The 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. 

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... 

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). 

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

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. 

The similar property principle implies that the NNs of a bioactive reference structure are also likely to possess that activity. If we assume that the NNs are not just likely to be active but actually are active, then we can use GF to combine the results of similarity searches that use them as the reference structures, using the strategy summarized in Fig. 2. 

The relevant polynomial corresponding to the reference structure is called the acyclic (77JA1692,77MI4) or reference (76JA2750,76JA6840) polynomial and since r(s) = 0, it has the form... 

The energy of the homodesmotic reaction does not exclusively reflect the effect of cyclic (bond) delocalization. The reference structure is hypothetical and one cannot write the equation of a reaction, where a cyclic and an acyclic structure participate, for which the difference between the energies of products and reactants was determined by a single factor, namely, aromatic stabilization (antiaromatic destabilization) (75TCA121). 

The electronic couplings in DNA r-stacks are very sensitive to conformational changes [31]. CT matrix elements were found to be very responsive to variations in the mutual positions of base pairs. As an example, let us compare the electronic couplings calculated for different conformations of the duplex [(GC),(GC)] (Table 4) [41]. In addition to the reference structure with a base-pair arrangement as in ideal B-DNA, we studied 12 distorted configurations each of them differed from the reference by a single step pa-... 

This section reviews the molecular shape descriptors developed by Amoore, Allinger, Simon et al. and Testa and Purcell. The illustrative examples discussed refer to the odour similarity and cardiotoxic aglycones. One has stressed the methods based on the reference structure because, correctly formulated, these methods seem to offer promising perspectives to model the steric effects in biological systems. Finally, a short discussion of possible connections between steric and other substituent constants (relevant in the context of multicollinearity in QSAR) is included. 

The correlations obtained with the intensity of the odour of fatty acids (the reference structure is the isovaleric acid) were U) not nearly as good as one would hope for . 

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an... 

Finally, incoherent interfaces can be regarded as the limiting case of semicoherent interfaces for which the density of dislocations is so great that their cores overlap and that essentially all of the coherence characteristic of the reference structure has been destroyed. The cores of incoherent interfaces are therefore continuous slabs of bad material, and consequently the interfaces lack long-range order. 

Scheme 23. Vertical Resonance Energy of the Reference Structure, B(R), for Benzene and Its Relation to the Vertical Energy of Hexatriene, B(h)...

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