Interatomic distance information

The second measure is that reported recently by Bemis and Kuntz (131). This again uses interatomic distance information, but in a rather different way in that a structure is decomposed into all possible three-atom substructures (so that a molecule containing N heavy atoms will produce N N — 1) N — 2)/6 such substructures). The procedure represents a molecule by a frequency... 

The similarity between two structures is calculated by means of an associated coefficient, usually the Tanimoto coefficient. Valence angles are 2D, and interatomic distances are ID. Most of the 3D searches of data bases have concentrated on interatomic distance information, e.g., hash codes for all distinct triplets of nonhydrogen atoms in pairs of isomeric structures. If one uses frequency distributions instead of hash codes, one can also compare nonisomeric molecules. 

Most of the 3D similarity measures that have been described involve the use of interatomic distance information and do not take conformational flexibility into account, other than through storing a compound in the database in... 

The 3D similarity measures described thus far are all based on interatomic distance information. Bath et al. " have described two measures for 3D similarity searching that are based on angular information and have compared the effectiveness of searches using these measures with those of the atom-triplet measures described in the previous section. It should be noted that all of these angular and atom-triplet measures make use only of geometrical information, that is, distances and angles between the constituent atoms of the pairs of molecules that are being compared, and do not involve chemical information such as atomic type, polarity, hydrophobicity, etc. 

Full structure search can be developed by using similar approaches to those employed in the case of 2D structure search. Thus, some topological indices can be modified in such a way that they include geometrical information. For example, the global index given by Eq. (4) can be modified to Eq. (11), where are real interatomic distances. 

The description of the atomic distribution in noncrystalline materials employs a distribution function, (r), which corresponds to the probability of finding another atom at a distance r from the origin atom taken as the point r = 0. In a system having an average number density p = N/V, the probability of finding another atom at a distance r from an origin atom corresponds to Pq ( ). Whereas the information given by (r), which is called the pair distribution function, is only one-dimensional, it is quantitative information on the noncrystalline systems and as such is one of the most important pieces of information in the study of noncrystalline materials. The interatomic distances cannot be smaller than the atomic core diameters, so = 0. 

The metric matrix is the matrix of all scalar products of position vectors of the atoms when the geometric center is placed in the origin. By application of the law of cosines, this matrix can be obtained from distance information only. Because it is invariant against rotation but not translation, the distances to the geometric center have to be calculated from the interatomic distances (see Fig. 3). The matrix allows the calculation of coordinates from distances in a single step, provided that all A atom(A atom l)/2 interatomic distances are known. 

EXAFS is a nondestructive, element-specific spectroscopic technique with application to all elements from lithium to uranium. It is employed as a direct probe of the atomic environment of an X-ray absorbing element and provides chemical bonding information. Although EXAFS is primarily used to determine the local structure of bulk solids (e.g., crystalline and amorphous materials), solid surfaces, and interfaces, its use is not limited to the solid state. As a structural tool, EXAFS complements the familiar X-ray diffraction technique, which is applicable only to crystalline solids. EXAFS provides an atomic-scale perspective about the X-ray absorbing element in terms of the numbers, types, and interatomic distances of neighboring atoms. 

Three years ago it was pointed out2 that observed values of interatomic distances provide useful information regarding the electronic structures of molecules and especially regarding resonance between two or more valence bond structures. On the basis of the available information it was concluded that resonance between two or more structures leads to interatomic distances nearly as small Us the smallest of those for the individual structures. For example, in benzene each carbon-carbon bond resonates about equally between a single bond and a double bond (as given by the two Kekul6 structures) the observed carbon-carbon distance, 1.39 A., is much closer to the carbon-carbon double bond distance, 1.38 A., than to the shrgle bond distance, 1.54 A. 

It is seen that a small amount of double bond character causes a large decrease in interatomic distance below the single bond value, whereas only a small change from the double bond value is caused by even as much as fifty per cent, single bond character.8 In consequence, the interatomic distance criterion for resonance provides quantitative information only through about one-half of the bond character region. 

The determination of values of interatomic distances in molecules has been found to provide much information regarding electronic structure, especially in the case of substances which resonate among two or more valence-bond structures. The interpretation of interatomic distances in terms of the types of bonds involved is made with use of an empirical function formulated originally for single bond-double bond resonance of the carbon-carbon bond.1 There are given in this... 

Because of- the similarity in the backscattering properties of platinum and iridium, we were not able to distinguish between neighboring platinum and iridium atoms in the analysis of the EXAFS associated with either component of platinum-iridium alloys or clusters. In this respect, the situation is very different from that for systems like ruthenium-copper, osmium-copper, or rhodium-copper. Therefore, we concentrated on the determination of interatomic distances. To obtain accurate values of interatomic distances, it is necessary to have precise information on phase shifts. For the platinum-iridium system, there is no problem in this regard, since the phase shifts of platinum and iridium are not very different. Hence the uncertainty in the phase shift of a platinum-iridium atom pair is very small. 

The oldest and most widely used structural restraints in NMR spectroscopy are distance restraints derived from NOE experiments [1]. Transient NOE, 2D NOESY and ROESY spectra provide valuable information for interatomic distances up to 5 A that will be discussed in the following. 

Table 8.53 shows the main features of XAS. The advantages of EXAFS over diffraction methods are that the technique does not depend on long-range order, hence it can always be used to study local environments in amorphous (and crystalline) solids and liquids it is atom specific and can be sensitive to low concentrations of the target atom (about 100 ppm). XAS provides information on interatomic distances, coordination numbers, atom types and structural disorder and oxidation state by inference. Accuracy is 1-2% for interatomic distances, and 10-25 % for coordination numbers. 

When specifying atomic coordinates, interatomic distances etc., the corresponding standard deviations should also be given, which serve to express the precision of their experimental determination. The commonly used notation, such as d = 235.1(4) pm states a standard deviation of 4 units for the last digit, i.e. the standard deviation in this case amounts to 0.4 pm. Standard deviation is a term in statistics. When a standard deviation a is linked to some value, the probability of the true value being within the limits 0 of the stated value is 68.3 %. The probability of being within 2cj is 95.4 %, and within 3ct is 99.7 %. The standard deviation gives no reliable information about the trueness of a value, because it only takes into account statistical errors, and not systematic errors. 

The basic intent behind any EXAFS data analysis is to be able to extract information related to interatomic distances, numbers, and types of backscattering neighbors. In order to accomplish this, there are a number of steps involved in the data analysis, and these include ... 

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