Preface -- Contents -- List of figures -- List of tables -- List of symbols -- Introduction and outline -- 1 Basics of graphs and molecular graphs -- 1.1 Graphs -- 1.1.1 Labeled graphs -- 1.1.2 Unlabeled graphs -- 1.2 Molecular graphs, constitutional isomers -- 1.2.1 Atom states in organic chemistry -- 1.2.2 Constitutional isomers -- 1.2.3 The existence of molecular graphs -- 1.3 Group actions on molecular graphs -- 1.3.1 Counting unlabeled structures -- 1.3.2 Counting by weight -- 1.3.3 Constructive methods -- 1.3.4 Generating samples -- 2 Advanced properties of molecular graphs -- 2.1 Substructures -- 2.1.1 Graph-theoretical elements -- 2.1.2 Subgraphs and their embeddings -- 2.2 Molecular substructures -- 2.2.1 Ambiguous molecular graphs -- 2.2.2 Substructure restrictions -- 2.3 Chemical reactions -- 2.4 Mesomerism -- 2.5 Existing chemical compounds -- 2.6 Molecular descriptors -- 2.6.1 Arithmetical descriptors -- 2.6.2 Topological descriptors -- 2.6.3 Geometrical descriptors -- 3 Chirality -- 3.1 Orientation and chirality -- 3.1.1 Barycentric placement of molecules in space -- 3.1.2 Symmetry operations, the point group -- 3.1.3 Chirality and handedness -- 3.2 Permutational isomers -- 3.2.1 Counting permutational isomers -- 3.2.2 Permutational isomers by content -- 3.2.3 Enumeration by symmetry -- 3.2.4 Constructive aspects -- 4 Stereoisomers -- 4.1 Basic stereochemistry -- 4.1.1 Symmetry, the orientational automorphism group -- 4.1.2 Partial orientation functions (POFs) -- 4.1.3 Generation of abstract POFs -- 4.1.4 Tests for chemical realizability -- 4.2 Radon partitions -- 4.3 Binary Grassmann-Plücker relations -- 4.4 Chemical conformation and cyclohexane -- 4.5 Perspectives -- 5 Molecular structure generation -- 5.1 Formula-based structure generation -- 5.1.1 Orderly generation of simple graphs -- 5.1.2 Introducing constraints.

5.1.3 Variations and refinements -- 5.1.4 From simple graphs to multigraphs -- 5.1.5 Applying the Homomorphism Principle -- 5.1.6 Orderly generation -- 5.1.7 Beyond orderly generation -- 5.2 Constrained generation and fuzzy formulas -- 5.2.1 Restrictions for a molecular formula -- 5.2.2 Structural restrictions -- 5.3 Reaction-based structure generation -- 5.3.1 Libraries of permutational isomers -- 5.3.2 Attaching substituents to a central molecule -- 5.3.3 Generation using the network principle -- 5.3.4 Generation of MS fragments -- 5.3.5 Construction using the network principle -- 5.3.6 Combinatorial libraries -- 5.3.7 Ugi's seven component reaction -- 5.4 Generic structural formulas -- 5.4.1 A simple generic structural formula -- 5.4.2 Patents in chemistry -- 5.5 Canonizing molecular graphs -- 5.5.1 Initial classification -- 5.5.2 Iterative refinement -- 5.5.3 Labeling by backtracking -- 5.5.4 Pruning the backtrack tree -- 5.5.5 Profiting from symmetry -- 5.6 Data structures for molecular graphs -- 6 Supervised statistical learning -- 6.1 Variables and predicting functions -- 6.1.1 Regression and classification -- 6.1.2 Validation of the predicting function -- 6.1.3 Preprocessing of data -- 6.1.4 Selection of variables -- 6.2 Models for predicting functions -- 6.2.1 Linear models -- 6.2.2 Neural networks -- 6.2.3 Support vector machines -- 6.2.4 Decision trees -- 6.2.5 Nearest neighbors -- 7 Quantitative structure-property relationships -- 7.1 Optimization of experiments in combinatorial chemistry -- 7.2 The use of molecular descriptors -- 7.2.1 Arithmetical, topological, and geometrical descriptors -- 7.2.2 Substructure counts -- 7.3 Mathematical composition of QSPRs -- 7.4 Case studies of QSPRs obtained by linear modeling -- 7.4.1 Linear modeling using topological indices -- 7.4.2 Linear modeling using substructure counts.

