues only between 0 and 1. Obviously, the higher the value of d the better thecatalyst performance. For example, the acceptable d value (0.4) in a selectivehydrogenation can be adjusted to 60 % of conversion, whereas the excellent d value(0.9) belongs to 80 % conversion. This selection always depends on the type ofreaction investigated and the researcher itself. The combined desirability function (D)is obtained by the determination of the geometrical average of d values calculated forconversion and selectivity:D = dα ⋅d s(2)It has to be emphasized that D can get good value only if none of the component dvalues are small.Variables and their Levels in a Simple Optimization TaskOne of the simplest optimization tasks is aimed to select the proper catalystcombination and the corresponding process parameters. In this case the main task is tocreate a proper experimental space with appropriate variable levels as shown in Table1. This experimental space has 6250 potential experimental points (N) (N = 2 x 5 5 =6250). This approach has been used for the selection of catalysts for ringhydrogenation of bi-substituted benzene derivatives. The decrease of the number ofvariable levels from 5 to 4 would result in significant decrease in the value of N (N= 2x 4 5 = 2048).Input Data for Catalyst Library DesignThe first step in the library design is the definition of the key metal or the combinationof key metals involved in the hydrogenation of the given functional group. The secondstep is the selection of the support, what is followed by choosing modifiers. Both theactive site and the support can be modified. In both types of modifiers thedetermination of their proper concentration levels is the most important task. Ingeneral, the modification of active sites requires less amount of modifier than that ofthe support. The modifiers can be added to the catalyst during its preparation or duringthe catalytic reaction ("compositional" and "process" modifiers, respectively).In the selection of modifiers the key issues are as follows:(i) which functional group has to be hydrogenated, (ii) what group has to bepreserved, and (iii) what type of undesired side reactions should be suppressed. Inselective hydrogenation the following differentiation was done between componentsused to prepare multi-component catalysts:(i) active metals, (ii) modifiers of the active metals, (iii) modifiers of the support,and (iv) selective poisons. The list of modifiers used in different hydrogenation orrelated reactions are given in Table 2.