Table Of Content661
Topics in Current Chemistry
retupmoC yrtsimehC
Editor: I. Ugi
With contributions by
K. Bley, .J Brunvoll, R. Carlson, .B N. Cyvin,
.S .J Cyvin, .B Gruber, E. Hladka, M. Knauer,
.J Koca, M. Kratochvil, .V Kvasnicka, L. Matyska,
A. Nordahl, .J Pospichal, .V Potucek, N. Stein, I. Ugi
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Berlin Heidelberg kroYweN
London Paris oykoT
Hong Kong Barcelona
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This series presents critical reviews of the present position and future trends
in modern chemical research. It is addressed to all research and industrial
chemists who wish to keep abreast of advances in their subject.
As a rule, contributions are specially commissioned. The editors and
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supplementary information. Papers are accepted for "Topics in Current
Chemistry" in English.
ISBN 3-540-55902-7 Springer-Verlag Berlin Heidelberg New York
ISBN 0-387-55902-7 Springer-Verlag New York Berlin Heidelberg
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Organisch-Chemisches Institut
Technische Universit~it Mfinchen
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Editorial Board
Prof. Dr. Michael J. S. Dewar Department of Chemistry, The University of Texas
Austin, TX 78712. USA
Pro Dr. Jack .D =tinuD Laboratorium fiir Organische Chemie der
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Blaise Pascal, .B P. Z 296/R8, F-67008 Strasbourg-Cedex
Prof. Dr. Kenneth N. Raymond Department of Chemistry, University of California,
Berkeley, California 94720, USA
ProL Dr. Charles .W Rees Hofmann Professor of Organic Chemistry, Department
of Chemistry, Imperial College of Science and Technology,
South Kensington, London SW7 2AY, England
Prof. Dr. Joachim meih"l" lnstitut for Organische Chemie, Universitfit Hamburg
Martin-Luther-King-Platz 6, 2000 Hamburg ,31 FRG
Prof. Dr. Fritz V6gtle Institat ffir Organische Chemie und Biochemie
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Preface
The considerable progress in chemistry made recently is due to the systematic
analysis, classification, generation and processing of chemical information. The
importance of abstract models, mathematical theories and computer-assistance
for chemistry is increasingly recognised.
Mathematics has entered chemistry via physics. Many quantitative mathematical
theories of chemistry, like quantum chemistry, are physical or physico-chemical
in nature. Such theories play an important role in the design and evaluation of
experiments, and they are used to compute numerical values of some observable
properties of well-defined molecular systems. The results that are obtained through
physics-based theories are indispensable to the indirect solution of a great variety
of chemical problems.
In chemometrics, quantitative mathematical methods are used in the direct solu-
tion of chemical problems without the intermediacy of physics. There are also direct
qualitative mathematical approaches to chemistry. More than a hundred years ago,
Cayley demonstrated the usefulness of graph theory for representing the chemical
constitution of molecules. The past decades have seen a vigorous renaissance of
chemical applications of graph theory. Balaban's and Harary's initiative played a
particularly important role in this resurgence. P61ya's group theoretical enumeration
of isomers was the beginning of the wide field of direct uses of group theory in
chemistry. The direct applications of graph theory and group theory are now the
essential contents of the rapidly expanding discipline of mathematical chemistry.
This discipline mainly deals with the static aspect of chemistry; it concentrates on the
description, classification and enumeration of individual static chemical objects.
About 20 years ago, the theory of the be- and r-matrices, a global algebraic
model of the logical structure of constitutional chemistry was formulated. This
theory is the first direct mathematical approach to chemistry which also accentuates
its dynamic aspect. The representation by mathematics comprises the individual
objects of chemistry and also their relations, including their interconvertibility by
chemical reactions. A decade later, the theory of the chemical identity groups was
published in a monograph. It is a unified theory of stereochemistry that is primarily
devoted to relations between molecular systems.
These two publications indicated the importance and feasibility of mathematical
approaches that describe the relations between molecular systems. They stimulated
the formulation of further mathematical models and theories of chemistry that
are of interest in their own right but are particularly useful for computer-assistance
in chemistry.
