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Chapter 3 introduces the important but obscure topic of enumerating molecules. Enumeration means two things: first to list things separately, one by one and second to determine the number of, or to count things; both aspects of enumeration in chemistry are described by these authors. The foremost application of enumeration is in structure determination. But for other applications such as in molecular design, especially with the advent of combinatorial technologies, enumeration also takes a central role for constructing virtual libraries, testing hypotheses, and for optimization of experiments. The authors begin by describing how enumeration is accomplished. Graph theory and algorithms that rely on it are introduced. The counting of labeled and unlabeled graphs, with particular attention to Polya's theorem, show the reader how to determine the number of isomers given a molecular formula. The number of isomers of acyclic compounds (including the possible number of stereoisomers), the number of benzenoids and the number of molecular cages (fullerenes and nanotubes) are examples provided by the authors. Elementary definitions used to count, enumerate and sample molecules are presented, replete with simple examples for the novice to study. In the second part of the chapter the authors review the practical applications of molecular enumeration and give the reader pointers to relevant techniques and existing codes. In particular, the number of isomers for a specific molecular series is given, popular structure elucidation codes are reviewed, computer-aided structure-elucidation successes are surveyed, and the connections between structure enumeration and combinatorial library design are established.

@Article{faulon05enumerating, author = {Faulon, Jean-Loup and Visco Jr, Donald P and Roe, Diana}, title = {Enumerating molecules}, journal = {Reviews in Computational Chemistry}, year = {2005}, volume = {21}, chapter = {3}, pages = {209--286}, abstract = {Chapter 3 introduces the important but obscure topic of enumerating molecules. Enumeration means two things: first to list things separately, one by one and second to determine the number of, or to count things; both aspects of enumeration in chemistry are described by these authors. The foremost application of enumeration is in structure determination. But for other applications such as in molecular design, especially with the advent of combinatorial technologies, enumeration also takes a central role for constructing virtual libraries, testing hypotheses, and for optimization of experiments. The authors begin by describing how enumeration is accomplished. Graph theory and algorithms that rely on it are introduced. The counting of labeled and unlabeled graphs, with particular attention to Polya's theorem, show the reader how to determine the number of isomers given a molecular formula. The number of isomers of acyclic compounds (including the possible number of stereoisomers), the number of benzenoids and the number of molecular cages (fullerenes and nanotubes) are examples provided by the authors. Elementary definitions used to count, enumerate and sample molecules are presented, replete with simple examples for the novice to study. In the second part of the chapter the authors review the practical applications of molecular enumeration and give the reader pointers to relevant techniques and existing codes. In particular, the number of isomers for a specific molecular series is given, popular structure elucidation codes are reviewed, computer-aided structure-elucidation successes are surveyed, and the connections between structure enumeration and combinatorial library design are established.}, doi = {10.1002/0471720895.ch3}, owner = {Sebastian}, publisher = {Wiley Online Library}, timestamp = {2019.02.07}, }

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