Interatomic distances, between

We can now proceed to the generation of conformations. First, random values are assigne to all the interatomic distances between the upper and lower bounds to give a trial distam matrix. This distance matrix is now subjected to a process called embedding, in which tl distance space representation of the conformation is converted to a set of atomic Cartesic coordinates by performing a series of matrix operations. We calculate the metric matrix, each of whose elements (i, j) is equal to the scalar product of the vectors from the orig to atoms i and j ... 

Single-Stack Acceptor. Simple charge-transfer salts formed from the planar acceptor TCNQ have a stacked arrangement with the TCNQ units facing each other (intermolecular distances of ca 0.3 nm (- 3). Complex salts of TCNQ such as TEA(TCNQ)2 consist of stacks of parallel TCNQ molecules, with cation sites between the stacks (17). The interatomic distance between TCNQ units is not always uniform in these salts, and formation of TCNQ dimers (as in TEA(TCNQ)2) and trimers (as in Cs2(TCNQ)Q can lead to complex crystal stmctures for the chainlike salts. 

Inleralomic distances vary with the type of bond and the nature of the other atoms or groups attached to the bonded atoms. For example, the formally single-bonded C-C distance varies from 146pm in Me-CN to 163.8pm in Bu PhC-CPhBu and 167 pm in 3,5-Bu j-C6H3)2C-C(QH3-3,5-Bu )3 and (CF3>2(4-FCeH4)C-C(C6H4-4-F)(CF3)2. Some typical examples are in Fig. 8.14. Note that because of the breadth of some of these ranges the interatomic distance between quite different pairs of atoms can be identical. For example, the value 133 pm includes C-F, C-O, C-N and C-C likewise the value of 185 pm includes C-Br, C-S, C-Se, C P and C Si. The conventional... 

Tellurium has only one crystalline form and this is composed of a network of spiral chains similar to those in hexagonal Se (Fig. 16.1c and d). Although the intra-chain Te-Te distance of 284 pm and the c dimension of the crystal (593 pm) are both substantially greater than for Scjt (as expected), nevertheless the closest interatomic distance between chains is almost identical for the 2 elements (Te Te 350 pm). Accordingly the elements form a continuous range of solid solutions in which there is a random... 

The niobium atom has a slightly distorted octahedral coordination. Interatomic distances between the niobium atom and the two oxygen atoms in trans positions, O-Nb-O are 1.81 and 2.14 A. The niobium atom is shifted from the base plane of the octahedron by 0.23 A, and this shift, in adjacent chains, is in opposite directions. Pakhomov and Kaidalova [204] concluded that the shorter Nb-O bond (1.81 A) is an intermediate between a single and double bond. 

Although (15.1) and (15.2) hold strictly only for a liquid in equilibrium with its vapor, they have been commonly apphed also to solid materials, in particular for describing nanoparticle sintering (see the discussion in [Campbell et al., 2002]). However, a number of comphcations must be considered for solid materials. First of all, y cr, since for a sohd a change in the surface area A can be reahzed either by increasing the number of surface atoms without changing the interatomic distances between them (this is related to the first term in (15.3)) or by introducing a strain (this is related to the second term in (15.3)) ... 

Table 11.1 Distances between adjacent atoms and bond angles in structures of the a-As, a-Se, a-Po and /3-Po type, rfj = bond distance, d2 = shortest interatomic distance between layers or chains distances in pm, angles in degrees...

The previous literature on the effects of partial covalence on interatomic distances is contradictory. Pauling (1960) cites the examples of CuF, BeO, AIN, and SiC where observed bond lengths are shorter than the sum of the covalent radii. He attributes these differences to partial ionic character and thus implies that partial ionic character shortens covalent bonds. This conclusion is in accord with the Schoemaker— Stevenson (1941) rule Dab = a + pb—C nx— b where > interatomic distance between A and B, rx and r = covalent radii of A and B, a and xb = electronegativity of A and B and C = constant. 

