Distance chemical

Twenty populations were sampled with plants from Hailuoto, at 65°00 N, representing the northernmost site and material from Hanko, at 59°49 N, representing the southernmost collection site (and, incidentally, the southernmost point of land in the country). Five samples represented central Finland with the remainder originating from the southern part. Fifty-five compounds were detected by GC-MS analysis, 53 of which were identified. The data obtained were subjected to complete linkage analysis, which differentiated several clusters that corresponded moderately well with geography. Genetic distance values derived from the RAPD data correlated well with chemical distance values determined from the terpene data (r=0.41, P<0.0001). 

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. 

Fig. 3. The full range of the two-angle structures. Shown are some example configurations with the arrows indicating their position in the 6, (/))-plane. The lines denote the boundaries to the forbidden structures where the nucleosomes would overlap. To the right of the dashed line nucleosomes i and i + 2 would overlap ( short-range excluded volume ). Below the dotted line nucleosomes further apart with respect to their chemical distance would overlap ( long range excluded volume ). For instance, for the circle, structure 2 , nucleosomes collide after one turn (10 nucleosomes).

However, if the total affinity A is spread over, let us say, n = 10 reaction steps, then each individual reaction step corresponds, on average, to a reduced chemical affinity of 0.1A/RT0 = 0.5, with a reduced chemical velocity of 0.4, according to Figure 4.3. So, the same chemical "distance" is now covered with a much smaller velocity and the corresponding lost work rate has been reduced accordingly. Point C in Figure 4.5. shows the reduced lost work per step, and Point C the total lost work for the multistep reaction. Point C in... 

This method was, however, discarded, because it would neglect too many worthwhile pathways outside the minima of chemical distance. 

The efficiency of this type of bilateral development of the networks is ensured by keeping track of the chemical distance that the individual trees cover, and by counting the intermediates on the pathways from EM(B) to E.M(E). 

Ugi, I., Wochner, M., Fontain, E., Bauer, J., Gruber, B. and Karl, R. Chemical similarity, chemical distance and computer assisted formalized reasoning by analogy. In Concepts and Applications of Molecular Similarity, Eds Johnson, M.A., Maggiora, G.M., John Wiley Sons Inc, New York, 1990, pp. 239-288. 

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... 

The input/output driver is also used for the (retro)synthetic tree inspection. The user can walk through the tree generated, inspect the selected nodes, edit them, and submit them for further processing by the SPS generator, thus creating new branches and levels of the (retro)synthetic tree. Each node of the (retrosynthetic trees stores not only the two-dimensional structure of the chemical compound, but also the distance from its father (i.e starting structure) measured by the reaction as well as chemical distances, and also its fragmentation level, measured by its order. 

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. 

Combination of all the above presented algorithms (and many others, especially the algorithm for the generation of the canonical code of a synthon, the algorithm for the computation of chemical distance between two synthons, etc.) gives the final algorithm for SPS generation ... 

Jochum C, Gasteiger J, Ugi I, Dugundji J (1982) The principle of minimum chemical distance and the principle of minimum structure change, Z Naturforsch 37B 1205... 

Wochner M, Brandt J, Scholley A v, Ugi I (1988) Chemical similarity, chemical distance and its exact determination, Chimia 42 217... 

But already at that point we realized that the accuracy of this method was not very good. Many physical and chemical quantities, like binding energy or chemical bond distances, could not be calculated directly with this method. When we finally also started calculations of real molecules at chemical distances this deficiency became even more obvious and we began to improve the method itself in order to calculate the total energy of a system within the Xa-approximation. 

Using relative topological distance or chemical distance as well as conventional bond order to weight each edge in the graph -> weighted matrices can be obtained. 

Balaban, A.T, Bonchev, D. and Seitz, W.A. (1993a). Topological/Chemical Distances and Graph Centers in Molecular Graphs with Multiple Bonds. J.Mol.Struct. (Theochem), 280,253-260. 

Crippen, G.M. (1991). Chemical Distance Geometry Current Realization and Future Projection. J.Math.Chem., 6,307-324. 

J. Pospichal, V. Kvasnicka, Fast evaluation of chemical distance by simulated-annealing algorithm. Journal of Chem. Inf. Comput. Sci., 33 (1993) 879. 

Table Bll Average experimental bond length r, carbon relative value r, conventional bond order n, relative topological distance RTD, and chemical distance CD.

The chemical distance matrix is a variant of the multigraph distance matrix defined by using the —> chemical distance as the weighting scheme for edges therefore, the path weight Wy in terms of bond chemical distances is calculated as [Balaban, Bonchev et al., 1993] ... 

The row sum of this matrix is a local vertex invariant called chemical distance degree the maximum entry in each row is called chemical atom eccentricity, which is the maximum distance weighted by relative atomic weights from each atom. The chemical atom eccentricity is used in the calculation of the —> superadjacency topochemical index, while the chemical distance degree in the calculation of the Wiener topochemical index. 

Note. The atomic weight-weighted distance matrix was originally called chemical distance matrix however, this name cannot be used here because it was previously attributed by Balaban [Balaban, Bonchev et al, 1993] to another weighted distance matrix (see below). 

Atomic weight-weighted distance matrix D of 5-methyl-l,3,4-oxathiazol-2-one VS, indicates the matrix row sum that is the chemical distance degree CSj is the matrix column sum andri is the chemical atom eccentricity. 

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