Interatomic separation

Wheatley R J and Meath W J 1993 Dispersion energy damping functions, and their relative scale with interatomic separation, for (H,He,Li)-(H,He,Li) interactions Mol. Phys. 80 25... 

What is the interatomic separation at the minimum potential energy For convenience, define the minimum potential energy of the system as zero at the minimum of the potential well. 

E10.6 For the diatomic molecule Na2, 5 = 230.476 J-K-1-mol" at T= 300 K, and 256.876 J-K-,-mol-1 at T= 600 K. Assume the rigid rotator and harmonic oscillator approximations and calculate u, the fundamental vibrational frequency and r, the interatomic separation between the atoms in the molecule. For a diatomic molecule, the moment of inertia is given by l pr2, where p is the reduced mass given by... 

FIGURE 3.2 Track formation according to Mott (1930). Simultaneous excitation of atoms at 1 and 2 has negligible probability in second-order perturbation theory unless the interatomic separation vector R is well aligned with the incoming and outgoing momentum vectors of the incident particle. Reproduced from Mozumder (1969), by permission of John Wiley Sons, Inc. ... 

In this compound, no intrachain D+A short contacts were found and the closest interatomic separation between the anion and the Cp ring corresponds to Ni... C contacts (cl) exceeding the sum of the van der waals radii, dw, by 11 %. In this salt the closest interchain arrangements are similar and present an out-of-registry disposition (pairs I—II and I-IV). This arrangement is shown in Fig. 8b. The closer interchain contacts (d2) involve C atoms from the Me groups of the cations and S atoms of the anions, with a separation exceeding dw by 8%. 

The crystal structure of [Fe(Cp )2][Ni(bds)2], as the salts described in Sect. 3.4.1, consists of 2D layers composed of parallel type IVa chains, which are separated by anion layers [15]. Besides contacts involving H atoms, no other short contacts were found in the structure. Within the IVa chains, one of the Cp fragments of the cation sits above a C6 ring of the ligand, while the second one is displaced towards the center of the anion. For the first Cp the closest D+A interatomic separation (C C) exceeds dw by 8%, while for the second Cp the closest D+A contact (C—Se) exceeds c/w by 4%. The D+D+A chains are relatively isolated and the solvent is located on cavities between the chains. No close interionic interlayer distances were observed involving molecules in the D+D+A layers and the anion layers or between the anions in the anionic layers. 

Figure 3. A schematic diagram describing the interatomic separations of the copper centers and their coordinating residues (see also Table 3.)...

The dispersion interactions are weak compared with repulsion, but they are longer range, which results in an attractive well with a depth e at an interatomic separation of am n = 21/6a. The interatomic distance at which the net potential is zero is often used to define the atomic diameter. In addition to the Lennard-Jones form, the exponential-6 form of the dispersion-repulsion interaction,... 

Fig. 2.6-8. Structurally characterized polybismuth cations and their basic (averaged) structural parameters. Gray bonds indicate long interatomic separations still below the sum of the van der Waals radii and symmetries given are idealized.

Rieke proteins, 47 337, 347-355 superoxide dismutases and, 45 129 Photosynthetic bacteria, 2[4Fe-4S] and [4Fe-4S] [3Fe-4S] ferredoxins, 38 255-257 Photosystem 1, 38 303-304 Pa/Fb proteins, 38 262-263 reaction center X proteins, single [4Fe-4S] ferredoxins cluster bridging two subunits, 38 251-252 Photosystem II, 46 328 interatomic separations, 33 228 mechanisms for water oxidation, 33 244-247... 

Solution According to Eq. (5.5), the elastic modulus, E, is proportional to the stiffness of the theoretical springs that model the bonds between atoms in the solid, Sq. According to Equation (5.1), So is in turn proportional to the second derivative of the potential energy function, U, with respect to interatomic separation distance, r. 

Notice that the stiffness is the slope (first derivative) of the force versus interatomic separation distance plot in the vicinity of ro, as shown in Figure 1.3. So, for small deformations (i.e., r ro) we can relate the stiffness to the applied force, F ... 

Figure 5.37 Sine-wave representation of stress variation with interatomic separation distance for two atomic planes. From Z. Jastrzebski, The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Herre and Richter (20) studied liquid B203 at 450°C and 600°C. At these temperatures, only two distinct maxima corresponding to interatomic separations r = 1.38 A (B—O) and 2.40 A (0—O) are found. These values are identical to those found for the solid glass and indicate that at least up to 600°C, the basic structural unit, probably BO i, is still unchanged. The other maxima at larger values of r observable at room temperature have... 

Fig. 6.7 Interatomic pair potentials for (a) Na, (b) Mg, and (c) Al as a function of the interatomic separation in units of the Wigner-Seitz radius / ws. The positions of the fee first and bcc first and second nearest neighbours are marked. Since fee and ideal hep structures have identical first and second nearest neighbours, their relative structural stability is determined by the more distant neighbours marked in the figures. (After McMahan and Moriarty (1983).)...

The average, interatomic separation of 354 pm is somewhat larger than the interplanar separation. 

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