Shared-shell interaction

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). 

Atoms of a single element may combine into one molecule, and atoms of different elements may combine to form compounds, which are also molecules. The latter usually happens when elements having incomplete electron shells interact. Atoms of different elements can attain full and stable electron shells by transferring or sharing electrons with each other. When this happens, these atoms are then held closely together by chemical bonds. Elements whose atoms have full electron shells, like helium and neon, tend to be the most stable and least likely to form compounds with other elements. 

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)...

Fig. 7.19. Contour maps of the Laplacian of p for second- and third-row diatomic hydrides. The intersection of the interatomic surface with the plane of the diagram is also shown. These maps illustrate the transition from closed-shell to shared atomic interactions.

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-... 

H- and 0-atoms separated at the experimental distances) without any fitting parameter. The Fbcp values are however underestimated in magnitude at short distances because the Laplacian corresponding to the non-interacting density fails to mimic shared-shell charge concentrations. 

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