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

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54 CHAPTER 6. COMPUTATIONAL RESULTS 100 Cumulative degree distribution 10 1 1 10 100 Degree 100 Cumulative degree distribution 10 1 1 10 Degree Figure 6.3: Cumulative degree distribution of repetitive Diels-Alder (top) and the Formose reaction network (bottom). Datapoints are ranked by decreasing degree. Datapoints, power-law regressions, and theoretical Poisson distribution are represented by □, solid, and dashed lines. Regressions: y = 68x −1.19 with r 2 = 0.92 (top), y = 57x −1.19 with r 2 = 0.87 (bottom).
Chapter 7 Conclusion and Outlook The present Toy Model is at least close to a minimal implementation of an artificial chemistry exhibiting what we consider the defining features of “real” chemistry. Molecules were represented only by their connectivity information and atom types, as labeled graphs, and their energy was defined along the lines of quantum chemistry, using an extremely simplified function. This energy model forms the basis of full-fledged chemical thermodynamics and kinetics. Chemical reactions are implemented as graph rewriting rules that have to obey the principle of conservation of matter. These features distinguish the Toy Model from artificial chemistries that are defined on abstract algebraic structures such as the λ calculus, Turing machines, or term rewriting. The application of the model to examples of complex organic and prebiotic chemistry allowed an quasi-ab initio simulation of the resulting networks and prediction of their properties. Now the emergence of generic properties of CRNs can be studied given only starting material, generic reactions and atom and bond parameters. A true ab initio simulation would not need the introduction the latter parameters for the energy calculation and would simulate reactions without even specifying generic reactions. Yet both “educated guesses” are founded on the results of quantum chemistry and synthetic chemistry, and their validity could be estimated by the judicious comparison of predicted to experimental results. A number of extensions of the present Toy Model are desirable. For instance, the addition of the corresponding parameters (see appendix A) would extend the current implementation of the model, considering only molecules composed of C, H, O, and N, to an expanded set of chemical elements, most importantly S, P, Si, and the halogens. The inclusion of charged particles and radicals also does not seem to pose problems in the current framework. Charges situated on specific atoms can be indicated in SMILES, e.g. HC([O−]) = O. In fact, it does not matter to which atom the 55
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A Toy Model of Chemical Reaction Ne
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i Dank an alle, die zum Gelingen di
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v Zusammenfassung Chemische Reaktio
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viii CONTENTS B GRW 61 C Organic re
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2 CHAPTER 1. INTRODUCTION ▽ △
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Page 16 and 17: 6 CHAPTER 1. INTRODUCTION and symme
Page 18 and 19: 8 CHAPTER 2. ARTIFICIAL CHEMISTRIES
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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
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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 and 44: 3.6. FRONTIER MOLECULAR ORBITAL THE
Page 45 and 46: Chapter 4 Chemical reactions A mole
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: 6.3. GRAPH-THEORETIC PROPERTIES 53
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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A Toy Model of Chemical Reaction Networks - TBI - UniversitÃ¤t Wien

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