Preface to the 2nd edition

Abstract

The new edition of Mathematical Stereochemistry has been revised and rewritten by surveying recent advances during about 6 years after the publication of the first edition (2015). The most significant change is the addition of a new Chapter 13, which is entitled “Combined-Permutation Representations (CPRs) for GAP Calculation”. This chapter is concerned with the development of CPRs as computer-oriented representations of point groups, which enable us to treat reflection operations rationally in the GAP (Groups, Algorithms and Programming) system. This results in enhancing the applicability of Fujita’s proligand method, Fujita’s unit-subduced-cycle-index (USCI) approach, as well as Fujita’s stereoisogram approach. Soonafter thepublicationof thefirst edition, I hasdiscussed chirality (for supporting Le Bel’s way to stereochemistry) and RS-stereogenicity (for supporting van’t Hoff’s way to stereochemistry) from a viewpoint of two kinds of handedness (S. Fujita, “Chirality and RS-Stereogenicity as Two Kinds of Handedness. Their Aufheben by Fujita’s Stereoisogram Approach for Giving New Insights into Classification of Isomers”, Bull. Chem. Soc. Jpn., 89, 987–1017 (2016)). Experimental approaches (e.g., catalytic asymmetric synthesis by Ryoji Noyori (Nobel-Prize 2001)) have mainly relied on chirality, while approaches for nomenclature (e.g., the Cahn-Ingold-Prelog system by Vladimir Prelog (Nobel-Prize 1975) et al.) have mainly relied on stereogenicity proposed by Mislow et al. (not RS-stereogenicity). Fujita’s RS-stereogenicity is differentiated from Mislow’s stereogenicity by rational treatment of reflection operations to discuss the net interaction between chirality and stereogenicity, so that the RS-stereogenicity can be recognized as the second kind of handedness as compared with chirality as the first kind of handedness. Soon after the publication of the first edition, I have also reported an account article entitled “Half-Century Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics” (S. Fujita, Iranian J. Math. Chem., 7, 155–221 (2016)). This article has stated three phases of my career, which have been summarized by respective monographs: – Synthetic organic chemistry for investigating sterically-hinderedmolecules (that is to say, aziridines, heterophanes, and so on) and for developing sterically-enhanced dye-releasers of instant color photography (S. Fujita, “Organic Chemistry of Photography”, Springer-Verlag, Berlin-Heidelberg (2004) xix+587 pages). – Chemoinformatics for retrieval of organic reactions by means of imaginary transition structures (ITSs) as newly-developed representations (S. Fujita, “ComputerOriented Representation of Organic Reactions”, Yoshioka-Shoten, Kyoto (2001) x+371 pages). – Mathematical stereochemistry for Fujita’s USCI approach (S. Fujita, “Symmetry andCombinatorial Enumeration inChemistry”, Springer-Verlag, Berlin-Heidelberg (1991) x+368 pages; S. Fujita, “Diagrammatical Approach to Molecular Symmetry