Molecules , family isomeric ensembles

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). 

Another scheme for systematic synthesis analysis has been proposed by Ugi and Gillespie The system is based on the recognition that aU chemical reactions correspond to interconversions of isomeric ensembles of molecules (lEM) within a family of isomeric ensembles of molecules (FIEM) 20), They have shown that distinguishable lEM of a FIEM can be represented by a family of be matrices (bond and electron matrices) F = Mo,Ml,... Mf). The be matrix Mt of an ensemble of molecules, EM(, consisting of a set A containing n atoms, A = (A i,..., A ) is an X matrix as shown below ... 

An FIEM(4), the family of isomeric ensembles of molecules of A, is the set of all Thus, an FIEM is described simply by a gross empirical... 

Since isomeric molecules may differ constitutionally and stereochemically, a partitioned ensemble formula generally corresponds to more than one EM(A). The constitutional formula of an EM(A) contains the constitutional formulas of all molecules in that EM(A). An FIEM(A), the family of isomeric ensembles of molecules of an atom set A is the collection of all... 

In the constitutional model of Ugi, rather than molecules, "ensemble of molecules (EM) are used in which the molecules can be either chemically different or identical. Like molecules, an EM has an empirical formula, which is the sum of the empirical formulae of the constiment molecules and describes the collection A of atoms within the EM under consideration. All the EM s which can be formed from A have the same empirical formula . Therefore, an EM(A) consists of one or more molecules which can be obtained from A using each atom which belongs to A only once. Moreover, a FIEM(A) or a family of isomeric EM, is the collection of all EM(A) and it is determined by the empirical formula . On the other hand, a chemical reaction, or a sequence of chemical reactions, is the conversion of an EM into an isomeric EM, and therefore a FIEM contains all EMs which are chemically interconvertible, as far as stoichiometry is concerned. In summary, a FIEM(A) contains, at least in principle, the whole chemistry of the collection A of atoms and since any collection of atoms may be chosen here, Ugi concludes that a theory of FIEM is, in fact, a theory of all chemistry. 

The synthon S(A) over an atomic set A is defined as one or several molecules (or their parts) composed of atoms from the set A. In contrast to the definition of the Ensemble of Molecules, EM (A) [13], S(A) is more general because it may also involve free valences, i.e. bonds which do not connect two atoms but only start from an atom. The set of all synthons constructed over the atomic set A is called the Family of Isomeric Synthons and is denoted FIS(A). Implicitly, it means... 

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],... 

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