Shared interactions

Relief maps of the charge density and L(r) in the plane of the water molecule are shown in Fig. 6.9. The L(r) at the bond critical point shows an accumulation in the internuclear surface. This is due to the shared electrostatic attraction of the electrons by both nuclei. Such a shared interaction is typical for covalent bonds. 

The quantity Ail/A3, that is, the ratio between the largest perpendicular contraction at the (3, — 1) critical point and the parallel concentration towards the nuclei, is < 1 for closed-shell interactions. For shared interactions, its value increases with bond strength and decreasing ionicity of a bond. It decreases, for example, in the sequence ethylene (4.31), benzene (2.64), ethane (1.63). 

The comparison of the properties at the critical points in the P-NTO electron density with those in the atomic procrystals (Table 6) reveals the contraction of the electron density towards the shared interaction lines during crystal/molecule formation. This contraction is accompanied by a significant enhancement of the local kinetic, potential and electronic energies (Table 7). 

The Laplacian distributions for and S2N2 in Fig. 7.13 provide further examples of shared interactions, the unequal sharing of the charge concentration in the latter molecule being an example of a polar system. The final molecule in this figure, illustrates both types of interactions. This... 

Fig. 7,16. Relief maps of the negative of the Laplacian distribution of p to contrast the distinguishing features of the shared and closed-shell limits of atomic interactions as represented by Nj and Arj, respectively. The map for Fj is intermediate between the two limits. While V pfr.,) is positive for F2 as found for Ar2, its value of p(r J Is three times larger than that forArj. Electronic charge is accumulated in the binding region of F2, as is typical of a shared interaction, but is concentrated in the atomic basins, as is typical of a closed-shell interaction. While V pfrJ > 0 for both Ar2 and Fj, the Laplacian distribution is a minimurn at r, for Arj, but a maximum at the same point in Fj. The charge densities are calculated using a 6-31IG (2d, 2p)...

The Laplacian distributions for the shared interactions illustrated in Figs 7.15 to 7.17 clearly indicate the predominance of the concentration of electronic charge over the binding region for such interactions. In all of these molecules < 0 over the binding region for each interacting pair of nuclei. 

One approach to this situation is to research low latency update mechanisms across a group of participants, either by sophisticated communication schemes or the sheer reduction of information that has to be synchronized. A Virtual Reality application usually processes a lot of data for the visualization. In comparison to that, interaction events that actually steer the application are both, small in size and less frequent in comparison to video interrupts from the graphics hardware. A simple, but working approach is to share interaction events between collaborative applications in order to ensure data locking. This approach can be used for the synchronization of PC cluster based large displays and is depicted in the following section. 

This relationship indicates that the potential (kinetic) energy dominates over the total energy (H( ) = G(r) + V(r)) in those regions of space where charge is locally concentrated (depleted). The combination of the above formulas, provided G(r) is accessible (wavefunction-based studies), leads to simple energetic characterization of chemical bonds [34] (Table 1). For closed-shell interactions (V Pbcp > 0)> Ik BCpI/GBCP > 2, while for shared interactions (V pbcp < 0), I k BCpI/GBCP < 1-... 

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