Ionization radii bond order

An unexpected feature of Table 5.1 is the remarkable similarity between the energies calculated from the characteristic radius rc and those calculated from the ionization radius r0, for the same interactions, but with bond orders increased by unity. It means that the steric factor which is responsible for the increase in bond order i.e. screening of the internuclear repulsion) is also correctly described by an adjustment to r o to compensate for modified valence density. Calculating backwards from first-order D0 = 210 kjmol-1, an effective zero-order C-C bond length of 1.72 A is obtained. 

With the relationship between ionization radius and bond order in hand, the calculation of covalent interaction parameters becomes an almost trivial exercise. The common volume, e, between overlapping spheres of radius tq at characteristic separations d for given bond order, and considered proportional to dissociation energy, varies in a quantized fashion similar to d. This allows definition of a dimensionless dissociation energy D = Dro K, as explained in the paper on Covalent Interaction (see p. 93), AT is a dimensional constant. Noting the connection of e with spherical volume, one looks for a dependence of the type... 

Keywords Bond order Dipole moment Force constant General covalence Ionization radius Golden ratio... 

For ease of reference, we tabulate atomic ionization radius (ro), bond order (b) and exponents (n) of lowest-order observed homonuclear interactions in Table 6. 

These results are in line with the small ionization radius of hydrogen, which shows that its entire charge sphere becomes embedded into a larger sphere on molecular formation. The effective point position of the proton relative to the wave structure of the larger atom decides the bond order. 

It is not the purpose of this chapter to produce and present a new force field. We rather want to provide a theoretical basis for MM and therefore also to be able to efficiently produce generic force-field parameters. As it stands, one parameter (ionization radius) is needed to initiate the derivation of all other parameters to model all bond orders of any covalent interaction. It is therefore reassuring to note that the uniform valence density within a characteristic atomic sphere has the same symmetry as the Is hydrogen electron. The first-order covalent interaction between any pair of atoms can therefore be modeled directly by the simple Heitler-London method for hydrogen to predict d, D and kr [44]. The results are in agreement with those of the simpler number-theory simulation [38], which is therefore preferred for general use. 

As an example of a spectrum obtained with a 10 m instrument (grating radius 10m) a recording of the carbon K emission line from the CO2 molecule is shown in Fig.5.7. As can be seen, the high resolution reveals a clear structure due to molecular vibration. Through careful analysis of a spectrum of this kind it is possible to evaluate the C-O bond length very accurately in the core-ionized molecule. It turns out that the bond length is shortened by about 2% when the Is core vacancy has been formed in the carbon atom. From the linewidth it is also possible to evaluate the natural lifetime of the C Is state (Sect.9.4.5). The lifetime is of the order 10" s. Atomic structure research using X-ray emission spectroscopy has been discussed in [5.9-13]. 

Another layered structure has been determined [343] on Ag3TlTe2 which, from its formula, might be a normal valence compound with monovalent cations. Its orthorhombic cell can be built up from layer packs Ag—Te—(Ag + Tl)—Te—Ag. These AgaTlTe2 units are stacked in such a way that the atoms of the two contacting Ag layers form zig-zag chains in [100] direction with a rather short Ag—Ag distance of 3.05 A which seems to indicate bonding between the layer units. For Ag ions (ionic radius 1.26 A) such an Ag—Ag distance would not be critical. However, if the outer Ag atoms of each layer unit really were ionized we would rather expect that adjacent units would shift by b/2 in order to increase the Ag—Ag distance. Anyway, on vapor-depositing the AgaTlTe2 films onto NaCl crystals, plate-like textures always formed. 

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