Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation

This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods. Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules. Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments. Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV. Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).

Probing unoccupied electronic states in aqueous solutions

Water is one of the most common compounds on earth and is essential for all biological activities. Water has, however, been a mystery for many years due to the large number of unusual chemical and physical properties, e.g. decreased volume during melting and maximum density at 4 °C. The origin of the anomalies behavior is the nature of the hydrogen bond. This thesis will presented an x-ray absorption spectroscopy (XAS) study to reveal the hydrogen bond structure in liquid water. The x-ray absorption process is faster than a femtosecond and thereby reflects the molecular orbital structure in a frozen geometry locally around the probed water molecules. The results indicate that the electronic structure of liquid water is significantly different from that of the solid and gaseous forms. The molecular arrangement in the first coordination shell of liquid water is actually very similar as the two-hydrogen-bonded configurations at the surface of ice. This discovery suggests that most molecules in liquid water have two-hydrogen-bonded configurations with one donor and one acceptor hydrogen bond compared to the four-hydrogen-bonded tetrahedral structure in ice. This result is controversial since the general picture is that the structure of liquid water is very similar to the structure of ice. The results are, however, consistent with x-ray and neutron diffraction data but reveals serious discrepancies with structures based on current molecular dynamics simulations. The two-hydrogen-bond configuration in liquid water is rigid and heating from 25 °C to 90 °C introduce a minor change in the hydrogen-bonded configurations. Furthermore, XAS studies of water in aqueous solutions show that ion hydration does not affect the hydrogen bond configuration of the bulk. Only water molecules in the close vicinity to the ions show changes in the hydrogen bond formation. XAS data obtained with fluorescence yield are sensitive enough to resolved electronic structure of water molecules in the first hydration sphere and to distinguish between different protonated species. Hence, XAS is a useful tool to provide insight into the local electronic structure of a hydrogen-bonded liquid and it is applied for the first time on water revealing unique information of high importance.