A Toy Model of Chemical Reaction Networks - TBI - UniversitÃ¤t Wien

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34 CHAPTER 3. MOLECULES with increasing bond order) vanish because their overlap integrals are zero. Thus ∆E = ∑ ( G ab + q(a)q(b) ) − F ab;ab − ∑ F ab;a ɛr ′ b ′ (3.19) ab (a,b) (a,b)̸=(a ′ ,b ′ ) where the sums run only over newly formed bonds (a, b). The same formalism can be applied to intra-molecular reactions by setting A = B; in eq. 3.18 we then retain only one of the two double sums (which become identical in this case). The reactivity ∆E allows us to model regioselectivity. If more than one subgraph isomorphism, i.e. more than one possible reaction channel, has been found one simply has to evaluate ∆E for all of them. Then the rewrite with the smallest ∆E value is chosen. Eq. 3.16 has three terms which allow to classify reactions in three groups [38, 67, ch. 2 resp. ch. 15]. The first term is mainly constant and depends mostly on the steric configuration during a reaction. The second term is most important for polar reactants, in charge controlled reactions. The third term will dominate for non-polar reactants, in orbital controlled reactions. FMO theory only considers the last term. Although its numerical contribution is small, this approach is justified by the fact that the shapes of the HOMO and LUMO resemble to the total electron density important for the reactivity. Keeping in mind that MOs do not exist in reality, they are still constructs of MO thoery useful for explaining energy differences between “real” electronic states. The situation can be simplified further by considering only the frontier orbitals [46], i.e. the HOMO of one system and the LUMO of the other one. In this case the sums in eq. 3.18 reduce to a single term. Often this is approximated by ∆E ‡ = ξ/(E ζ −E α ) with an empirical constant ξ that depends only on the reaction mechanism [38]. The reaction rate and activation energy are related by Arrhenius’ law ∆E ‡ = RT ln k . The regioselectivity is determined by the MO coefficients at the reactive sites, such that ∑ i C HOMO,i C LUMO,i is maximal. This simplification was used for generating the two examples in chapter 6, figs. 6.1 and 6.2.
Chapter 4 Chemical reactions A molecule is composed of atoms that are tied together by aid of the electrons. Atomic nuclei and electrons are not at rest but are constantly moving. The paths of the electrons are usually called orbitals. The forms of these orbitals are determining the bonds between the atoms. In a reaction molecules are impinging against each other. During the collision the electrons are influenced by new atomic nuclei and the orbitals are changed. Some of the bonds are broken and others are created. Afterwards, new molecules have been formed. The Nobel Prize in Chemistry 1981. Presentation Speech by Professor Inga Fischer-Hjalmars of the Swedish Royal Academy of Sciences 4.1 Graph rewriting This section summarizes the work of Dörr [29] and [37] and explains how it can be applied to the problem of implementing chemical reactions. As we represented molecules as graphs, it is natural to simulate the set of reactions by generic reactions (see sect. 2.2) in the framework of a graph grammar [82, 97]. A graph grammar is a finite set of rules operating on edge and vertex labeled graphs. The term “graph grammar” is rather used for graph-generating applications. In our context, the similar term “graph rewriting system” used for graph-transforming application is more appropriate. Graph transformations have been studied first 30 years ago [84] for the generation, manipulation, recognition of graphs. Four types of applications 35
Page 1 and 2: A Toy Model of Chemical Reaction Ne
Page 3: i Dank an alle, die zum Gelingen di
Page 7: v Zusammenfassung Chemische Reaktio
Page 10 and 11: viii CONTENTS B GRW 61 C Organic re
Page 12 and 13: 2 CHAPTER 1. INTRODUCTION ▽ △
Page 14 and 15: 4 CHAPTER 1. INTRODUCTION ¡ ¡ ¡
Page 16 and 17: 6 CHAPTER 1. INTRODUCTION and symme
Page 18 and 19: 8 CHAPTER 2. ARTIFICIAL CHEMISTRIES
Page 20 and 21: 10 CHAPTER 2. ARTIFICIAL CHEMISTRIE
Page 22: 12 CHAPTER 2. ARTIFICIAL CHEMISTRIE
Page 25 and 26: 3.1. EXTENDED HÜCKEL THEORY 15 is
Page 27 and 28: 3.2. FURTHER APPROXIMATIONS 17 K. F
Page 29 and 30: 3.2. FURTHER APPROXIMATIONS 19 Figu
Page 31 and 32: 3.2. FURTHER APPROXIMATIONS 21 are
Page 33 and 34: 3.3. CHEMICAL STRUCTURE REPRESENTAT
Page 35 and 36: 3.3. CHEMICAL STRUCTURE REPRESENTAT
Page 37 and 38: 3.4. WAVE FUNCTION ANALYSIS 27 Derw
Page 39 and 40: Table 3.6: Overlap matrix for prope
Page 41 and 42: 3.5. PERFORMANCE 31 3.5 Performance
Page 43: 3.6. FRONTIER MOLECULAR ORBITAL THE
Page 47 and 48: 4.1. GRAPH REWRITING 37 Graphical t
Page 49 and 50: 4.1. GRAPH REWRITING 39 C C C C C C
Page 51 and 52: 4.2. GRAPH REWRITE ENGINE 41 O O O
Page 53 and 54: Chapter 5 Reaction networks 5.1 Net
Page 55 and 56: 5.3. NETWORK PROPERTIES 45 O 3 NO 3
Page 57 and 58: 5.3. NETWORK PROPERTIES 47 (see ch.
Page 59 and 60: Chapter 6 Computational results Whe
Page 61 and 62: O O O O O O O O O O O O O O O O O O
Page 63 and 64: 6.3. GRAPH-THEORETIC PROPERTIES 53
Page 65 and 66: Chapter 7 Conclusion and Outlook Th
Page 67 and 68: Using the rules of mass action kine
Page 69 and 70: Appendix A Parameters The energy ca
Page 71 and 72: Appendix B GRW GRW is implemented i
Page 73 and 74: Appendix C Organic reactions Fromht
Page 75 and 76: Bibliography [1] R. Albert and A.-L
Page 77 and 78: BIBLIOGRAPHY 67 [25] O. Diels and K
Page 79 and 80: BIBLIOGRAPHY 69 [50] J. Gasteiger a
Page 81 and 82: BIBLIOGRAPHY 71 [76] W. Langenbeck.
Page 83 and 84: BIBLIOGRAPHY 73 [102] S. Schuster,
Page 85: BIBLIOGRAPHY 75 [126] R. Woodward a
Page 89 and 90: The Wooing of Archibald Modern tren

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