Mathematical model of constitutional chemistry

The mathematical model of constitutional chemistry. The programs EROS and IGOR... 

It has been demonstrated that a mathematical model of constitutional chemistry can serve as a basis for a computer program to automatically generate sequences of reactions and for planning organic syntheses. This gives credibility to other applications of this model. 

The mathematical model of constitutional chemistry which has been described in the preceeding sections can be used as a basis for a modular system of computer programs for the deductive solution of chemical problems. 

Ugi and co-workers have developed a mathematical model of constitutional chemistry and used it as a basis for deductive computer programs synthetic routes may be designed in this way/ but there is a problem in minimizing the number of routes so generated. Weise and Scharnow have critically discussed some existing computer programs for designing syntheses and provided their own approach to the subject. The topic has also been discussed briefly by Bruns in an article which includes comment on quantitative structure-activity relationships. 

The purpose of this work is to formulate such a mathematical model of constitutional chemistry that allows a simple description of the topology of molecular systems and their changes during chemical reactions. 

Ugi and Dugundji developed a mathematical model of constitutional chemistry. This model is based on the concept of isomerism of molecules which has been extended to ensembles of molecules. For example, a theoretical reaction A -I- B C -I- D can be seen as the conversion of an ensemble of molecules (A - - B) into an isomeric ensemble (C D). As an extension, the discovering of a synthesis Target = Precursor 1 Precursor 2 => Starting materials, may... 

An R-matrix has a series of interesting matheinatical properties that directly reflect chemical laws. Thus, the sum of all the entries in an R-matrix must be zero, as no electrons can be generated or annihilated in a chemical reaction. Furthermore, the sum of the entries in each row or column of an R-matrix must also he zero as long as there is not a change in formal charges on the corresponding atom. An elaborate mathematical model of the constitutional aspects of organic chemistry has been built on the basis of BE- and R-matriccs [17. ... 

The mathematical model chosen as a basis is confined to constitutional chemistry. The formal concepts for the treatment of the stereochemical features of molecules and reactions have been given elsewhere10, and a computer program based on these ideas is being developed. For the initial phase of the development of a computer program for the design of syntheses, stereochemistry has temporarily been set aside to concentrate on the more important aspects of constitutional chemistry. 

From 1970 to 1984 Dugundji, Ugi et al. [9, 10] analyzed the logical structure of chemistry. They found that chemistry consists of two parts with distinct logical structures, constitutional chemistry and stereochemistry. This division is already implied by the nongeometric definition of stereoisomers [11] (see Sect. 1.3). Accordingly, Dugundji and Ugi formulated a qualitative mathematical model of the logical structure of chemistry that consists of two distinct parts. 

Mathematical Models of the Logical Structure of Constitutional Chemistry... 

The inclusion of bonds with fractional bond orders extends the scope of the mathematical model of the constitutional chemistry from classical organic chemistry also to modern inorganic and organometallic chemistry. 

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. 

The basic theories of physics - classical mechanics and electromagnetism, relativity theory, quantum mechanics, statistical mechanics, quantum electrodynamics - support the theoretical apparatus which is used in molecular sciences. Quantum mechanics plays a particular role in theoretical chemistry, providing the basis for the valence theories which allow to interpret the structure of molecules and for the spectroscopic models employed in the determination of structural information from spectral patterns. Indeed, Quantum Chemistry often appears synonymous with Theoretical Chemistry it will, therefore, constitute a major part of this book series. However, the scope of the series will also include other areas of theoretical chemistry, such as mathematical chemistry (which involves the use of algebra and topology in the analysis of molecular structures and reactions) molecular mechanics, molecular dynamics and chemical thermodynamics, which play an important role in rationalizing the geometric and electronic structures of molecular assemblies and polymers, clusters and crystals surface, interface, solvent and solid-state effects excited-state dynamics, reactive collisions, and chemical reactions. 

Let us finally dwell on one more type of model, which in principle does not require any preliminary experimental study of the process. Models of this kind themselves can be considered as tools for investigation of complex processes on a very intimate level. They constitute a hypothesis about the detailed chemical mechanism of the process (its micro-chemistry) that includes types of species present in the reacting system and chemical interactions between them. Being filled with kinetic parameters and treated in accordance with proper mathematical procedures, this type of model is supposed to reproduce the behavior (or evolution in time) of the system, which can be compared with some experiment in order to see if there are any matches or common features. 

Any progress in chemistry may be interpreted as the recognition of new equivalence relations and classes. Until recently, a universal model of chemistry could not be defined, because we lacked the concepts for a mathematical treatment of the constitutional aspect of chemistry. Therefore it is necessary to consider any constitutionally different molecular systems as equivalent regardless of the number of molecules which they contain, if, in principle they are interconvertible through chemical reactions. 

Mathematical modeling is the translation of a physical description to mathematical expressions. One translates by applying relations from physics and chemistry. Some relations are universal laws, such as the conservation of energy. Some relations are constrained laws (constitutive equations), such as the ideal gas law. The behavior of a physical process is governed by the laws of physics and chemistry. The behavior of a model is governed by the rules of mathematics. 

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