Interatomic screens

Finally, one should not overlook the possible role of correlation effects in atom-metal differences. In atoms the dominant contributions to the correlation energy arise from interaction between electrons of the same principal quantum number n, since these have the greatest overlap. As far as purely intraatomic electrons are concerned, the correlation terms differ very little between atom and metal correlation does, of course, affect interatomic screening of the final state vacancy in metals. 

In a metal like Ni or Cu there are, below the d bands, non-ci conduction band states, as yet unresolved in XPS spectra there are heavily hybridized -non d states at the bottom of the d bands and there are relatively localized, little hybridized states at the top of the d bands. Because the d and non-rf components differ in spatial extent, interatomic screening of the final state hole should vary through the bands. There is little known about how this affects a valence electron XPS spectrum. It is these coexisting complex problems which at times make it difficult to assess agreement or disagreement between predictions of core or valence spectra and the measurements. Does the agreement seen in Fig. 5 indicate that the important physical effects are properly accounted for or is it only the consequence of accidental numerical cancellation ... 

Here fl,- is the force constant for atom i and is the thermally averaged mean-square displacement for atom i in the protein the latter quantity is proportional to the crystallographically determined Debye-Waller factor if static disorder is neglected (see Chapt. VI). To simplify the treatment, average mean-square displacements can be used to represent the different types of atoms. The factor 5(r,) is an empirical scaling function that accounts for the interatomic screening of particles which are away from the RZ-RR boundary, 108 it varies from 0.5 at the reaction zone boundary to zero at the reaction region (see Fig. 8). 

Jakes SE, Willett P. Pharmacophoric pattern matching in files of three-dimensional chemical structures. Selection of interatomic screens. J Mol Graph 1986 4 12-20. 

In addition to this term, account must be taken of the decreasing screening of the nucleus by the electrons as the interatomic distance becomes very small. At very small distances the core-core term should approach the classical form. To account for this, an additional term is added to the basic core-core repulsion integral in MINDO/3 to give ... 

In conclusion, the repulsive interactions arise from both a screened coulomb repulsion between nuclei, and from the overlap of closed inner shells. The former interaction can be effectively described by a bare coulomb repulsion multiplied by a screening function. The Moliere function, Eq. (5), with an adjustable screening length provides an adequate representation for most situations. The latter interaction is well described by an exponential decay of the form of a Bom-Mayer function. Furthermore, due to the spherical nature of the closed atomic orbitals and the coulomb interaction, the repulsive forces can often be well described by pair-additive potentials. Both interactions may be combined either by using functions which reduce to each interaction in the correct limits, or by splining the two forms at an appropriate interatomic distance . 

The interatomic pair potential ( 0) in eqn (6.73) represents the electrostatic interaction between an ion and a second ion and its screening cloud some distance, R, away. From eqn (6.71) it is given by... 

One property of a transition metal ion that is particularly sensitive to crystal field interactions is the ionic radius and its influence on interatomic distances in a crystal structure. Within a row of elements in the periodic table in which cations possess completely filled or efficiently screened inner orbitals, there should be a decrease of interatomic distances with increasing atomic number for cations possessing the same valence. The ionic radii of trivalent cations of the lanthanide series for example, plotted in fig. 6.1, show a relatively smooth contraction from lanthanum to lutecium. Such a trend is determined by the... 

In point-charge simulation this electronic rearrangement is of no immediate consequence except for the assumption of a reduced interatomic distance, which is the parameter needed to calculate increased dissociation energies. However, in Heitler-London calculation it is necessary to compensate for the modified valence density, as was done for heteronuclear interactions. The closer approach between the nuclei, and the consequent increase in calculated dissociation energy, is assumed to result from screening of the nuclear repulsion by the excess valence density. Computationally this assumption is convenient and effective. 

Interatomic distances are determined by steric factors, of which the most important is the exclusion principle that depends directly on the geometry of space-time, observed as the golden ratio. Bond order depends on the ratio between the number of valence electrons and the number of first neighbours, or ligands, and affects interatomic distances by the screening of internuclear repulsion. 

The empirical finding that increased strength of multiple bonds over electron-pair bonds is mainly caused by an increase in single-bond strength at the closer interatomic approach that becomes possible due to screening of inter-nuclear repulsion, can now be examined more closely. Whenever the number of valence-electron pairs on an atom exceeds the number of electron-pair bonds to that atom, the excess density may screen the nucleus. Screening becomes effective when the excess density occurs in atomic s-type states with an appreciable s contribution. The first-period diatomics considered before illustrate this screening condition well. 

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