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

化学反应的高频率分辨率和大量光谱的光谱观测产生了大量的数据。这些光谱数据包含来自纯成分的叠加贡献。化学计量学的因子分析方法允许从这些数据中提取潜在纯成分的数量、它们的光谱和相关的浓度分布。在该项目目前的资助期内，正在开发用于多组分系统因素分析的新的数学技术和新的数值解方法。化学计量学中所谓的自建模因子分析方法通常只建议单一可行的纯成分分解，而我们新的系统方法允许计算所有可行解的全集。为了确定正确的纯组分因式分解，已经开发了更多的方法，例如通过与反应的动力学模型耦合或通过新的互补理论。已在FAC-PACK软件中发布了快速稳定的数值求解器。我们的工作主要是开发化学计量学方法，但也伴随着与位于罗斯托克的莱布尼茨催化研究所的密切合作。不同化学反应体系的光谱数据被用来验证数值方法的有效性。均相催化反应体系的原位傅里叶变换红外光谱研究已取得重大进展。

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.