7.4.3 Linear modeling using TI and SC -- 7.4.4 Further descriptors and regression methods -- 7.4.5 Prediction -- 7.5 Case studies with separate learning and test sets -- 7.5.1 Preprocessing of structures -- 7.5.2 Choice of descriptors -- 7.5.3 Linear modeling by best subset selection -- 7.5.4 Linear modeling by stepwise subset selection -- 7.5.5 Linear modeling using principal component regression -- 7.6 A case study of QSARs with discrete values -- 7.6.1 Choice and redundancy of descriptors -- 7.6.2 Regression -- 7.6.3 Multi-classification -- 7.6.4 Binary classification -- 7.6.5 Prediction -- 7.7 Outlook: Unsupervised learning and diversity considerations -- 8 Molecular structure elucidation -- 8.1 Spectroscopic methods -- 8.2 Automated molecular structure elucidation -- 8.3 Basics of mass spectrometry -- 8.3.1 Mode of operation of an EI mass spectrometer -- 8.3.2 Problems in EI mass spectrometry -- 8.3.3 Mass spectra and isotope distributions -- 8.3.4 Database of elucidated mass spectra -- 8.4 Ranking functions for mass spectra -- 8.4.1 Ranking of molecular formulas -- 8.4.2 Ranking of structural formulas -- 8.5 Classification of mass spectra -- 8.5.1 MS descriptors -- 8.5.2 MS classifiers -- 8.5.3 Search for substructures amenable to MS classification -- 8.6 Automated structure elucidation via MS -- 8.6.1 Example methyl n-pentanoate -- 8.6.2 Example ethyl 3-hydroxyphenylacetate -- 8.7 High resolution MS -- 8.7.1 Exact isotope masses -- 8.7.2 Molecular formulas of identical exact mass -- 8.7.3 Mass differences between molecular formulas -- 8.7.4 Molecular formulas from exact molecular masses -- 8.8 High resolution MS/MS -- 8.8.1 Generating molecular formulas -- 8.8.2 Calculating MS match values -- 8.8.3 Calculating MS/MS match values -- 8.8.4 Verifying MS/MS match values experimentally -- 8.8.5 Scope, limitations and outlook for HR-MS.

9 Case studies of CASE -- 9.1 CASE with MOLGEN-MS -- 9.1.1 Example for a single spectrum -- 9.1.2 Multiple spectra -- 9.2 Calculated properties to improve CASE -- 9.2.1 Mass spectrum prediction -- 9.2.2 Retention properties -- 9.2.3 Partitioning properties -- 9.2.4 Steric energy -- 9.2.5 Filtering candidates by calculated properties -- 9.2.6 Consensus scoring -- 9.3 Examples of CASE at work -- 9.3.1 Blue rayon unknown 1 -- 9.3.2 Blue rayon unknown 2 -- 9.3.3 Diclofenac transformation product -- 9.4 CASE conclusions and outlook -- 9.4.1 GC-EI-MS -- 9.4.2 CASE with high accuracy data -- A Lists of molecular descriptors -- A.1 Arithmetical descriptors -- A.2 Topological descriptors -- A.3 Geometrical descriptors -- B Substructures for MS classifiers -- B.1 Alkyls -- B.2 Aromatics -- B.3 Bonds -- B.4 Elements -- B.5 Functional groups -- B.6 Rings -- C Molecular formulas by mass and ion type -- D Isomers by mass and molecular formula -- Bibliography -- List of abbreviations -- Index.