In general, the representation of chemical objects, facts and processes by
mathematics not only improves the interpretation of chemistry but often it also
forces chemists to express statements and definitions with greater precision and
to specify exactly the conditions and range of their validity. It is increasingly
recognised, that it is not only inevitable to use mathematical formalisms as
quantitative theories and as a basis of numerical computations, but also as a
foundation of computer programs for the qualitative solution of chemical problems
such as the design of syntheses. The answers to the latter type of problems are
molecules and chemical reactions.
When this kind of computer-assistance is mathematically-based and does not
rely on detailed empirical chemical information, it can reach beyond the horizon
of known chemistry, and the desirable solutions of given problems can be picked
from the wealth of conceivable results by formalized selection procedures without
the lottery of heuristic selection procedures. Appreciable advances in chemistry
can be expected from further combinations of new concepts and models with
mathematical formalisms and formal algorithms.
This issue of Topics in Current Chemistry contains four articles whose common
denominator is the computer-oriented'use of abstract concepts and mathematics
in chemistry. The present articles will, hopefully, not only spread information
about these types of endeavours but also stimulate some interest therein.
The contribution of Cyvin, Cyvin and Brunvoll on the enumeration of benzenoid
chemical isomers is the continuation of a series that began with two articles in
Volume 162 of this journal. These three articles constitute a definitive and
exhaustive treatment of the given topic.
Carlson and Nordahl present a comprehensive account on the screening and
optimization of organic syntheses by computer-assisted multivariate statistical
methods. This article is rather an introduction to a philosophy than the description
of a computer-assisted methodology. Thus it is particularly useful to those who
are trying to understand the principles of this increasingly important technique
to optimise syntheses.
In the past decade Kvasni6ka and his colleagues at Bratislava and Brno have
published a series of graph-theory-based contributions to mathematical chemistry.
The underlying concept is related to the algebra of be- and r-matrices. The present
paper describes the Synthon Model of organic chemistry and the corresponding
synthesis design program PEGAS. It is part of the aforementioned series.
The fourth paper in this volume is devoted to some extensions and generaliza-
tions of the algebra of the be- and r-matrices. The latter is only valid for the
chemistry of molecular systems that are representable by integer bond orders and
thus is not applicable to the great variety of molecules with multi-center bonds
and delocalized electron systems. This deficiency is overcome by the introduction
of the so-called extended be- and r-matrices the xbe- and xr-matrices. They contain
additional rows/columns which refer to the delocalized electron systems. Some
corresponding data structures are presented that also account for stereochemical
aspects.
Miinchen, October 1992 Ivar Ugi
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Table of Contents
Exploring Organic Synthetic Experimental Procedures
R. Carlson, A. Nordahl . . . . . . . . . . . . . . .
Enumeration of Benzenoid Chemical Isomers with a Study
of Constant-Isomer Series
.S J. Cyvin, B. N. Cyvin, J. Brunvoll . . . . . . . . . . 65
The Synthon Model and the Program PEGAS for Computer
Assisted Organic Synthesis
E. Hladka, J. Koca, M. Kratochvil, .V Kvasnicka,
L. Matyska, J. Pospichal, .V Potucek . . . . . . . . . . 121
New Elements in the Representation of the Logical
Structure of Chemistry by Qualitative Mathematical Models
and Corresponding Data Structures
K. Bley, B. Gruber, M. Knauer, N. Stein, I. Ugi ..... 199
Author Index Volumes 151-166 . . . . . . . . . . . . 235
gnirolpxE Organic citehtnyS
latnemirepxE serudecorP
Rolf Carlson and Ake Nordahl
Department of Organic Chemistry, Ume~i University, S-90187 Ume/t, Sweden
Table of Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Problem Area . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Optimization . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Theme and Variations . . . . . . . . . . . . . . . . . . . . 5
3 Methods for Exploring the Experimental Space . . . . . . . . . . . 7
3.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Two Common Problems: Screening and Optimization . . . . . . 10
3.3 Screening Experiments . . . . . . . . . . . . . . . . . . . . 11
3.3.1 Models for Screening . . . . . . . . . . . . . . . . . . 11
3.3.2 Two-Level Designs . . . . . . . . . . . . . . . . . . . 12
3.3.3 Identification of Significant Variables . . . . . . . . . . . 14
3.4 Examples: Factorial Design,
Fractional Factorial Design, D-Optimal Design . . . . . . . . . 15
3.4.1 Enamine Reduction, z 2 Factorial Design . . . . . . . . . 15
3.4.2 Catalytic Hydrogenation of Furan, 24 Factorial Design 17
3.4.3 Significant Variables in a Willgerodt-Kindler Reaction,
25-1 Fractional Factorial Design . . . . . . . . . . . . . 19
3.4.4 Enamine Synthesis over Molecular Sieves, D-Optimal Design 20
3.5 Optimization . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5.1 Response Surface Techniques . . . . . . . . . . . . . . 23
