Environmentally-benign transition metal catalyst design using optimization techniques
Section snippets
Scope and significance
Transition metal catalysts play a crucial role in many industrial applications, including the manufacture of lubricants, smoke suppressants, corrosion inhibitors and pigments. The development of novel catalysts is commonly performed using a trial-and-error approach which is costly and time-consuming. The application of computer-aided molecular design (CAMD) to this problem has the potential to greatly decrease the time and effort required to improve current catalytic materials in terms of their
Background
This work employs connectivity indices, which are numerical values which describe the electronic structure of a molecule, to characterize the molecule and to correlate its internal structure with physical properties of interest. Kier and Hall (1976) report correlations between connectivity indices and many key properties of organic compounds, such as density, solubility, and toxicity. The correlations to compute the physical properties are then combined with structural constraints and
Property prediction via connectivity indices
The basis for many computational property estimation algorithms is a decomposition of a molecule into smaller units. Topological indices are defined over a set of basic groups, where a basic group is defined as a single non-hydrogen atom in a given valency state bonded to some number of hydrogen atoms. Table 1 gives the basic groups used in this work, along with the atomic connectivity indices for each type of group. In this table, the δ values are the simple atomic connectivity indices for
Correlation of connectivity indices with physical property values
Molecular connectivity indices have been chosen as descriptors in this work based on previous examples of successful property predictions based on these general values. Bicerano (1996) has provided a set of correlations applicable for a wide range of polymers which predict a large number of physical and chemical properties to a very high degree of accuracy. While that work uses correction terms to generate more accurate correlations, the correlations generated here are intended to be used
Problem formulation
The optimization problem which determines the best molecule for a given application uses an objective function s which minimizes the difference between the target property values and the estimated values of the candidate molecule. This can be written as:where R is the set of all targeted properties, Pm the estimated value of property m, Pmscale a scale factor used to weight the importance of one property relative to another, and Pmtarget the target value for
Solution methods
In this work, two solution methods have been evaluated for the solution of the final MINLP: the deterministic method known as outer approximation, which was implemented through the GAMS interface by calling the commercial solver DICOPT (Duran & Grossmann, 1986), and the stochastic algorithm Tabu search (Glover, 1986, Glover & Laguna, 1997). While outer approximation guarantees that the global optimum will be found within a finite number of steps for a convex MINLP, the formulation as listed
Examples
The first example is a test to ensure that the formulation as written does find a known target catalyst molecule for an epoxidation reaction. A smaller set of four basic group types was used (di- and tetravalent molybdenum, chloride, and divalent oxygen, listed in Table 1), and the maximum number of groups allowed in the molecule was 10. The properties of molybdenum dichloride were computed from its connectivity indices using the correlations given above for density, toxicity and
Conclusions
This work has focused on the use of optimization techniques within a molecular design application to derive novel catalyst structures. The use of connectivity indices to relate internal molecular structure to physical properties of interest provides an efficient way to both estimate property values and recover a complete description of the new molecule after an optimization problem is solved. The use of molecular connectivity indices to generate structure–property correlations was extended to
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