Representation unambiguous

A nomenclature or notation is called unambiguous if it produces only one structure. However, the structure could be expressed in this nomenclature or notation by more than one representation, all producing the same structure. Moreover, uniqueness" demands that the transformation results in only one - unique -structure or nomenclature, respectively, in both directions. 

A special extension of SMILES is USMILES (sometimes described as Broad SMILES) [23-25]. This Unique SMILES of Daylight is a canonical representation of a structure. This means that the coding is independent of the internal atomic numbering and results always in the same canonical, unambiguous, and unique description of the compound, granted by an algorithm (see Section 2.5.2). 

If the indexing of the atoms is changed, the CT will have a different appearance. Thus, the representation of a chemical structure in a CT is unambiguous but not unique, which can only be achieved by canonicalization (see below). 

Figure 5 Schematic representation of a Cartesian dynamics protocol starting from random torsion angles. The weights for non bonded (i.e., van der Waals) interactions, unambiguous distance restraints, and ambiguous distance restraints are varied independently. The covalent interactions are maintained with full weight, co.aie - for the entire protocol. Weights for other experimental terms may be varied in an analogous way. Coupling constant restraints and anisotropy restraints are usually used only in a refinement stage.

It is not currently possible to examine the configuration of the adsorbed species unambiguously. However, since thermodynamic arguments do not require a specific model at the molecular level, it is still possible to analyze equilibrium data within a thermodynamic context. Most surface reactions are inferred from experimental observations of reaction stoichiometries and perhaps only in a limited range of T. Consequently, the choice of specific surface species is dependent on two considerations (1) the need to explain the observed measurements in terms of reaction stoichiometries, and (2) the selection of a model to allow the representation of metal/ surface site interaction intensities. 

Protein X-ray crystallography gives a snapshot of the structure of a protein as it exists in a crystal. This technique provides a complete and unambiguous three-dimensional (3-D) representation of a protein molecule. It is important to note that the model generated from a crystallographic study is a static or time-averaged view of the molecular structure. Information about molecular motions can be obtained from precise diffraction data however, the motions of molecules within a crystal are usually severely restricted in comparison to the motions of molecules in solution. 

Unfortunately, our present understanding of sorption kinetics is inadequate to allow unambiguous representation of the sorption-desorption process. Clearly the states of sorbed pesticides include fractions which vary in their lability with respect to desorption (9. 10, 21). The fraction of the sorbed molecules in relatively labile and non-labile states is a function of the nature of the pesticide and sediment and the time of contact between the sediment and pesticide solution. 

A homopolymer that can be represented by a source-based name can usually be given a completely unambiguous structure-based representation, and such a representation should therefore be ideally accompanied by a structure-based name. A source-based name was therefore deemed redundant in these cases. 

Graphic representations (chemical formulae) of macromolecules are used extensively in the scientific literature on polymers including lUPAC documents on macromolecular nomenclature. This document establishes rules for the unambiguous representation of macromolecules by chemical formulae. The rules apply principally to synthetic macromolecules. Insofar as is possible, these rules are consistent with the formulae given in lUPAC documents [2-4] and they also cover the presentation of formulae for irregular macromolecules [5], copolymer molecules [1, 6] and star macromolecules. 

Clearly, for a one-dimensional representation the character and the full matrix are the same thing. Hence, the incomplete projection operator is complete in these cases, and will provide the appropriate SALC unambiguously and automatically. Let us illustrate by asking what SALCs can be formed by the Is orbitals of the four hydrogen atoms in ethylene. 

It is now necessary to look for a subgroup of Oh such that each of the representations Alg, ER, TlR, and T2r of Oh goes over into a different onedimensional representation or sum of one-dimensional representations of the subgroup. Unless these are all different, it will not be possible to obtain a complete and unambiguous result. Inspection of the correlation table for Oh in Appendix IIB shows that the subgroups Q>/, and C2v will be satisfactory. We shall use Cy, here the reader may obtain practice in applying the method by using C2v to verify the results. In the chart above we have listed under each of the Olt representations the Qy, representations that correspond to it as obtained from the correlation table. 

The representation is unambiguous since it corresponds to one and only one substance, but it is not unique because alternative numberings of the connection table would result in different representations for the same chemical substance (the connection table representation is discussed in more detail below). In addition to being categorized according to their uniqueness and ambiguity, chemical substance representations commonly used within computer-based systems can be further classified as systematic nomenclature, fragment codes, linear notations, connection tables, and coordinate representations. 

Eakin [13] describes the chemical structure information system at Imperial Chemical Industries Ltd., where registration is based on Wiswesser Line Notation. For connection tables, the unique, unambiguous representation is derived automatically, i.e., a single, invariant numbering of the connection table is algorithmically derived. 

With the variety of chemical substance representations, i.e., fragment codes, systematic nomenclature, linear notations, and connection tables, a diversity of approaches and techniques are used for substructure searching. Whereas unique, unambiguous representations are essential for some registration processes, it is important to note that this often cannot be used to advantage in substructure searching. With connection tables, there is no assurance that the atoms cited in the substructure will be cited in the same order as the corresponding atoms in the structure. With nomenclature or notation representation systems, a substructural unit may be described by different terms or... 

The conversion from a connection table to other unambiguous representations is substantially more difficult. The connection table is the least structured representation and incorporates no concepts of chemical significance beyond the list of atoms, bonds, and connections. A complex set of rules must be applied in order to derive nomenclature and linear notation representations. To translate from these more structured representations to a connection table requires primarily the interpretation of symbols and syntax. The opposite conversion, from the connection table to linear notation, nomenclature, or coordinate representation first requires the detailed analysis of the connection table to identify appropriate substructural units. The complex ordering rules of the nomenclature or notation system or the esthetic rules for graphic display are then applied to derive the desired representation. 

We noted in Chapter 6 that the seniority quantum number v in reduction chain (14.38) unambiguously classifies the irreducible representations of S P4i+2 group. Then one may well ask how can the earlier group-theoretical schemes include a rotation group defined by the operators of quasispin angular momentum ... 

We conclude, therefore, that the identification of A and E with the concentration of the surface precursor to product formation and the energy barrier to a bond redistribution process in the dominant step of a surface reaction, respectively, is not always or necessarily justified and may not be a realistic representation of the kinetics of a surface change. More direct information concerning the concentrations and reactivities of surface intermediates is required to substantiate meaningfully the kinetic properties of reactions proceeding on surfaces. Such considerations also call into question the application of the transition state theory to systems for which the transition complex has not been characterized unambiguously. 

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