Identification of Important Experimental Variables in Organic Synthetic Procedures by Near-Orthogonal Experiments

Abstract

A new strategy is presented for the design of screening experiments in synthetic chemistry when the objective is to identify the important experimental variables from a limited number of experimental runs. The methodology is based on Taylor expansion (response surface) models The experimental design is constructed in such a way that the vector of the variables in the Taylor model in each run are near-orthogonal to each other. This is achieved by laying out a grid of possible experiments in the experimental space, expanding this candidate experimental design matrix to the corresponding model matrix, i.e. the matrix containing columns for all variables in the Taylor expansion. This model matrix is then factorised by singular value decomposition, SVD. The row in the model matrix that is most parallel to the first singular vectors is selected as the first experiment. .The variation displaced by this first experiment is removed from the elements of the model matrix by projections. The resulting matrix is the orthogonal complement to the first selected row. The procedure is repeated until all dimensions of the model space have been spanned by the selected experiments The singular vectors are mutually orthogonal, and selected experiments will be nearly orthogonal and span the dimensions of the model space. The experiments can be run in sequence and thus allow for a systematic search, one experiment at a time. It is shown that subset selections from such designs in combination with PLS modelling can be used to identify the important variables. The principles are illustrated with two examples: (a) a dibromination of an acetyl with four experimental variables and (b) a synthesis of an enamine by condensing a ketone and morpholine in the presence of molecular sieves in which seven experimental variables are involved. In the acetal bromination, it was found that 5 experiments out of 12 were sufficient for identifying the most important variables. In the enamine example, 8 experiments out of 30 were sufficient.