Numerical methods for the computation of mutli-component decompositions with spectroscopic applications

• Applicant: Professor Dr. Klaus Neymeyr
• Subject Area: Technical Chemistry ; Mathematics
• Term: from 2012 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 214012032

The spectroscopic observation of chemical reactions with high frequency resolution and a large number of spectra results in a high volume of data. These spectral data contain the superposed contributions from the pure components. Factor analytic methods of chemometrics allow to extract from these data the number of underlying pure components, their spectra and the associated concentration profiles. New mathematical techniques and new numerical solution methods for the factor analysis of multicomponent systems are under development in the current funding period of the project. Whereas the so-called self-modeling factor analytic methods in chemometrics generally suggest only a single feasible pure component decomposition, our new systematic approach allows to compute the full set of all feasible solutions. Further methods have been developed in order to identify the correct pure component factorization for instance by coupling with a kinetic model of the reaction or by the new complementarity theory. The fast and stable numerical solvers have been published in the FAC-PACK software. Our work primarily aims at the development of chemometric methods but is also accompanied by a close cooperation with the Leibniz-Institute for Catalysis e.V. in Rostock. Spectroscopic data for various chemical reaction systems with the focus on transition metal catalyzed carbonylation reactions have been used for the validation of the numerical methods. Significant progress has been made for in-situ FT-IR studies on reaction systems of homogeneous catalysis.

• DFG Programme: Research Grants