3.5.2 Central Composite Designs . . . . . . . . . . . . . . . 24
3.5.3 A Sequential Approach is Possible . . . . . . . . . . . . 25
3.6 Example: Modified TiCI4 Method for Enamine Synthesis ..... 25
3.7 Canonical Analysis of Response Surface Models . . . . . . . . . 27
3.7.1 Example: Synthesis of 2-Trimethylsilyloxy-l,3-Butadiene.
Exploration of a Ridge System by Canonical Analysis .... 30
Topics in Current Chemistry, Vol. 661
© Springer-Verlag Berlin Heidelberg 1993
Rolf Carlson and Ake Nordahl
4 Methods for Exploring the Reaction Space . . . . . . . . . . . . . 32
4.1 The Reaction Space . . . . . . . . . . . . . . . . . . . . . 32
4.2 Principal Properties . . . . . . . . . . . . . . . . . . . . . 33
4.3 Principal Component Analysis, PCA . . . . . . . . . . . . . . 34
4.3.1 Geometrical Description of PCA . . . . . . . . . . . . . 35
4.3.2 Mathematical Description of PCA . . . . . . . . . . . . 37
4.4 Principal Properties and Organic Synthesis . . . . . . . . . . . 39
4.4.1 Example: Screening of Lewis Acid Catalysts in Synthetic
Procedures . . . . . . . . . . . . . . . . . . . . . . 40
4.5 Classes of Compounds . . . . . . . . . . . . . . . . . . . . 42
4.5.1 Organic Solvents . . . . . . . . . . . . . . . . . . . . 43
4.5.2 Lewis Acids . . . . . . . . . . . . . . . . . . . . . . 43
4.5.3 Aldehydes and Ketones . . . . . . . . . . . . . . . . . 43
4.5.4 Amines . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5.5 Other Examples of the Use of Principal Properties ..... 44
4.6 Strategies for Selection . . . . . . . . . . . . . . . . . . . . 44
4.6.1 Use a Maximum Spread Design . . . . . . . . . . . . . 44
4.6.2 Explore the Vicinity of a Promising Candidate . . . . . . . 44
4.6.3 Use a Uniform Spread Design . . . . . . . . . . . . . . 45
4.6.4 Use a Statistical Design to Explore Several
Dimensions of the Reaction Space . . . . . . . . . . . . . . 45
4.7 Example: Fractional Factorial Design for Exploring the
Reaction Space . . . . . . . . . . . . . . . . . . . . . . . 45
5 Quantitative Relations Between the Response Space, the Experimental
Space, dna the Reaction Space . . . . . . . . . . . . . . . . . . 48
1.5 Evaluation of Multiresponse Screening Experiments . . . . . . . 48
5.1.1 Example: Evaluation of a Screening Experiment
for the Synthesis of Pyridines . . . . . . . . . . . . . . 49
5.2 PLS: Projections to Latent Structures . . . . . . . . . . . . . 52
5.2.1 Basic Principles of PLS . . . . . . . . . . . . . . . . . 52
5.2.2 Geometrical Description of PLS . . . . . . . . . . . . . 52
5.2.3 Mathematical Description of PLS . . . . . . . . . . . . 53
5.3 Examples of the Use of PLS Modelling in Synthesis . . . . . . . 53
5.3.1 Prediction of Optimum Conditions for New Substrates
in the Willgerodt-Kindler Reaction . . . . . . . . . . . . 54
5.3.2 Factors Controlling the Regioselectivity in the
Fischer Indole Synthesis . . . . . . . . . . . . . . . . 55
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 Appendix: Computer Programs . . . . . . . . . . . . . . . . . . 60
8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
