Chemistry, constitutional

Dugundji, J., and Ugi, I. An Algebraic Model of Constitutional Chemistry as a Basis for Chemical Computer Programs. 39, 19-64 (1973). 

About the same time, Kekuld 15> discovered the quadrivalency of C-atoms laying the foundations for constitutional chemistry. 

An FIEM(A), the family of isomeric ensembles of molecules of A, is the set of all EM(A), Thus, an FIEM is described simply by a gross, empirical formula an EM is described by a list of molecular species in terms of constitutional formulas. The constitutional chemistry of a set of atoms A can be described by the structure of its FIEM(A). 

The chemical constitution of a molecule or an ensemble of molecules (EM) of n atoms is representable by a symmetric n X n BE-matrix and corresponds accordingly to a point P in TR ( +D/a an n(n +1)/2 dimensional Euclidean space, the Dugundji space of the FIEM(A). The "city block distance of two points P i and P 2 is twice the number of electrons that are involved in the interconversion EMi EM2 of those EM that belong to the points Pi and P2. This chemical metric on the EM of an FIEM provides not only a formalism for constitutional chemistry, but also allows us to use the properties of Euclidean spaces in expressing the logical structure of the FIEM, and thus of constitutional chemistry 3e>32c>. 

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

According to the theory of constitutional chemistry, a chemical reaction is interpreted as a redistribution of the valence electrons i.e., as the transformation of an EM into an isomeric EM (in which both the atomic cores and the valence electrons are preserved). The difference between the final E (End) and the initial B (Begining) BE-matrices is called the R-matrix (Reaction matrix) ... 

This chapter is devoted to computer programs for PCs. These solve chemical problems by generating reaction pathways and are based on the theory of the BE-and R-matrices, an algebraic model of constitutional chemistry. 

An essential prerequisite for a deductive approach to chemistry would be a theory that affords the prediction of the existence of molecular systems and their interconversions. The theory of the BE- and R-matrices, an algebraic model of the logical structure of constitutional chemistry, is precisely such a theory (ref. 2, 3). A brief outline of the theory of the BE- and R-matrices is given below. 

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. 

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. 

Keywords Carbonic anhydrase Dynamic constitutional chemistry Dynamic interactive systems Hybrid materials... 

Non-biomimetic interfaces which are constructed as they are from supramolecular associations or reversible covalent linkages. An approach to such an interface can be envisaged through the application of supramolecular chemistry and dynamic constitutional chemistry which are both conducive to adaptive structures. 

Initially, the notion of the synthon was, in the frame of formalization of synthetical chemistry, introduced by Corey [23]. Based on the Corey approach, and on the Dungundji-Ugi formalization of chemistry [13], the synthon model of constitutional chemistry was introduced [18,19,21,22,24,16]. In general, it can be understood as a generalized concept of valence states of atoms and their combinations. 

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. 

The theory of the be- and r-matrices [9] represents the logical structure of constitutional chemistry. 

According to these definitions of constitutional chemistry and stereochemistry, they are two disjoint aspects of chemistry. It follows that their treatment by qualitative mathematics must differ profoundly. The logical structure of constitutional chemistry is represented by the algebra of be- and r-matrices. The logical structure of stereochemistry is essentially permutation group theoretical in nature. 

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

The algebra of be- and r-matrices is well-suited as a theoretical basis for computer programs that solve problems of constitutional chemistry, provided that the formal... 

The use of this data structure for constitutional chemistry comprises three parts ... 

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. 

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