Determination of the Quantitative Composition of Mixtures of Substances and Chemical Reaction Products by Multidimensional Spectroscopy

We consider general questions arising in formulation of the problem of determining the quantitative composition of mixtures of substances and chemical reaction products as a function of time, using multidimensional spectroscopy data. We have analyzed the basic variants of the problem of quantitative standardless spectral analysis that are of practical importance, and propose algorithms for their solution. We show that the solution of the problem over the entire time interval is robust with respect to possible uncertainties in specifying the initial spectral data. The result obtained is quite satisfactory even when quantum beats are not only present but can even be observed. This allows us, based on the spectral data, to obtain a complete picture of the course of the chemical reaction and to determine the probability of chemical interconversions. The proposed algorithm allows us to construct time-dependent multidimensional surfaces of histograms showing the distribution of the concentrations found. The performance of the algorithms has been studied using computer experiments.