Environmentally-benign transition metal catalyst design using optimization techniques

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Abstract

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 efficacy and biological effects. This work applies an optimization approach to redesign environmentally-benign homogeneous catalysts, specifically those which contain transition metal centers, to improve certain physical properties. Two main tasks must be achieved in order to perform the molecular design of a novel catalyst: biological and chemical properties must be estimated directly from the molecular structure, and the resulting optimization problem must be solved in a reasonable time. In this work, connectivity indices are used for the first time to predict the physical properties of a homogeneous catalyst. The existence of multiple oxidation states for transition metals requires a reformulation of the original equations for these indices. Once connectivity index descriptors have been defined for transition metal catalysts, structure–property correlations are then developed based on regression analysis using literature data for various properties of interest, including toxicity and electronegativity. These structure–property correlations are then used within an optimization framework to design novel homogeneous catalyst structures for use in a given application. The use of connectivity indices which define the topology of the molecule within the formulation guarantees that a complete molecular structure is obtained when the global optimum is found. In this work, second-order connectivity indices are used to obtain more information about steric features of the catalyst molecules, and non-linear correlations are employed to improve the accuracy of the property prediction equations. The structure–property correlations are then combined with linear structural feasibility constraints to form a mixed-integer non-linear program (MINLP), which when solved to optimality results in a catalyst molecule which most closely matches given property targets. To solve the resulting optimization problem, two methods are applied: Tabu search (a stochastic method), and outer approximation, a deterministic approach. For the outer approximation solution, a data structure is used which permits all equations except for the property prediction expressions to be written in linear forms. The computational efficiency of Tabu search is not strongly dependent on the existence of non-linear constraints, so for solution using this method, a non-linear form for the second-order connectivity index was chosen, which decreases the number of binary variables required. The solution methods are compared using three examples involving the design of environmentally-benign homogeneous catalysts containing molybdenum centers. Results show the efficacy of the formulation, and provide evidence that the Tabu search algorithm is more suitable for this type of molecular design algorithm than the commercially available deterministic approach.

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:mins=m∈R1Pmscale|Pm−Pmtarget|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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