The Logical Structure of Chemistry

The physical nature of the molecides and their subunits suggests that, in principle, the logical structure of chemistry could be derived from quantum mechanics. This would, however, require methods by which the potential energy siurface of any system containing the same set. 4 of w atoms could be analyzed. 

An attempt in this direction has, in fact, been made by Preuss , who recognized the importance of the above problem and developed methods for the treatment of the incomplete associations of atoms which contain the FIEM (see Section A.) as subsets. The complexity of the Preuss approach limits its application to systems which contain much fewer nuclei and electrons than those involved in complicated chemical problems, such as synthetic design. For the latter, a different type of theory is needed, a theory that affords insights into the relations between complex chemical systems, without the sometimes formidable effort of solving the pertinent quantum mechanical problems. It is, however, conceivable that the potential energy surfaces of polyatomic systems will be the basis of future computer programs for the solution of chemical problems. 

The logical stracture of chemistry is separable into the logical structure of stereochemistry iv,2i-26) and the logical structure of constitutional chem-istry. Since the stereochemical systems are representable in terms of 

Our present knowledge of constitutional chemistry indicates that there exists some universal principle of order to which the chemical systems and their relations axe subject. What concepts do we need, and how do we have to define the chemical systems and their relations in order to be able to spell out this universal structure  

Two generally accepted ideas provide the basis for achieving this the principle of conservation of matter during chemical transformations and the approximation standpoint that the atoms which participate in a molecular structure can be treated in terms of a core A composed of the nucleus and tightly bound inner electrons with a positive formal core charge et,o together with a valence shell of dectrons t that are less tightly bound, and are responsible for the chemical bonds, such as the ionic bonds, the covalent electron pair bonds, and the multicenter bonds. 

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Bley, K., Gruber, B., Knauer, M., Stein, N, and Ugi, I. New Elements in the Representation of the Logical Structure of Chemistry by Qualitative Mathematical Models and Corresponding Data Structures. 166, 199-233 (1993). 

The ASI and RASI provide the common reference system that is needed for the full use of the above model of the logical structure of chemistry for a computer oriented representation. 

Similarity of molecules [40-44] is an important phenomenon serving, for example, by qualitative and quantitative estimation of chemical reactivity or biological activity of chemical species. Distance is a possible way to measure similarity. In the frame of a mathematical model of the logical structure of chemistry, the notion of chemical distance, CD, has been introduced [13], The CD is defined as the sum... 

New Elements in the Representation of the Logical Structure of Chemistry by Qualitative Mathematical Models and Corresponding Data Structures... 

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. 

Since 1970 [12] the term logical structure of chemistry has been used for a system of relations between the objects of chemistry. Isomerism, the interconvertibility by chemical reactions and the other types of chemical similarity [19] belong to the most important relations between molecular systems. The logical structure of chemistry is determined by the valence chemical properties of the approximately 100 chemical elements [27],... 

Any two distinguishable molecules are said to be isomeric, if they have the same empirical formula and are based on the same collection of atoms. The hierarchic classification of molecules, according to isomerism, constitutional isomerism and stereoisomerism, is a centerpiece of the logical structure of chemistry [28]. 

An extension of isomerism from molecules to ensembles of molecules (EM) leads to new perspectives in chemistry. The left and right hand sides of a stoichiometrically balanced reaction equation are isomeric EM. Any chemical reaction may be regarded as an isomerization, i.e. the conversion of an EM into an isomeric EM. Let A = A1(... A be a finite collection of atoms with the empirical formula A. Any EM that contains each atom of A exactly once is an EM (A). The family of all isomeric EM (A), the FIEM(A) contains the complete chemistry ofA = At,... A . The FIEM(A) is closed and finite. It has well-defined limitations and invariancies. Accordingly, the logical structure of the chemistry of an FIEM(A) is much easier to elucidate than the logical structure of chemistry without the above restrictions [9],... 

The chemistry of an FIEM(A) of a finite collection of atoms is a finite closed system with a variety of well-defined properties. Thus its logical structure is easier to analyze than the logical structure of chemistry in general. Since any collection of atoms may serve as A, any qualitative relations that exist in an FIEM(A) are analogously also valid for chemistry as a whole [9]. 

Thus, the investigation of the constitutional aspect of the chemistry of an FIEM(A) provides us with knowledge about the constitutional aspect of the logical structure of chemistry. 

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