Intermediate range interactions

This procedure has been theoretically justifled and it appears to work numerically reasonably well if the basis sets arc not too badly chosen. At the Cl level similar, though somewhat more (XMnplicated, procedures have been proposed 106. m) but there is less experience available yet as to their numerical performance. 

Koide , but his method for calculating is practical only for atoms. 

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The alternate approach to developing interaction potentials is to consider the solid surface as a very large molecule. One can then apply theoretical techniques based on gas-phase reaction ideas. The simulation of real systems, however, often requires that both reactive adsorbed atoms as well as a large number of substrate atoms be explicitly treated, and so these techniques rapidly become computationally infeasible. It is apparent that to simulate the general situation, bonding ideas from both regimes should be used. This breakdown does, however, provide a useful format within which to discuss intermediate-range interaction potentials, and so it will be used to illustrate potentials which are in current use in simulations of gas-surface interactions. 

A further consequence of intermediate-range interactions adding up are very high almost isotropic repulsive barriers around compact clusters. This has consequences for the density scaling [32] and favors small islands with more narrow distributions of sizes and spacings than the ones obtained without interactions [29]. We finally note that atomic superlattices with smaller lattice constant may be stabilized by dipolar interactions of relatively short range. The most prominent examples for such interactions are alkali metals on metal surfaces. A phase transition from a dilute liquid into a well-ordered solid has been reported for Cs/Ag/Si(lll)-( /3 x %/3) [33]. 

Migration clusters may be defined by intermediate-range interactions ( ). These give rise to intermediate-range bonds and clusters ("secondary clusters"). Excitation delocalization will usually happen within "primary clusters", defined by near neighbor interactions. 

The role of dopants should be clarified further. Although there have been some efforts to elucidate the electronic structure and spatial size of isolated dopants (Teramae et al., 1982, 1983), almost no attempts have been made with respect to the treatment of the composite system of the polymer and the dopant except the work of Br6das et al. (1981). This is probably because of difficulty in the description of the electronic structure of the intermolecular charge-transfer complex with intermediate-range interactions using the current (ordinary) SCF-CO scheme. This will also be developed rapidly in the near future. 

The three terms in (2.7.6) correspond to the short-range, long-range and intermediate-range interactions between the water-like particles. 

Fig. 6 Force nonnahzed by radius between mercaptobexadecane-modifled gold surfaces (a flat and a colloidal probe) carrying a preadsorbed mucin layer as a function of separation. Data are shown for interactions across 30 mM NaNOy, and across a range of NaCl solutions. The top graph focuses on the intermediate-range interaction, whereas the bottom graph shows the same data on an expanded distance scale...

At intermediate distances, for example, 10 < zo < 100 A, a long-range interaction between the tip and the sample takes place. The wavefunctions of both the tip and the sample are distorted, and a van der Waals force arises. The van der Waals interaction follows a power law, with an order of magnitude of a few meV per atom. 

Molecular beam scattering experiments provide direct and detailed information about the repulsive part of the interaction potential between the colliding particles. With such scattering data available, detailed studies of the short and intermediate-range parts of the potential energy surfaces can readily be made, provided that accurate theoretical methods, e.g. quantum close-coupling approach, are used to describe the scattering phenomena. 

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