Reference structure

Redundant, isomorphic structures have to be eliminated by the computer before it produces a result. The determination of whether structures are isomorphic or not stems from a mathematical operation called permutation the structures are isomorphic if they can be interconverted by permutation (Eq. (6) see Section 2.8.7). The permutation P3 is identical to P2 if a mathematical operation (P ) is applied. This procedure is described in the example using atom 4 of P3 (compare Figure 2-40, third line). In permutation P3 atom 4 takes the place of atom 5 of the reference structure but place 5 in P2. To replace atom 4 in P2 at position 5, both have to be interchanged, which is expressed by writing the number 4 at the position of 5 in P. Applying this to all the other substituents, the result is a new permutation P which is identical to P]. 

Comparisons among the four reactions of this study could be made by defining one reaction (reaction 1, say) as the standard reaction and relating the empirical changes in temperatures for the other three reactions to the empirical changes in temperatures for the standard reaction. If reaction 1 is defined as the standard reaction and if entry 5 (Table I) is chosen as the reference structure, experimental T minus T(reference) for reaction 1 versus T minus T(ref) for the o her three reactions can be correlated. 

Similarity searching requires the specification of an entire molecule, called the target structure or reference structure, rather than the partial structure that is required for substructure searching. The target molecule is characterized by a set of structural features, and this set is compared with the corresponding sets of features for each of the database structures. Each such comparison enables the calculation of a measure of similarity between the... 

In references Structure and Bonding is abbeviated Struct Bond and is cited as a journal. 

The results of the various semi-empirical calculations on the reference structures contained within the JSCH-2005 database (134 complexes 31 hydrogen-bonded base-pairs, 32 interstrand base pairs, 54 stacked base pairs and 17 amino acid base pairs) are summarised in Table 5-10. The deviations of the various interaction energies from the reference values are displayed in Figure 5-5. As with the S22 training set, the AMI and PM3 methods generally underestimate the interactions whereas the dispersion corrected method (PM3-D) mostly over-estimates the interactions a little. Overall the PM3-D results are particularly impressive given that the method has only... 

FhuA and FepA will prove to be the reference structures for a large group of bacterial outer-membrane transporters that take up bacterial Fe3+-siderophores, Fe3+ released from host transferrin and lactoferrin, haem, and haem released from haemoglobin and haemopexin. It is assumed that all iron sources are transported... 

The concept of scaffold hopping invokes the use of computational tools that when given a reference structure can propose a different structure likely to have similar biological properties. A comprehensive scaffold database to serve for scaffold-hopping purposes has been created and is publicly available [59]. The database was based on the analysis of more than 4 million compounds to identify 241,824 unique scaffolds. In addition to the scaffold structure, the database contains information about the original molecule and its biological activity as well as its calculated physicochemical properties. 

In this section the salts based on metallocenium cations and metal bisdichalcogenate anions will be reviewed according to the previously referred structural classification. After referring to the general characteristics of the crystal structures the supramolec-ular features will be correlated with the magnetic properties. 

As expected, the nitronate fragment is planar in all nitronates. The C=N bond is shortened (in comparison with standard C—N bond), and its length is similar to the C=N bond lengths in reference structures (86) and (87). Two... 

For consistency of comparisons, the four tabulated structures were assigned as reference structures ( NRTSTR keylist) with full density-matrix averaging (NRTFDM keyword) for each species. 

The randomly distributed sheet clearly exhibits areas of low and high density but it still remains a good target and a unique reference structure in making paper. The small scale non-uniformities of paper structure are particularly important in their influence on pore size distribution and the distribution of areal mass density, and both of these properties have an influence on mechanical and other properties of the final sheet. 

A derivative structure can be considered as being obtained from a reference structure by ordered atomic substitution, subtraction or addition processes or by unit cell distortions (or both). The opposite kinds of transformation correspond to the so-called degeneration processes. A derivative structure has fewer symmetry operations than the reference structure (a degenerate structure has more). A derivative structure has either a larger cell or a lower symmetry (or both) than the reference structure. 

In the preceding paragraphs examples of a number of so-called superstructures have been considered. Generally, it has been observed that a derivative structure has fewer symmetry operations than the reference structure it has either a larger cell or a lower symmetry (or both) than the reference structure. Typically the passage from the reference structure to the derivative structure (superstructure) may be related to the fact that a set of equipoints of a certain structure (the reference one) has to be subdivided into two (or more) subsets in order to obtain the description of the other structure. The structure of the Cu type (cF4 type), for instance, corresponds to 4 Cu atoms in the unit cell, placed in 0, 0, 0 14, 14, 0 14, 0, 14 0, 14, 14, whereas in the cP4-AuCu3 type structure the same atomic sites are subdivided, in another space group, into two sets with an ordered distribution of the two atomic species (1 Au atom in 0, 0, 0 and 3 Cu atoms in 14, 14, 0 14, 0,14 0,14,14). 

Electron-precise, electron-deficient and electron-rich clusters. A cluster classification often adopted in several books, and related to the rules previously presented, corresponds to a subdivision into three categories electron-precise, electron-deficient and electron-rich types. The electron-precise clusters may be considered as reference structures. 

Cu-derivative, substitutional and interstitial superstructures. As discussed in 3.8.1 ff, the Cu-type structure is also an important reference structure because it may be considered the ancestor of several derivative structures. 

The square net layer sequence of TiAl3 is shown in Fig. 7.47 it is compared with those of AuCu3 (and of Cu as reference structures) and of ZrAl3. 

Data for the reference structure of Y3Fe5012 (= Y3Fe2 Fe3012) (Hyde and... 

Fio. 15. Reference structures for the transition state for the adsorption of 4-substituted methylenecyclohexanes. 

The planar form of phosphole is a first-order saddle point on the potential energy surface, 16—24 kcal/ mol above the minimum (at different levels of the theory). ° (The calculated barriers are the highest at the HF level, which underestimates aromatic stabilization of the planar saddle point, while the MP2 results are at the low end.) It has been demonstrated by calculation of the NMR properties, structural parameters, ° and geometric aromaticity indices as the Bird index ° and the BDSHRT, ° as well as the stabilization energies (with planarized phosphorus in the reference structures) ° and NIGS values ° that the planar form of phosphole has an even larger aromaticity than pyrrole or thiophene. 

---