Mathematical chemistry and chemoinformatics. Structure generation, elucidation and quantitative structure. Property relationships (Q2869805)

We are fairly used by now to the fact that mathematics has arrived at various disciplines of natural science, as a means to describe, construct and classify relevant structures, taking into account quantitative as well as qualitative aspects. The advent of the computers has opened up the possibility to put theory into practice, thereby in turn exerting a stimulating effect on shaping theory.NEWLINENEWLINEThe book presented here is about all aspects of computer handling molecular structures in chemistry, in particular organic chemistry, such as generation, description, classification, reactions, quantitative properties, comparison with reality in connection with mass spectrometry, data libraries and software applications. It supplies the theoretical background for using software packages such as MOLGEN and provides a guideline for its usage by going through applications and examples at each stage.NEWLINENEWLINEA chemical compound is represented by a graph, the chemical elements (atoms) being the nodes (vertices) and the bonds being the edges, together with additional information on the molecule such as atom states (valence number, free electron pairs, charge, and impaired electrons) and bond multiplicities, all neatly stacked in a mathematical object suitable to be manipulated by a computer. To disregard unnecessary labeling, symmetries and placement in space, the introduction of equivalence relations and group actions is unavoidable. Chemical reactions are described within the framework of the molecular models. The notion of chirality deals with the question of whether a molecule is equivalent to its mirror image, important because both can have completely different effects if administered as medication. For treating stereoisomers, partial orientation functions and chirotopes are introduced, based on the mathematical concept of oriented matroid. Two approaches to creating and classifying molecular structures are discussed, leading to applications in the context of combinatorial and patent libraries. A section headed ``Supervised statistical learning'' attacks the connection between structures of organic compounds and their observed physicochemical, biological and pharmaceutical properties both ways, i.e., predicting properties and deriving structures. Statistics enter when predicting (= fitting) functions are constructed and used. These methods come into play in studying quantitative structure-property relationships, the necessary coarsening of the information on a molecular structure is taken care of by molecular descriptors. Mass spectrometry lends itself as a prominent source to derive structure formulae best fitting to experimental data. Finally, several case studies of computer aided structure elucidation, based on mass spectrometry and with the help of the MOLGEN software, are worked through.NEWLINENEWLINEThis book is a milestone in that it presents the results of a project, in the center of interest and pursued over decades, starting with the basics of the theory and extending all the way to applications in the real world. It should also be mentioned that mathematics is not overemphesized, a feature facilitating access for non-mathematicians.