Constitutional symmetry

The methine carbon atom also obtains an EC value of 4 (= 1 -h 1 + 2) in the second iteration. This process is repeated iteratively until the number of different EC values (c) is lower than or equal to the number of EC values in the previous iteration. Then the relaxation procc.ss is terminated. Next, the EC numbers of the previous iteration are taken for a canonical numbering and for the determination of constitutional symmetry (Figure 2-44),... 

NMR spectroscopy derives its usefulness, in large measure, from its ability to detect constitutional symmetry. If constitutional symmetry is not taken into account in synthetic design computer programs, a redundancy of pathways may result. 

The Morgan algorithm 5> is a device used by the Chemical Abstracts Service for assigning indices to the nodes of constitutional formulas whose H-atoms have been omitted, i. e. their reduced graphs. If the indices of all atoms are needed, e.g. for the representation of stereochemistry, an additional procedure is needed for establishing those for the H-atoms. Constitutional symmetry is not indicated directly by Morgan indices. 

Circular substructures of various sorts have been widely used for applications such as structure and substructure searching, constitutional symmetry, structure elucidation and the probabilistic modeling of bioactivity inter alia The work reported here demonstrates that this type of fragment is also very well suited to virtual screening using multiple reference structures. 

Fand G Matrices. The internal coordinates are shown in the sketch below. The SALCs, which constitute symmetry coordinates, have already been derived for an AB3 molecule in Section 6.3 and are reproduced here. 

Because the double bond has an E configuration, the total number of configurational isomers which are theoretically possible is 24 = 16 (four chirality centres). However, as a result of constitutional symmetry twelve of the theoretically possible isomers are in fact six pairs of identical compounds. Therefore only ten stereoisomers are possible lRyVRy2RyTR lRyVRy2Sy2 S ... 

As atoms can be numbered in ways, up to n different bond lists can be given for a single molecule. A program which indexes the atoms such that a unique bond list results has been developed24. This program also finds atoms which are constitutionally equivalent, i.e., atoms which are equivalent because of global or local constitutional symmetry in the molecule. 

Accordingly an EMB(A) is representable by up to n distinct but equivalent fee-matrices [31]. One of these fee-matrices of the EMB(A) may be chosen as the canonical representation, e.g. by the algorithm CANON [32]. Note that any constitutional symmetries in EMB(A) are also detected by CANON. 

Jochum, C. and Gasteiger, J. (1977). Canonical Numbering and Constitutional Symmetry. J.Chem.Inf.Comput.ScL, 17,113-117. 

Ivanciuc, O. (2003b) Canonical numbering and constitutional symmetry, in Handbook of Chemoinformatics, Vol. 1 (ed. J. Gasteiger), Wdey-VCH Verlag GmbH, Weinheim, Germany, pp. 139-160. 

Schubert, W. and Ugi, I. (1978) Constitutional symmetry and rmique descriptors of molecules. 

See, for example, M. Razinger, K. Balasubramanian, and M. E. Munk,/. Chem. Inf. Comput. Sci., 33, 197 (1993). Graph Automorphism Perception Algorithms in Computer-Enhanced Structure Elucidation. C. Jochum and J. Gasteiger, J. Chem. Inf. Comput. Sci., 17, 113 (1977). Canonical Numbering and Constitutional Symmetry. See also Ref. 7... 

Constitutional symmetry is important for the interpretation of NMR and ESR spectra, and computer-assisted structure elucidation systems use this information. 

Artificial intelligence systems (see Artificial Intelligence in Chemistry) for synthesis design use canonical codes and constitutional symmetry information to generate and evaluate reaction paths (see Synthesis Design). 

The problem of canonical coding, graph isomorphism, and graph automorphism has both mathematical and chemical significance. The mathematical formulation of the problem is briefly set out below, and some cormections with the chemical counterpart are presented. In the subsequent sections, the main algorithms used in chemistry for canonical coding of molecular graphs and constitutional symmetry perception are presented and compared. 

From the above properties of the permutations E, A, B, and C, one may conclude that they form the automorphism group of the graph (5). This automorphism group describes all constitutional symmetry relationships of isopropylcyclopropane. 

This number can be further reduced by the use of more powerful vertex invariants, like the distance sum. The distance sum, DS, of a vertex i is the sum of the topological distances from vertex i to all other vertices in the molecular graph. The partitioning in the DS equivalence classes of atoms from 4-ethyloctane is presented in (10), showing that only two atoms have identical DS values. Using this partitioning, the constitutional symmetry of 4-ethyloctane can be determined with 1 1 1 1 1 1 1 1 2 = 2 permutation labelings. 

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