Ensembles of molecules, isomeric

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). 

In this model molecules are represented by BE-matrices (see Section 2.1.), reactions are taken as transformations of BE-matrices of isomeric ensembles of molecules by R-matrices (see Section 2.2.). These A-matrices indicate the changes in the distribution of bonds and free electrons occurring in a reaction. The / -matrices can be generated quite formally thereby obtaining all conceivable reactions irrespective of whether a reaction is already known or is completely novel, i.e., without any precedence. 

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. 

It represents the conversion of an ensemble of educt molecules EM(B) into an isomeric ensemble of product molecules EM(E) by a chemical reaction. The ensembles of molecules (EM) at the Beginning and the End of the reaction are described by their BE-matrices B and E. The so-called reaction matrix R corresponds to a pattern of valence electron redistribution, or also a scheme of bond breaking/making during the reaction (ref. 4). 

The basis for the formulation of BB-matrices for ensembles of molecules is an extension of the concept of isomerism to ensembles of molecules The cyanohydrin of formaldehyde 1 is isomeric with the ensemble of its components formaldehyde 2 and hydrocyanic acid 3. Both 1 and 2 + 3 have the same set of atoms and the same number of valence electrons. 

In our system, reactions are considered as isomerizations of ensembles of molecules both sides of the reaction equation contain the same set of atoms and the same number of valence electrons. Then, for generating reactions, all compounds which can conceivably take part in these reactions have to be known. Generally there is not only one compound reacting - exceptions are rearrangements or decompositions — but there are several reaction partners. 

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],... 

Extension of the equivaleiice relation of isomerism to ensembles of molecules leads to a unified theory for the relations between chemical systems. Previously, the potential importance of this extended equivalence relation to the interpretation of chemistry and systematic planning of chemical experiments seem to have been overlooked. 

Extending the concept of isomerism from molecules to ensembles of molecules (EM) leads to a mathematical model of cons itutional chemistry ). An EM is described by its list of the molecular species in the form of suitable chemical formulas. For an EM one can define two types of empirical elementary formulas, on one hand the ensemble formula, on the other hand a partitioned empirical ensemble formula which consists of the molecular formulas of the molecules in the EM. 

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... 

Figure 8.1 Simplified representation of slice of free-energy hypersurface for C10H22 is shown. Free energy vs. configuration (conformation) for two molecules, ensembles of which represent two isomeric compounds n-decane (A) and isodecane (B) are given.

Conformational isomerism of molecules may exert a significant effect on the physical properties of a thermodynamic systen. This effect depends not only on the structures of the molecules and the molecular ensembles, but also on tte nature of the external perturbation and the thermodynamic boundary conditions to which the system is subjected. Consequently, questions about the thermodynamic effect of conformational isomerism should never be expressed in absolute, but always in relative terms. 

The essential signature of a molecule is tiiat it vibrates. For a molecule composed of N atoms, there are 3N mechanical degrees of freedom associated with the motions of the system. Three degrees of freedom are determined by the translational motions of the center of mass, and for a nonlinear molecule there are three degrees of freedom connected with the overall rotational motion of the molecule. For a macromolecule, some of the remaining 3N - 6 degrees of freedom are associated with isomerizations of the chain backbone and the side chains. Finally, there exists a set of quantized vibrational states for the molecule. If the frequencies of the vibrational states depend on the conformational state of the molecule, the measurement of the vibrational spectrum can be used to infer the conformational composition of the ensemble of macromolecules. The frequencies of quantized molecular vibrations greatly exceed the frequencies associated with isomerization of the chain backbone. 

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