Minimal chemical distance

In this approach chemical reactions are first classified according to the minimal number of valence electrons that must be redistributed in order to convert the reacting molecules into the products of the given reaction. This is accomplished by determining the minimal chemical distance between the reactants and products. 

The algorithm for the computation of the reaction distance is one of the most important algorithm of the synthon model of organic chemistry. The Principle of Minimal Reaction Distance is a reaction distance analog of the Ugi s Principle of Minimal Chemical Distance and is used as the main heuristic to reduce the number of transformations employed, and synthons generated. The efficiency of the algorithm for the computation of the reaction distance is crucial for unable implementation of the whole synthon model. 

Exhaustive enumeration all atoms with the same atomic number are permuted and the permutation corresponding to the minimal chemical distance is taken. 

This requirement is automatically satisfied due to the definition of reaction graph based on the notion of the maximal common subgraph. Ugi et al. [12,16] summarized the above property as the principle of minimal chemical distance, a very effective heuristic rule for the construction of reaction matrices. 

The chemical distance (CD)i initially introduced by Dugundji and Ugi [1,2], combined with their principle of minimal chemical distance, reflects mainly a thermodynamical standpoint, it "quantifies a similarity or dissimilarity between educt and product molecules. What happens in the course of a chemical transformation of the educt molecule into the product molecule, does not actually play a role. The notion of reaction distance (RD) [4,5] reflects, to some extent, the process of chemical transformation from the point of view of the number of elementary reaction steps into which the overall chemical reac-... 

Another approach is to identify equivalent molecules which are quite similar, or are separated by a minimal chemical distance. In this way all members of a group of molecules are replaced by a single member. 

Warner and his collaborators 80, 106) first proposed involvement of tyrosyl residues as ligands for the ferric ion on the basis of potentiometric and spectrophotometric titration data. This has been further substantiated by chemical modification 107, 108) and other difference spectrophotometric 67) studies. Apparently two or three tyrosyl 81, 108), two histidyl 83, 108—110) and an equivocal number of tryptophanyl 111 a, b) residues are present at each binding site 112). EPR evidence indicates that oxygen and as many as 4 nitrogen nuclei interact with the metal 113, 114). Furthermore, bicarbonate is bound to the protein, resulting in the usual salmon-pink colored form of the ferric complex which is otherwise colorless (115 a,b). The minimal possible distance be-... 

At Astex, the initial partitioning of fragments into cocktails is achieved using a computational procedure that minimizes chemical similarity [43]. Fragments are described as feature vectors, which encode such properties as the number of donors/ acceptors/non-hydrogen atoms, number of five- and six-membered rings and their substitution patterns. The chemical dissimilarity between two molecules, d(i, j), is then calculated as the distance between the two vectors. 

For the chemically meaningful representation EM(B) EM(E) the atoms of EM(B) must be assigned to atoms of EM(E) in such a manner that the chemical distance D has its minimal value. 

In the computer program which we have developed for the minimization of the chemical distance we use algorithms from the field of operations research known as "optimal assignment "-methods. ... 

Among the early approaches to the vaporization problem was the proposal by Beuhler and co-workers [1] that the vaporization/decomposition ratio could be substantially increased by rapid heating of the sample. Dell et al. showed that, by minimizing the distance between the vaporization and ionization sites through the use of a special in-beam probe, significant improvements in the electron ionization (El) spectra of thermally labile compounds could be obtained [2]. Baldwin and McLafferty observed a similar enhancement when samples were introduced directly into the plasma within a chemical ionization (Cl) source [3], The logical combination of both rapid heating and in-beam techniques quickly followed, and heatable in-beam probes became commercially available for most spectrometers at relatively low cost. 

We see for instance that the chemical distance between graphs and G2 is equal to twice their graph distance where by the term "graph distance" [1] we understand the length (number of edges) of a minimal path between the vertices. 

A number of methods have been developed to introduce context to on-line databases, enabling searches to be refined to minimized false retrieval. One of the earliest techniques is proximity searching, in which two words are required to be adjacent, or within a limited distance from each other in text. The assignment of roles to chemical substances is a method of precoordinating concepts. A substance can be identified as a reactant, as a product, and in some systems in a number of additional roles. For example, by searching for documents in which formaldehyde is a product, documents in which it is a reactant, or in which it undergoes no reaction, are thus eliminated. 

Thus, when acid 76 was crystallized as a salt with (S)-(-)-l-phenylethylamine ([S]-PEA), the X-ray structure showed that the conformational enantiomer 76a was trapped in the crystal, displaying O - H and O - Ht distances of 2.47 A and 3.41 A, respectively. The conformation of 76a placed the carbonyl oxygen and Hj, closer to the ideal values mentioned in Figure 7.26 as compared to H. A significant preference for Hj, was demonstrated after photolysis at 0 °C and diazomethane workup, when ester 77a (B) was obtained in 65% ee after 90% conversion. Figure 7.27 illustrates the minimal atomic displacements required for reaction by comparing the X-ray structure of the reactant with that of the product, and with a structure obtained at 50% conversion. Better chemical results were obtained by photolysis of 76a with (/ )-CEA, which gave 90% ee of ester of 77a (B) after diazomethane workup. 

The average value of A must be conserved over long distances to minimize both the elastic energy and the chemical (core) energy. Also, there will be little tendency for a dislocation line to remain in a single plane. It will tend to follow the plane of maximum shear stress. This is observed experimentally. 

A common problem encountered in large chemical companies involves the distribution of a single product (30 manufactured at several plant locations. Generally, the product needs to be delivered to several customers located at various distances from each plant. It is, therefore, desirable to determine how much Y must be produced at each of m plants (Yv Y2,..., Ym) and how, for example, Ym should be allocated to each of n demand points (YmV Ym2,. Ymnl The cost-minimizing solution to this problem not only involves the transportation costs between each supply and demand point but also the production cost versus capacity curves for each plant. The individual plants probably vary with respect to their nominal production rate, and some plants may be more efficient than others, having been constructed at a later date. Both of these factors contribute to a unique functionality between production cost and production rate. Because of the particular distribution of transportation costs, it may be... 

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