Chemical Reaction Networks

A Graph-Theoretical Approach

Oleg N. Temkin, Andrew V. Zeigarnik, D.G. Bonchev

• Publisher: CRC Press
• Year: 2020
• eBook ISBN:
  9781000141160
• Topic: Physical Sciences
• Subtopic: Discrete Mathematics

Over the last decade, increased attention to reaction dynamics, combined with the intensive application of computers in chemical studies, mathematical modeling of chemical processes, and mechanistic studies has brought graph theory to the forefront of research. It offers an advanced and powerful formalism for the description of chemical reactions and their intrinsic reaction mechanisms. Chemical Reaction Networks: A Graph-Theoretical Approach elegantly reviews and expands upon graph theory as applied to mechanistic theory, chemical kinetics, and catalysis. The authors explore various graph-theoretical approaches to canonical representation, numbering, and coding of elementary steps and chemical reaction mechanisms, the analysis of their topological structure, the complexity estimation, and classification of reaction mechanisms. They discuss topologically distinctive features of multiroute catalytic and noncatalytic and chain reactions involving metal complexes. With it's careful balance of clear language and mathematical rigor, the presentation of the authors' significant original work, and emphasis on practical applications and examples, Chemical Reaction Networks: A Graph Theoretical Approach is both an outstanding reference and valuable tool for chemical research.

Chapter 1

Graph Theory Assistance in Studies of Elementary Steps of Complex Reactions

Currently, numerous chemical reactions are widely believed to occur via several consecutive elementary reactions. This set of elementary reactions is usually called a reaction mechanism, or a mechanistic scheme. The study of reaction mechanism allows one to look inside a complex reaction and to predict its behavior under various conditions. Elementary reactions that are building blocks of a mechanism are usually the subject of special interest. Researchers involved in mechanistic studies carefully collect their experimental data to gain evidence for or to discard their conjectures related to elementary reactions. Proceeding along this avenue, in most cases, they intuitively use several paradigms related to chemical changes that can take place during one or another elementary reaction. The basis for these paradigms is analogies, heuristics, and generalizations. Among the latter are those that have a fundamental basis (e.g., the conservation of orbital symmetry, which is currently generally accepted). Others can stem from researcher’s experience. In all cases such paradigms cannot be completely proved, although substantial evidence can exist. Many recent efforts of mathematical chemists were directed toward the search for new reaction rules and hidden principles of chemical reactions. The goal of this chapter is to show what has been achieved.

1.1. The Concept of an Elementary Step

An elementary reaction is defined as follows: elementary reaction is a repeated reproduction of a unit act that involve transformation of some (in most cases, two) species at the instant they collide or the transformation of a single species. An elementary reaction is assumed to pass through a single transition state. No intermediates can be detected in the elementary reaction.¹

Several additional ideas are associated with an elementary reaction. Thus, elementary reactions are usually termed concerted in order to highlight that forming or breaking of chemical bonds occurs via a single step. Sometimes a reaction is said to be synchronous. This term is often used as a synonym of concerted. However, these are not synonyms. According to Dewar,² a synchronous reaction is that in which all bond changes “take place in unison, having all proceeded to comparable extents in the transition states.” An elementary reaction is usually suggested to have a certain direction; that is, the reverse reaction is assumed to be a separate process.

To determine whether a reaction is elementary or not, comprehensive studies are needed. However, sometimes a researcher can determine with a fair degree of certainty that a reaction is not elementary. What drives his reasoning? Analogies, intuition, and background knowledge. Heuristics and various reaction principles also play an important role. Sometimes new reaction principles can be discovered using the results of combinatorial analysis of reactions and the information stored in reaction databases. The typical scheme of this study is shown in Figure 1.1. As can be seen, there are two key steps in this study: combinatorial enumeration and generalization of reactions. These two steps are parts of a broader process called classification.

As was mentioned by Bawden, “There are a number of clearly understood benefits of classification… They are involved in four distinct, though interrelated, processes. The first is ‘straightforward’ retrieval of information [in information systems]. The second is less-well-understood processes of information discovery, through analysis, correlation, and reasoning by analogy. The third is teaching and exposition of the variety and scope of chemical reactions. The fourth is the systematization of chemical reaction information…”³ Our primary interest here lies within this less-well-...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Preface
• Table of Contents
• Introduction
• 1 Graph Theory Assistance in Studies of Elementary Steps of Complex Reactions
• 2 Reaction Mechanisms and Networks
• 3 Classification of Reaction Mechanisms Based on Bipartite Graphs
• 4 Complexity of Reaction Mechanisms
• 5 Topological Structure of a Mechanism and Its Kinetic Analysis
• Subject Index