Fig. 14 Dependence of relative reactivity on (minimum) interatomic distance between the electrophilic centre and the carboxyl oxygen, for (a) sulphonamides [76] and (b) malonate half-esters [77]. Reprinted with permission from Jager et al. (1984). Copyright 1984 American Chemical Society.

The principle source of experimental conformational data in an NMR structure determination is constraints on short interatomic distances between hydrogen atoms obtained from NMR measurements of the nuclear Overhauser effect (NOE). NOEs result from cross-relaxation mediated by the dipole-dipole interaction between spatially proximate nu-... 

As mentioned in the previous paragraphs, to define an atomic environment they used the maximum gap rule. The Brunner-Schwarzenbach method was considered, in which all interatomic distances between an atom and its neighbours are plotted in a histogram such as those shown in Fig. 3.17. The height of the bars is proportional to the number of neighbours, and all distances are expressed as reduced values relative to the shortest distance. In the specific case of CsCl, having a = 411.3 pm,... 

The participation of van der Waals forces in inclusion-complex formation is also found to be consistent with crystal structure analyses. Interatomic distances between the guest and the cyclodextrin thus determined are characteristic of van der Waals interactions. Hydrogen bonding between the guest and the hydroxyl groups of the cyclodextrin has also... 

In this formula, m and n are the number of ligand and receptor atoms, respectively r is the interatomic distance between atoms i and j the q s are the point charges on the atom, and A and B are adjustable van der Waals repulsion and attraction parameters, and D is the dielectric function. They assumed that this scoring function could account for hydrogen bond energies in the electrostatic term. 

EXAFS measurements on AU55 prepared by Schmid [39,41], as well as on independently prepared samples [40], have shown clearly that there is only a single interatomic distance between the gold atoms in this material, a distance about 4% shorter than that in bulk gold. 

Most of the examples of H- F bonds reported in the hterature concern intramolecular hydrogen bonds (fluoroalcohols, fluorophenols, and fluoroanihnes) (Figure 1.5). At this point, it is important to recall that the criterion to determine the existence of hydrogen bond with F is an interatomic distance between 2.0 and 2.3 A, equal to or less than the sum of the atomic radii. 

Covalent radii are calculated from half the interatomic distance between two singly bonded like atoms. For diatomic molecules such as F2, this is no problem, but for other elements, such as carbon, which do not have a diatomic molecule, an average value is calculated from a range of compounds that contain a C-C single bond. 

The atomic radius of an element is considered to be half the interatomic distance between identical (singly bonded) atoms. This may apply to iron, say, in its metallic state, in which case the quantity may be regarded as the metallic radius of the iron atom, or to a molecule such as Cl2. The difference between the two examples is sufficient to demonstrate that some degree of caution is necessary when comparing the atomic radii of different elements. It is best to limit such comparisons to elements with similar types of bonding, metals for example. Even that restriction is subject to the drawback that the metallic elements have at least three different crystalline arrangements with possibly different coordination numbers (the number of nearest neighbours for any one atom). 

The carrier can move, either by excitation out of this self-trapped state into the conduction band, or by hopping to a neighbouring site. For hopping to occur, the interatomic distances between two adjacent pairs must be equal, as illustrated in Fig. 2.3(b). Then the electron can move freely from one such pair to the other. Possibly the electron can move backwards and forwards several times before the system relaxes the transition is then adiabatic. Alternatively the chance of transfer in the time during which the configuration persists may be small. 

Some of the basic experiments with UPD have been carried out with Ag onto Au (hkl).94 This is because the radii of Ag and Au atoms are almost the same, so that the interpretation does nothave to involve a steric displacement effect. Figure 7.143 shows the underpotential deposition of Ag on Au (100). The A and D marks on the figure denote a number of underpotential processes. Using STM to study this system indicates that at AE> 650 mV, a stable Ag surface is formed with normal interatomic distance. Between 200 < AE < 550 mV, stable domains exist, but now (see Fig. 7.144) they are expanded in respect to their interatomic distance and in comparison with those formed at AE > 650. 

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