Correlation with interatomic distances

The profiles of thermodynamic data plotted in figs 7.1 and 7.2 bear striking resemblances to the plots of ionic radii shown in fig. 6.2. In both situations, there are non-linear trends of data across the transition metal series with maximum deviations occurring for cations with 3 P and 3d8 configurations. Such a similarity suggests that there is a connection between the thermodynamic and crystallographic data. 

In the ionic model, binding energies represent the nett effects of attraction between charges on the anions and central cation, repulsion between the anions and all electrons on the cation, and repulsion between the nuclei. The lattice energy, U0, of a binary ionic solid, such as periclase, may be expressed by the Bom equation, one form of which is 

---

Using the same kind of augmented correlation-consistent basis sets employed in the above coupled cluster methods, but working with the complete active subspace (CASSCF and CASSCF( +1, +2)) approximations to the Cl expansion, Lawson and Harrison101 have investigated the variation with interatomic distance and spatial distribution of the quadrupole moments of P2, S2 and CI2. The a and it contributions to the quadrupole are resolved and the poor results obtained at the SCF level are attributed to the inadequate representation of the it system in the SCF approximation for P2 and S2. 

The quantitative treatment of diffuse scattering was pioneered by Warren [112,136] and successively developed, in several of its many-fold aspects, by many authors [137-151]. A widely used approach consists of the derivation of analytical formulas for the calculation of X-ray diffraction intensity in terms of short-range chemical and/or displacement correlations associated with interatomic distances in the real space. In the hypothesis that short-range correlations are absent, disorder occurs at random, and this leads to a noticeable simplification in the formulas in use for the calculated scattered intensity. 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

This correction of i i for ligancy, together with the bond-number equation and a set of values of the new single-bond metallic radii, provides an improved system of correlating interatomic distances not only in metals and alloys but also in other crystals and molecules. 

Because surface curvature depends on radius and different atoms have different sizes, and because the atomic surface tension depends on atomic number, the atomic surface tensions also include surface curvature effects, which has recently been studied as a separate effect.7 Local surface curvature may also correlate with nearest-neighbor proximity and thus may be implicitly included to some extent when semiempirical atomic surface tensions depend on interatomic distances in the solute. 

Here, as in other branches of inorganic chemistry, interatomic distances show a considerable variation and, although some correlation with bond order is possible, attempts to do so should be regarded with caution.For metals with close-packed structures, the coordination number of any atom is 12 for cubic or hexagonal structures, and 14 (8 plus 6 more neighbors at about 15% further away) for body-centered cubic structures. In general, this number exceeds the number of electrons per atom available for metal-metal bond formation and precludes the formation of localized, two-electron bonds between metal atoms. Bond orders of less than 1 are therefore commonly recorded. For metal clusters, it is necessary to consider the variety of ways in which valence electrons may be utilized in chemical bonding within the Mm... 

Fig. 6.86. Oxygen-oxygen pair correlation function obtained from molecular dynamic simulations on the adsorbed layer of a Pt(100) surface. Ax and Ay are the projections of the interatomic distances in the x- and indirections, respectively. They reflect the positions of the oxygen atoms on the top site of the platinum lattice, and the pronounced form of the peaks refers to their relatively small displacement. (Reprinted from E. Spohr, G. Toth, and K. Heinzinger, Electrochim. Acta 41 2131, copyright 1996, Fig. 10a, with peimission from Elsevier Science.)...

The first quantitative estimate of the rotational diffusion tensor for simple molecules was accomplished by Grant et al. [163], By solving the Woessner equations, they were able to show e.g. for trans-decalin that the molecule rotates preferentially like a propeller, i.e. about the axis perpendicular to the plane of the molecule. The values given as a measure of the rotational frequencies do not correlate with the moments of inertia, but instead with the ellipticities of the molecule as defined [163]. They are accessible from the ratios of the interatomic distances perpendicular to the axes of rotation, and can be adopted as a measure of the number of solvent molecules that have to be displaced on rotation about each of the three axes. 

On the other hand, a more practical approach is to analyze the various parameters with respect to their influence on the anomalous multiplets. According to this procedure Li and Reid (1990) could show that taking into account only the parameters G410Aq, a pronounced improvement for the description of the 2H(2)n/2 multiplet of Nd3+ could be achieved. To study the dependence of correlation effects on the interatomic distances, Jayasankar et al. (1993) analyzed spectroscopic data for LaCbiNd3"1" at pressures up to 10 GPa. Using the superposition model, they could derive the distance dependences of the intrinsic parameters B4 —4... 

---