Graph synthon-reaction

For a fixed family 3 (A) of isomeric synthons we construct the so-called graph of reaction distances [18, 21, 16, 25] denoted by RD(A). The vertex set of this graph is formally identical with the family A) without forbidden synthons, its two distinct vertices v and v, assigned to the synthons S(d) and S (/l), are connected by an edge [u, v ] if such an elementary transformation i = a, p exists so that the synthon S(/l) is transformed into the synthon i.e. 

Fig. 7. An example of subfamily J (A), where A = landO < s 3, it contains 14 synthons indexed by 1 to 14. The corresponding graph of reaction distances 9R0(A) is composed of 14 vertices (synthons)...

The notion of a stable neighborhood of a synthon will be illustrated by using the subfamily J fA) displayed in Fig. 7, the corresponding graph of reaction distances is given in Fig. 8. Now we will assume that the synthons S3(A), S9(A), and Si 3(A) are the only stable synthons (they are denoted by encircled vertices), see... 

Fig. 11. Modified graph of reaction distances RD(A) from Fig. 7, now the synthons indexed by 3, 9, and 13 are declared as the only stable ones (encircled vertices)...

Given two isomeric synthons S(A) and S (A) construct all synthon-reaction graphs (SR-graphs) for the transformation... 

The graph of reaction distances (cf. Sect. 3.4) will be constructed for all synthons taken from the same family FIS(A), and it will be denoted by number of vertices need not be specified as it is equal to the cardinality of the atomic set). In the present approach, two distinct vertices [corresponding to synthons from FIS(A)] are connected by an edge iff there exists an elementary operator I-a, B, y, S that transforms one synthon into another. In Scheme 5.1 we show a small part of the graph constructed on the atomic set As(C,C,N>. 

Since the graph of reaction distances is connected [18], the reaction distance for synthons from the family FISreaction distance RD, may be formally treated as a metric space. The evaluation of the reaction distance between two synthons from the same family... 

Starting from a given educt synthon, we can form a set of all its possible synthon precursors/successors (SPS) that are generated by simple reaction graphs. It means that an over-all chemical reaction, passing through several SPS can be expressed as a sequence of the above mentioned reaction graphs. 

Each chemical transformation of two preselected synthons St(yl) and S2(/l) will be represented by the so called reaction graph [16,29] denoted by GR. 

The reaction distance [16,18,21,25] between two isomeric synthons Si (A) and S2(A) will be used as a proper tool for the construction of reaction graphs [29]. The reaction graph obtained corresponds to the minimal number of the so-called elementary chemical transformations, the number of which determines the reaction distance between the synthons SjfA) and S2(A). 

Definition 2.3 The reaction distance D(S(/1), S (T)) between two synthons S(4) and S 04) is equal to the graph (topological) distance between those vertices that are assigned to them in %d A). 

Sn(A). Applying the similar procedure for all synthons from the subfamily of A) we arrive at 9 XD(A) given in Fig. 7. From this graph one can simply evaluate the reaction distance for an arbitrary pair of synthons, e.g. S4(A)) = 6... 

The above outlined method can serve as an almost exact approach for the evaluation of reaction distance between two isomeric synthons S(A) and S (A). Its almost exactness follows from the fact that there can be no previously prescribed mapping of vertices and than the reaction graph is not unique. There can be constructed corresponding reaction graphs for every mapping and the reaction distance should be obtained as a minimum of minimal coverings of those reaction graphs. 

Definition 2.5 A stable synthon S (A) is called synthon precursor successor (SPS) of the stable synthon S(A) iff the reaction graph GR of the transformation S(A) => S (A) is of a cyclic or linear form, see Fig. 12. Both forms must have alternating evaluation of edges by +/— and the linear graph must have terminal virtual vertices. The set of all possible SPS of the synthon S(A) is denoted by S(S(A)). 

Let us consider a stable synthon S (A) e S(S(A)), the transformation S(A) => S (A) is represented by a reaction graph either of the linear or cyclic form. In order to verify that the synthon S (A) belongs to the stable neighborhood of the stable synthon S(A) it is sufficient to verify that each connected subgraph of GR produces the unstable synthon. As this subgraph would be of linear form, at least one nonvirtual atom would gain or loose one valence electron and therefore its valence state would be unstable and the synthon S (A) produced should not be stable. 

Fig. 13. Schematic illustration of definition 2.6. In the first row a chemical transformation is displayed in which a synthon with two nonincident vertices from the reaction set X is transformed into another synthon with already incident vertices which were initially nonincident. In the second row a possible reaction graph is displayed...

It should be mentioned that the notion of reaction distance, as defined for valence states of atoms, can be used also for synthons. It means that RD(S(A), S (A)) is defined as the length of the shortest path between S(A) and S (A) in the graph Gfis[Pg.160]

In this chapter we have described for molecular graphs the monolateral and bilateral approaches for the evaluation of reaction distances and the construction of precursors and successors. Both these techniques can be simply modified for S-graphs and/or synthons, and moreover, the concept of reduced reaction distance introduced here may be easily applied. 

The notion of reaction distance can be similarly interpreted in the framework of graph-theory model of synthons. Let Gjj be the SR-graph of isomerization S(A) — S (A) it can be written as follows [15,16]... 

In order to construct the string 82 we have to know the syuthon to which the considered reaction graph is applied. Until now we have no information about the multiplicities of formed and deleted bonds. The reaction graph may be applied, in principle, to an arbitrary synthon containing the bonds I-J and E-L. For instance let us consider the following four synthons ... 

The string 83 = 2222 indicates that the reaction graph is applied to the synthon O33. 

The third condition determines an upper bound for the reaction distance of isomerisations of two- or more-atom subsynthons of the reaction centre, all of which fulfill the previous condition of connectivity of the assigned SR-graphs. The purpose of this condition is to ensure "smoothness of electron changes in the course of isomerization it limits the number of ESRE s that could enable atoms of X to achieve a stable synthon SMX). In other words, the condition ensures that, in following the shortest path in from the synthon S(A) to its SPS, no stable synthons are omitted. 

The basic concepts and notions of our model are the chemical and reaction metrics, the synthon and subsynthon, the stable X-neighborhood of a synthon, immersion of a synthon, and so on. The principal concept of the present approach is the synthon, initially introduced at the end of the nineteen-sixties by E.J. Corey. The synthon is formulated as a molecular graph with two sorts of vertices — atoms and virtual atoms. 

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