A graph-theoretic method to identify candidate mechanisms for deriving the rate law of a catalytic reaction

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Abstract

Stoichiometrically, exact candidate pathways or mechanisms for deriving the rate law of a catalytic or complex reaction can be determined through the synthesis of networks of plausible elementary reactions constituting such pathways. A rigorous algorithmic method is proposed for executing this synthesis, which is exceedingly convoluted due to its combinatorial complexity. Such a method for synthesizing networks of reaction pathways follows the general framework of a highly exacting combinatorial method established by us for process-network synthesis. It is based on the unique graph-representation in terms of P-graphs, a set of axioms, and a group of combinatorial algorithms. In the method, the inclusion or exclusion of a step of each elementary reaction in the mechanism of concern hinges on the general combinatorial properties of feasible reaction networks. The decisions are facilitated by solving linear programming problems comprising a set of mass-balance constraints to determine the existence or absence of any feasible solution. The search is accelerated further by exploiting the inferences of preceding decisions, thereby eliminating redundancy. As a result, all feasible independent reaction networks, i.e. pathways, are generated only once; the pathways violating any first principle of either stoichiometry or thermodynamics are eliminated. The method is also capable of generating those combinations of independent pathways directly, which are not microscopically reversible. The efficiency and efficacy of the method are demonstrated with the identification of the feasible mechanisms of ammonia synthesis involving as many as 14 known elementary reactions.

Original languageEnglish
Pages (from-to)265-292
Number of pages28
JournalComputers and Chemistry
Volume26
Issue number3
DOIs
Publication statusPublished - 2002

Fingerprint

Pathway
Graph in graph theory
Synthesis
Reaction Network
Hinges
Ammonia
Stoichiometry
Linear programming
Linear Programming
Redundancy
Combinatorial Complexity
Combinatorial Algorithms
Graph Representation
Thermodynamics
First-principles
Axioms
Efficacy
Inclusion

Keywords

  • Algorithm
  • Identification
  • P-graph
  • Reaction pathways
  • Synthesis

ASJC Scopus subject areas

  • Applied Microbiology and Biotechnology
  • Biotechnology
  • Chemical Engineering(all)

Cite this

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abstract = "Stoichiometrically, exact candidate pathways or mechanisms for deriving the rate law of a catalytic or complex reaction can be determined through the synthesis of networks of plausible elementary reactions constituting such pathways. A rigorous algorithmic method is proposed for executing this synthesis, which is exceedingly convoluted due to its combinatorial complexity. Such a method for synthesizing networks of reaction pathways follows the general framework of a highly exacting combinatorial method established by us for process-network synthesis. It is based on the unique graph-representation in terms of P-graphs, a set of axioms, and a group of combinatorial algorithms. In the method, the inclusion or exclusion of a step of each elementary reaction in the mechanism of concern hinges on the general combinatorial properties of feasible reaction networks. The decisions are facilitated by solving linear programming problems comprising a set of mass-balance constraints to determine the existence or absence of any feasible solution. The search is accelerated further by exploiting the inferences of preceding decisions, thereby eliminating redundancy. As a result, all feasible independent reaction networks, i.e. pathways, are generated only once; the pathways violating any first principle of either stoichiometry or thermodynamics are eliminated. The method is also capable of generating those combinations of independent pathways directly, which are not microscopically reversible. The efficiency and efficacy of the method are demonstrated with the identification of the feasible mechanisms of ammonia synthesis involving as many as 14 known elementary reactions.",
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